Download Denver Montessori Junior/Senior High School Innovation Plan

Denver Montessori Junior/Senior High School
Innovation Plan
Respectfully submitted by:
Katy Myers
Principal
Denver Montessori Junior/Senior High School
(303) 431-2385
[email protected]
Denver Montessori Junior/Senior High School
Co-located with Gilpin Montessori Public School
2949 California St.
Denver, CO 80205
(720) 424-2600
dmhs.dpsk12.org
December 19, 2012
Board of Education
900 Grant St.
Denver, CO 80203
Dear Board of Education,
Thank you for the opportunity to submit this Innovation plan on behalf of Denver
Montessori Junior/Senior High School. Please find enclosed the plan, requested
waivers, and the finalized budget. I have also included the original school design
as presented in the Performance School Application. This school design was
thought out and presented to the Board of Education during the 2012 Call for
Quality Schools and was unanimously approved in June, 2012.
This submission builds on the Performance School Application by providing a list
of waiver requests and detailed replacement policy language regarding State,
District and DCTA agreements. These waivers and replacement policies will
allow DMHS to run the school consistent with the vision and mission as outlined
in the school’s Performance Plan Application.
I look forward to your questions and ideas as we move forward through the
Innovation approval process.
Sincerely,
Katy Myers
Principal
Denver Montessori Junior/Senior High School
Table of Contents:
Part I: Innovation Plan Statements
Mission Statement:
Page 2
Succession Plan and School Governance:
Page 4
Efficiencies, Cost Savings, NCLB
Page 8
Part II: Requested Waivers and Replacement Policies
District Policies
Page 10
DCTA Policies
Page 34
State Policies
Page 40
Part III: Evidence of Support
Page 47
Part IV: Curriculum Components
DMHS Alignment to DPS Graduation Standards
Page 55
DMHS Evidence of Math Curricular Alignments
Page 65
Part V: Performance School Application
Page 103
Part I: Innovation Plan Statements
Page 1
Mission Statement
Denver Montessori Junior/Senior High School (DMHS) will combine Montessori
best practices with current research on adolescent brain development to provide a
learning environment that promotes high achievement for each student while also
supporting them socially and emotionally. Graduates, regardless of ethnicity or income
status, will be prepared for college or a career as well as demonstrate ingenuity,
adaptability, creativity, initiative and excellent communication and problem solving skills.
1. How will innovation status help you more fully realize your mission?
DMHS is requesting Innovation Status through the DPS Innovation School
Application. For a school to achieve excellence, it must hold on to its vision and
implement the vision as clearly and effectively as possible. DMHS will require the
innovative school status to maintain fidelity to its mission and vision.
Montessori secondary education focuses on the whole child, self- construction,
valorization and preparation for adult life. By creating a high quality 7th through 12
grade program on these principles, students will graduate with the academic skills
necessary to thrive in both post secondary education or career options, while at the
same time have well developed communication and problem solving abilities along with
strong interpersonal relationship skills. Finally, they will have developed creativity,
ingenuity, adaptability and initiative through the many problem solving, community
building and real world experiences they will encounter at DMHS.
During year one and possibly year two, DMHS will also have 6th grade in order to
provide continuity to Gilpin students as that program ends after 5th grade. Both DMHS
and Gilpin would like to see 6th grade eventually remain with Gilpin, as that is
fundamentally how Montessori grade orientations are configured. In Montessori, 4th, 5th
and 6th grade students work together within an “upper elementary” classroom. Sandoval
and Denison currently have this upper elementary configuration, and Lincoln will also
retain its sixth grade students in their upper elementary classrooms starting next year
(2013).
Montessori secondary schools are divided into two “sub-planes”. The 7th - 9th
grade program is a land based program with real life problems solving scenarios.
Students combine didactic, academic lessons with real world scenarios. They are daily
working with both their head and their hands to deeply internalize academic concepts.
The 10th - 12th grade program is a highly academic program preparing students for
university. Having come through the Montessori program to this point, students are well
able and ready to handle the most rigorous content. The high school remains centered
on core Montessori values. This includes Montessori trained teachers, long periods of
uninterrupted work time, key lessons, and a variety of methods whereby a student can
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Denver Montessori Junior/Senior HS
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demonstrate mastery of knowledge. Assessments will include rubrics, portfolios,
presentations, quizzes on vocabulary and skills, end of unit knowledge assessments
plus all Federal and Colorado State mandated testing.
The 6th grade through 12th grade Montessori curriculum that DMHS will
implement is rigorous, innovative, interesting and is designed to engage students to
produce optimal academic achievement as well as social and emotional maturity and
well-being. Montessori adolescent curriculum has been designed and tested over the
last fifteen years at both private and public Montessori schools. This curriculum,
referenced throughout this application as Montessori National Curriculum, has been
collected, refined and reported through The NAMTA Journal, A Montessori National
Curriculum Report, The NAMTA Journal, Volume 37, No. 1, Winter 2012. DMHS will
design its program using this curriculum. Recently, the Montessori National Curriculum
for the Adolescent Program from Twelve to Fifteen/Sixteen Years was reviewed by the
Australian Curriculum Assessment and Reporting Authority. Their findings, as reported
in A National Montessori Curriculum Report, are as follows: ACARA (Australian
Curriculum Assessment and Reporting Authority) established an extremely rigorous
recognition process to determine the extent to which a well-established alternative
national curriculum can deliver comparable educational outcomes for students to those
based on the Australian National Curriculum. ACARA have advised that (the National
Montessori Curriculum) aligns with the Melbourne Declaration on Educational Goals for
Young Australians, meets the particular principles and guidelines in relation to the
Shape of the Australian Curriculum v3 paper, and allows for broadly comparable
educational outcomes in English, mathematics, science and history by the end of year
10.
In order to effectively implement the curriculum, DMHS will need to adopt its own
schedule, its own standards for hiring teachers, its own school calendar and
professional development plan, its own assessments, and, of course the National
Montessori Curriculum.
DMHS will be using the National Montessori Curriculum for grades 7-9 for
science, history and language arts. The 7,8,9 Spanish curriculum will be the TPRS
curriculum. TPRS matches the meaningful, relative approach that defines Montessori
education.
DMHS will use a math curriculum that is individualized for each student
combined with small group lessons. For grades 7 and 8, this math curriculum will be a
combination of Khan Academy, Montessori Math materials, project based math, and
small group lessons by a highly qualified math teacher. The small group lessons will be
designed to meet each student at the particular benchmark the student is currently
working, and the teacher will use a variety of instructional methods, including
Montessori math materials, to assist the student in mastering that benchmark and
preparing to work on the next on-line unit. Students will also be expected to apply math
towards a variety of hands-on projects utilizing the farm, the culinary arts program and
micro-economy. For grades 9 – 12, the project based math curriculum will be replaced
Innovation Plan
Denver Montessori Junior/Senior HS
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with Exeter Math. Exeter math is the math curriculum used by Philips Exeter Academy,
and is widely recognized as an innovative college preparatory math curriculum. This 6th
grade through 12th grade math curricular approach has been fully aligned to the
Common Core State Standards and has been submitted to DPS’ Office of School
Reform and Innovation (OSRI).
The high school, grades 10, 11 and 12, will create an integrated college
preparatory curriculum using DPS approved curriculum, with the exception of math as
noted above. Compass Montessori High School uses a similar curriculum and
curriculum delivery method. Their three year SPF results for this curriculum are a
median growth percentile of 58 for reading, 54 for mathematics and 66 for writing, and
an academic achievement score for science of 59%. The academic growth gaps
achieved a level of exceeds for reading and writing and meets for math. The three year
ACT composite is 21.7.
Although the most of the curriculum for high school will be similar to DPS’s
conventional schools, there will still be innovative differences. First, the curriculum will
be integrated so that literature studied in Language Arts will, at the same time, support
the history curriculum for an overall integrated humanities curriculum. The math and
science teacher will work together to insure students are obtaining the mathematical
skills needed to work out currently studied complex scientific equations. Linkages
between science, math and history will be explored. Throughout all areas of study, there
will be in-depth reading and writing instruction.
The schedules for both the junior high and the senior high will support the
Montessori approach. There will be minimal required transition times. Instead, students
will be called to small group lesson as those lessons are needed to support the next
level of study. This schedule is currently in place at Compass Montessori high school.
During the morning, students are independently working on a variety of assignments
and further exploration of their current units of study. At the same time, teachers are
giving small group lessons to students in math, science, language arts and history. The
culture of respect and hard work is resolutely held by both the staff and the students.
One hundred percent of the students are on task and engaged because they are
enjoying their academic studies. This on task and engaged behavior is the hallmark of
Montessori education, and this is what we intend to create at DMHS.
Succession Plan and School Governance
A. Succession Plan
If not addressed in the school’s performance application, please provide specifics of a
succession plan (or process) that will ensure consistency and stability in implementing the
innovation plan in the school in the case that there are leadership changes.
DMHS will work with the “Self-Governance” leadership model as outlined in
Appendix G of the Performance School Application. During year one and two, the
school will have up to 80 students. In order to be economically sustainable, the school
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Denver Montessori Junior/Senior HS
Page 4
leader will also work half time in the classroom. During that time, she will work with the
other advisors to create a culture of shared leadership. Key leadership roles and
responsibilities will be reviewed with staff to insure reasonable redundancies can be
created. In year two, a junior high program director will be identified and that person will
start attending professional leadership and administration development as offered
through DPS. In year three, the school principal will no longer be teaching in order to
focus on the well being of DMHS students, data analysis, and professional development
for staff. She will also conduct curriculum and programmatic review to insure that 9th
grade is successfully meeting DPS high school standards and that DMHS is ready to
move forward with adding the high school program. Also In year three, a high school
program director will be identified and will start attending professional leadership and
administration development as offered through DPS. In year four, the leadership team
will consist of the principal, the junior high and the senior high program directors. At that
point, the principal will insure that both program directors have the knowledge base
needed to assume the principal role of the school should that event be necessary.
The principal’s roles and responsibilities include creating and maintaining the
school’s mission and vision, hiring and evaluating staff, maintaining a culture of high
expectation regarding behavior and academic achievement, creating and reviewing
measurable data systems to insure the students are obtaining a rich and rigorous
education, creating and linking staff to professional development, visiting classrooms
every day and conducting monthly, longer staff observations, creating and maintaining a
welcoming environment for all community members, high level student discipline and
attendance.
The program director’s roles and responsibilities include maintaining a culture of
high expectations regarding student behavior and academic achievement, daily check in
with fellow staff, weekly staff meetings to insure that the school is holding to its mission
and vision, ground level parent communication, and resolving low level student conflict
and discipline. Program Directors will also be advisors / teachers.
Program directors must be highly qualified teachers who are Montessori trained
in both elementary and adolescent education. They need to have completed or be
willing to complete a Master’s level leadership program. They must demonstrate either
in their DMHS position or in past positions they can create a culture of respect,
inclusivity, shared decision-making, recursive learning, and empowering staff to work at
their highest level.
Should a leadership change be necessary, both the junior high and senior high
program directors will be qualified to become the school leaders. The school staff will
work with its School Accountability Committee to interview both candidates along with
any other DMHS teachers who are qualified and any outside candidates who are
qualified. The staff and School Accountability Committee will interview candidates and
determine two finalists through a majority vote conducted by secret ballot in order to
maintain confidentiality. The Chairman of the SAC along with one community member
shall be in charge of the voting process. The final decision for hiring the new school
principal from the two qualified finalists will be made by the School District
Superintendant.
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Denver Montessori Junior/Senior HS
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B. School Governance: If not addressed in the school’s performance application, what plans are
being made to ensure that a robust and participatory school governance structure will provide
accountability and support to the school?
DMHS will create a vibrant School Accountability Committee (SAC) that will
include no less then one staff member along with the principal, three parents and two
community members. The SAC will assess school performance based on agreed upon
outcomes that include academic goals, student well-being and community involvement.
The SAC will meet once per month to discuss school progress and make
recommendations to the principal.
Each year, the chairperson of the school accountability committee will insure that
the DPS parent satisfaction survey measuring parent satisfaction regarding the school
achieving established outcomes is delivered to all parents and guardians. All surveys
will be delivered in English and the parent’s native language. Surveys will be
anonymous but the SAC chairperson will assess percentage of surveys returned based
on school population. If that percentage is less than 75%, the SAC committee will
assess the current population and find solutions on how to bring that percentage up to
75%. Should parent satisfaction not meet the standard on the SPF rubric, DMHS will
take the following steps:
1. Hold community meetings to determine the root of parent dissatisfaction
2. Increase parent education to insure that parents are comfortable with the Montessori
Method and how it is being implemented at DMHS.
3. Create a strategic plan that includes both tactical and strategic steps to resolve
parent concerns.
DMHS will use a variety of data points and observation to determine the school
leader’s need for coaching and professional development. First, the SAC team will
review monthly achievement data and the annual SPF to see if the school has met set
targets. Second, the SAC will review annual parent, staff and student surveys to
determine the overall health of the school and community opinions of the school. Third,
the SAC will meet with a Montessori consultant who will be hired in year 1, 2, 3 and year
5 to observe the school and provide feedback to the SAC, school leadership and staff.
The SAC will use the DPS Framework for Effective School Leadership as their
evaluative tool. The principal will also welcome designated DPS leadership to observe
the school and provide feedback using the DPS Framework. Every month, the principal
will meet with the SAC to discuss the school’s successes and challenges based on data
and observation. During those meetings, the principal will seek out feedback regarding
current leadership effectiveness. The principal will also solicit feedback from staff and
community members during informal meetings. At all times, the DMHS principal will
model the value of recursive learning, seeking and accepting feedback, and inclusive
problem solving in order to continue to evolve towards distinguished leadership.
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Denver Montessori Junior/Senior HS
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Should the SAC and/or DPS leadership determine that the principal require
additional coaching and professional development, the principal, SAC and DPS
Leadership will create a professional development plan along with benchmarks to
measure progress. Progress will be reviewed monthly. If, after six months, the principal
has not made satisfactory improvement, DPS will replace him or her with a program
director and begin the search for a new principal.
Innovation Plan
Denver Montessori Junior/Senior HS
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Efficiencies, Cost Savings and NCLB
A.
What cost savings and/or efficiencies that are projected through attainment of
innovation status?
DMHS projects that it will obtain cost efficiencies by using primary source
materials and free on-line programs, such as Khan Academy, versus using conventional
textbooks. DMHS also intends to use free resources such as Edmodo and Google Apps
for Education.
DMHS will meet or exceed the salary schedule set forth by DPS for teacher and
staff salaries. However, DMHS will use the actual salaries for teachers versus the cost
averaging model. This will result in demonstrating the true cost of running a Montessori
Junior/Senior high school. DMHS has incorporated into the annual teacher salary,
versus as additional costs, time spent on overnight trips, professional development and
after school events. This will allow DMHS to offer these very important Montessori
elements without making the cost of the school program prohibitive.
By having innovation status, DMHS will be able to complete the hiring process on
a schedule that more closely aligns with the hiring window for high quality Montessori
teachers.
B.
Will the school continue to comply with the Highly Qualified Teacher requirement
of No Child Left Behind?
DMHS will work closely with Denver Public Schools’ Human Resources
Department to insure that the school is in compliance with the Highly Qualified Teacher
requirement of No Child Left Behind.1
1
Clarification to CDE: All teachers who teach core content classes will meet the Highly Qualified requirements by holding a
Colorado teaching license and demonstrating subject matter competency.
Innovation Plan
Denver Montessori Junior/Senior HS
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Part II: Requested Waivers and
Replacement Policies
Page 9
Denver Montessori Junior/Senior High School
Request for Innovation Status December 19,
2012
Waivers Requests and Replacement Policies
DPS, DCTA, and Colorado State Statutes
School
Proposal
Policy
CFBA: Evaluation of Evaluators
Human Resource Management:
Teacher Evaluation
Provision shall be made for periodic evaluation of evaluators…All persons who evaluate
professional staff members shall possess an administrative certificate issued by the
Colorado Department of Education and shall have received education and training in
evaluation skills approved by the department. Evaluation instruments for all professional
staff administrators shall include a section dealing with their evaluation skills. The
superintendent or his/her designee shall review all evaluations done by professional staff
administrators and when necessary shall discuss with them procedure and form…the
district…shall seek evidence that evaluators are implementing the process in a fair,
professional and credible
Only the following individuals may serve as evaluators for DMHS: The school principal, the
school's program directors at the permission of the school principal, other professional
teacher evaluators through the LEAP Peer Observer program.
The school principal, as hired by the district, shall be allowed to evaluate professional staff
members regardless of whether the administrator has an active administrative certificate.
Replacement
No other individual will have de facto authorization to evaluate staff without the explicit
Policy
designation by the school principal with the following exceptions: the school principal will
continue to be evaluated by the superintendent or his/her designee and will receive
feedback on the quality of evaluations being given at the school. The school principal will
be responsible for evaluation of other evaluators on campus, but may discuss evaluations
with district staff as well to ensure meaningful calibration of scores. P. 43 of PSA
Page 10
School
Proposal
DF: Revenue from Non Tax Sources/DF-R: Revenue
from Non Tax Sources Procedures for School-Based
Sponsorships
Budget
No agreements for sponsorship shall be made with commercial entities that promote
products or services that are inconsistent with the mission and image of Denver Public
Schools
School-Based Sponsorships…These sponsorships include the following components:
*involve local commercial entities, *do not conflict with exclusivity agreements within the
district, *have district approval for any visibility components involved, *offer a minimum of
$10,000 in benefits to the school with ongoing annual visibility for the sponsor, *offer less
than $10,000 in benefits to the school but are limited to single season/event visibility., *can
be negotiated by the principal with the approval of the superintendent or his/her designee.
DF-R: Process: 1. Obtain a Sponsorship Proposal form from the Community Partnership
Policy
Office, complete, and submit 2. Community Partnership Office will review the proposal 3.
The Community Partnership Office will refer the proposal to the Superintendent for review.
If appropriate, the Superintendent will present the proposal to the Board of Education for
approval. 4. Following approval, the Superintendent will direct that a "Memorandum of
Agreement" be developed 5. The appropriate district staff will review and, if appropriate,
execute the Agreement. 6. The school(s) will be provided with a copy of the Memorandum
of Understanding.
Evaluation: Within thirty days of the end of the contract stipulation sponsorship, the
Community Partnership Office will provide a Sponsorship Evaluation form to be completed
by the principal.
School will have the ability to request and secure school-based sponsorships independent
of the district according to the following policies:
-The sponsorship must not compromise or show inconsistency with the beliefs/values of
the district and school.
- The sponsorship will not alter any district owned resources unless permission is granted
by the district
Replacement - The sponsorship does not create a real or perceived conflict of interest with school
Policy
administrators or staff
- The sponsorship agreement will be reported to the district budget office at least 30 days
before an agreement is to take effect. The budget office will have the ability to refuse the
agreement only in situations where said agreement will adversely impact funding
arrangements for other schools in the district more than it would benefit Denver
Montessori or because it would be in conflict with existing fund regulations (such as federal
grants).
School
EEAA – Walkers and Riders
Student Transportation
Proposal
Generally, students eligible to receive transportation provided by the school district if they
attend the school serving their residential area and are enrolled in
1. Elementary schools more than one mile walking distance from their home
2. Middle schools more than two and one-half miles walking distance from their home
Policy
3. High schools more than three and one-half miles walking distance from their home
4. Magnet and other special educational programs may also have trans-portation provided
as approved by the Board. Such transportation will be reviewed annually
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The School may request that students find alternative methods for transportation to and
from school. The principal will work with district budget staff on an annual basis to
establish a transportation budget for the school. Based on the budget, the school principal
will develop a transportation plan that maximizes the availability of transportation services
Replacement
to students to and from school. Should the school develop a plan that applies a different
Policy
policy from the one specified in EEAA, the plan will be shared with and approved by the
district transportation department and then published and made available to parents no
later than 6 weeks prior to the school year. The DMHS 2013 transportation plan will be
located on the school's website at dmhs.dpsk12.org.
School
Proposal
Policy
GBEBA: Staff Dress, Accessories and Grooming for
Human Resource Management:
Certificated Staff (Teachers)
Certificated staff must exercise good judgment in their choice of professional appearance
for work or work-related activities by always appearing in a manner:
* that is appropriate to the situation,
* that will invoke a positive impression from the community,
* that provides appropriate role modeling for students,
* that promotes a working and learning environment that is free from unnecessary
disruption, and
* that is conducive to high student and staff performance.
The professional appearance of school staff members includes dress, accessories, body
adornments, and grooming. Appropriate professional appearance reinforces a sharedvision of the school. Therefore, all staff must exercise appropriate judgment in their choice
of professional appearance for work or work-related activities by always appearing in a
manner:
* that is appropriate to the situation,
Replacement
* that promotes ideals of respecting others, respecting self and respecting the environment
Policy
* that demonstrates a readiness to work in all of the school's environments
* that promotes a working and learning environment that is free from unnecessary
disruption, and
* that is conducive to high student and staff performance.
During the work day and any time employees attend work-related activities, employees
shall appear in appropriate dress. Items that are not acceptable in the workplace shall be
Page 12
identified in an annual school dress code by the school principal.
The principal is delegated the authority and bears the responsibility for ensuring
compliance with the school dress policy and is expected to counsel employees upon initial
infractions and implement further disciplinary procedures when violations continue to
persist
School
Proposal
Policy
Replacement
Policy
School
Proposal
GBEBA-R: Staff Dress, Accessories and Grooming for
Human Resource Management:
Certificated Staff (Teachers)
Examples of professional attire include, but are not limited to, collared shirts, dress slacks,
dress coordinates, suits, dresses, ties, and sport coats.
Items that are not acceptable in the workplace include the following: * attire that is
prohibited in the student dress code, * shorts or other similar article of clothing shorter
than mid-thigh…
Principals are delegated the authority and bear the responsibility for ensuring compliance
with this policy and are expected to counsel employees and discipline any violators
See replacement language for GBEBA (above)
GBEBB: Dress Code for Non-Teaching Staff
Human Resource Management:
Employees of the District project an image to the community and to students about the
professionalism of the District. Therefore, the Board of Education hereby adopts this Dress
Code Policy for all non-teaching staff… employees covered by this policy shall adhere to a
standard of dress appropriate to their position…Uniformed workers shall continue to wear
Policy
the approved uniform…
Unacceptable items
1. Shorts, dresses, skirts or other similar clothing shorter than mid-thigh length…
Replacement See replacement language for GBEBA (above)
Policy
School
Proposal
GCB: Professional Staff Contracts and Compensation
Human Resource Management:
Hiring, Compensation, Job
Descriptions
It is the Board's intent to review all compensation plans annually with representatives of
the district's teaching staff. Administrator's salaries shall be determined by Board action
with consideration given to the assigned responsibilities and specialized training. Salaries
Policy
shall be reviewed annually at the regular Board meeting in June, and contracts as
appropriate. The school district shall adhere strictly to the employment contract
procedures established by Colorado statutes.
The school will adhere to district salary schedules for all staff but requires autonomy in
determining the years of experience for educators and administrators in order to account
for private and other school experience. For exempt employees, the School reserves the
Replacement right to not provide additional compensation for additional time that occurs during
overnight and extended trips, after school meetings, after school activities, school
Policy
performances, events, or games, evening meetings and professional development. If the
school does give compensation for such additional time, the compensation will be provided
evenly to all teachers and staff working such additional time. Relative to employment
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contracts, the school will have the ability to require teachers obtain specified levels of
Montessori training, minimum licensure, and meet requirements for Highly Qualified
Teacher status. The school will be able to develop the contract in a way to monitor
employee progress toward accomplishing these requirements and terminate the contract
when progress is not being met. P. 45-46 PSA.
School
Proposal
Policy
GCCBB – Administrative & Non-Licensed Leave
Human Resource Management,
Personal Leave
Personal leave -Personal leave is not restricted to reasons of hardship or other pressing
business or emergency needs. Personal leave also may be used to extend a period of school
intermission or used in conjunction with the observance of a district holiday…Must be preapproved …Shall not accumulate from year to year. A … form shall be completed.
Administrative Staff - An administrator has ...leave annually.
Four are paid; …Unused paid personal leave will be automatically converted to sick leave
Non-Licensed Support Staff - Employees who work a minimum of 20 hours per week and
are not covered by a collective bargaining agreement … shall be granted up to a total of five
days
Jury Leave- Employees shall be granted leaves of absence for jury service …Full wages and
salaries shall be granted … All fees received for such service …shall be turned in to the
Disbursing Office …In the event that an employee reporting to the court for jury duty is
excused for the day, he shall report to his school or unit for duty within a reasonable time
Personal leave is not restricted to reasons of hardship or other pressing business or
emergency needs. Personal leave also may be used to extend a period of school
intermission or used in conjunction with the observance of a district holiday with specific
permission of the principal, or, in the case of the principal, by the principal supervisor. All
personal leave must be pre-approved by the supervisor. Unused portions of such leave for
personal reasons shall not accumulate from year to year. A "Request for Short Leave of
Absence for Personal Reasons" form shall be completed in sufficient time for approval
before the time of the requested leave.
An administrator has up to four days of personal leave annually.
All other personnel have up to four days of personal leave annually, all paid.
Unused paid personal leave will be refunded to staff at the end of every year at the rate of
Replacement $75 per day. The minimum time allowed per personal day shall be one-half day.
Policy
The superintendent may approve short leaves of absence for the Principal without pay for
no more than 10 days if such a leave does not interfere with the programs of the school.
No short leaves without pay shall be granted during the first or last three weeks of the
school year, the last two weeks of the fall semester or the first two weeks of the spring
semester. The Principal may approve short leaves of absence for the staff without pay for
no more than 10 days if such a leave does not interfere with the programs of the schools.
No short leaves without pay shall be granted during the first or last three weeks of the
school year, the last two weeks of the fall semester or the first two weeks of the spring
semester.
Jury Leave
Page 14
Employees shall be granted leaves of absence for jury service and when the employee is the
subject of a properly issued subpoena. Full wages and salaries shall be granted during such
period of jury service. All fees received for such service during regular working days shall be
turned in to the Disbursing Office of the school district. Unless otherwise agreed by the
supervisor, employees shall take personal leave or vacation if available or leave without pay
for leaves attributable to subpoenas.
Other Legal Leaves
Jury or witness fees earned during holidays or vacations may be retained by the employee.
In the event that an employee reporting to the court for jury duty is excused for the day, he
shall report to his school or unit for duty within a reasonable time.
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School
Proposal
GCBC- Professional Staff Supplementary Pay Plans /
Overtime (Coaches)
Human Resources, Compensation,
Job Descriptions
Coaches shall not receive any pay, gift or other remuneration for teaching or coaching
other than the stipulated contract salary or pay scale agreed upon by the Board of
Education.
Athletic coaches may be selected and assigned coaching duties for one or more threemonth period, i.e., September through November, December through February, and/or
Policy
March through May. Remuneration shall be on a monthly basis.
All coaches shall report for duty on the opening practice dates of their respective sports as
set by the Colorado High School Activities Association. In addition, coaches shall attend
required meetings and meet all terms and conditions established by the athletic board of
control.
Should the school elect to hire and pay for coaching duties, then extra duty pay for coaches
for the school will be set at an hourly rate for the year by the school principal. The school
Replacement
principal will consult with the school's leadership team to evaluate various proposals for
Policy
hourly compensation but will eventually make a determination that follows a clear policy
for the year that will be equally followed for any school coaches.
School
Proposal
Policy
Human Resource Management:
Hiring
From the list of available candidates for teaching positions in the Denver Public Schools, the
superintendent shall recommend those persons best fitted to serve…Applicants for
probationary appointments shall be required to have a bachelor's degree…Teachers in the
Denver Public Schools shall hold a…teacher certificate…Exceptions to this certification
requirement may be made by the superintendent in cases of teachers of adult vocational
education and in other unusual cases…Prior to hiring any person, in accordance with state
law the district shall conduct background checks
Reappointment after resignation: Teachers reappointed to teaching positions after
resignation shall be employed on probationary appointments. A teacher who has been
absent five years or less may be considered for reappointment at the salary to which he
was entitled at the time of resignation.
Reappointment of probationary teachers: Reappointment of probationary teachers shall
by considered annually at a meeting of the Board prior to June 1.
Teachers in the Denver Public Schools shall hold a Type A general teacher certificate, Type
B professional teaching certificate, Type C vocational teaching certificate, Type D
administrative certificate or Type E special service certificate issued by the Colorado
Department of Education. Provisional certificates also shall be accepted. Exceptions to this
certification requirement may be made by the superintendent in cases of teachers of adult
vocational education and in other unusual cases.
GCF: Professional Staff Hiring
Replacement
Policy
DMHS will work with the district HR office to post teaching positions through the district
website. From this posting, DMHS will engage in independent outreach efforts to recruit
candidates outside of the centralized recruitment channels.
Teachers shall be hired based on the following criteria: DMHS will create a rubric that
values Montessori training, NAMTA or other Montessori Adolescent training, Highly
qualified, teacher licensure, demonstrated ability to team teach, experience with
Page 16
Montessori adolescent programs, and demonstrated understanding and ability to
implement a Montessori adolescent program. Initial hiring decisions will be made by the
school principal. Subsequent hiring decisions will be made as the school’s “personnel
committee”, with final determination to be made by the school principal. The personnel
committee shall consist of volunteer representatives from all staffing areas that will be
affected by the new hire, such as the teaching team, the program director, special
education and support staff. All candidates must pass a DPS background check, which will
be conducted through the district HR process.
The school will adhere to district salary schedules for all teachers but requires autonomy in
determining the years of experience in order to account for private and other school
experience.
School
Proposal
GCF-2: Professional Staff Hiring (Athletic Coaches)
Human Resource Management:
Priority shall be given to hiring qualified athletic coaches from among the regularly
certificated teachers employed by the district. Effort shall be made to assign qualified
coaches from the existing school faculty.
Policy
When a program is in jeopardy or a coaching position cannot be filled within the high
schools, other certificated teachers or individuals holding a Coaching Registration from the
Colorado High School Activities Association who are qualified to coach may be assigned.
Should the school elect to hire and pay for coaching duties, the school will hire athletic
coaches from its current teaching staff based on a position announcement and
Replacement establishment of minimum qualifications for the position. If the school is unable to secure a
Policy
qualified candidate through this the process, the school shall attempt to recruit a coach
from a list of parents or other adults who meet the minimum qualifications for the
position. Any person hired will need to pass a DPS background check.
School
Proposal
GCID: Professional Staff Training, Workshops and
Conferences
Human Resource Management:
Professional Development
Attendance by school personnel at professional meetings shall be justified by meaningful
guidelines or rationale for such attendance. Such guidelines or rationale may differ by
department but shall be well-defined and understood by appropriate personnel. An
Policy
understanding of reasonable expenses should be developed prior to travel. The budgetary
allocation of departmental travel accounts shall not be construed as automatic approval for
expenditure. Travel outside the continental United States shall be considered only as an
exception.
Staff professional development will be determined in accordance with the plan proposed in
the Performance School Application as also specified below. The school will determine the
value of all Staff Training, Workshops and Conferences as it relates to the school's mission
and vision. All out of school professional development will need to be approved by the
Replacement school principal or program director. Any staff that attends an out of school professional
Policy
development opportunity will need to then disseminate that information to staff. Ability to
attend an out of state conference will be based on budget ability and rotated among staff
unless a particular staff person is presenting at that conference and therefore has their
expenses covered by other means. In-school professional development will be determined
based on how well it furthers the school's ability to meet its mission and vision. All
Page 17
professional development will be surveyed for relevance, quality and ability to implement
lessons learned.
From the school innovation plan:
The principal at DMHS will ultimately be responsible for managing and evaluating
professional development. There will be several areas of professional development. The
first area will be DPS sponsored. This will include RtI, ELA-T and ELA-E, Positive behavior
support, and any other DPS professional development that will insure our staff is well
educated in providing an optimal education to a diverse student body.
The second area of professional development will be on Montessori education and
adolescent brain development. All teaching staff will be required to attend training on
Montessori adolescent education such as the AMI Montessori Orientation to Adolescent
Education. This five week intensive course of study includes all aspects of adolescent
Montessori education.During the school year, each member of the teaching staff and
leadership team will lead a seminar based on Montessori literature. The North American
Montessori
Teachers Association has given DMHS a $3,000 grant and an additional $5,000 in-kind for
professional development. The principal will create a professional development plan to
utilize this grant throughout the first three years.
The third area of professional development will be led by the principal and will be on data
collection and evaluation. The principal, working with DPS, will work with staff to create
appropriate data collection tools and methods whereby the data is frequently reviewed.
The fourth area of professional development will be led by the special education provider
and/or the psychologist social worker. This area will cover adolescent brain development,
differentiated learning, implementing effective teaching strategies with students who have
special needs, and ongoing professional development on RtI. The Special Education teacher
and/or school psychologist/social worker will attend professional development on these
topics at DPS and review materials and/or attend workshops by professionals such as Dr.
Steve Hughes and the Gurian Institute.
Prior to the first day of the first school year, DMHS will have ten professional development
(PD) days in order to insure that we are fully prepared for the very first day of school.
During this time staff will attend DPS professional development for ELA and RtI. Because
staff will already be trained in Montessori at both the elementary and adolescent levels, a
majority of the planning time will allow for staff to prepare their environments and review
curriculum for the first series of Occupations. The Occupations curriculum requires a deep
understanding of the land, the local area, public transportation, and local community
resources. Staff will work with the principal to make sure that all necessary materials to run
successful Occupations are readily available so that the school year can start as smoothly as
possible. There will also be professional development around positive behavior support
and Discipline through Love and Logic offered by the Love and Logic Institute. The principal
will review with staff the DMHS farm school portfolio, rubrics, record keeping, assessment
and all other tools necessary to frequently and accurately obtain data regarding student
achievement.
Page 18
After the first year, DMHS will have five PD days prior to the first day of school. During the
school year, DMHS will have an additional five professional development days. The topics
for the professional development days during the first school year will be as follows:
Record keeping and assessment, RtI and meeting the individual learning needs for all of
students, review of and creating best practices for writing and implementing Occupations
curriculum, further work regarding RtI and meeting the individual learning needs for all
students, and understanding the Urban Farm and how it applies to Montessori adolescent
education. In addition, on Wednesday afternoons from 1:30 - 3:30, staff will attend staff
integration meetings. These meetings will include data review, discussion on recent
observations, curriculum review and student discussion.
DMHS will have monthly ninety minute staff meetings on where the primary focus is
Montessori theory and understanding adolescent brain development. These staff meetings
will support the recursive learning environment. The meetings will allow for reflective
conversation to evaluate and improve practice. Staff will improve Montessori practice by
examining the principles of Montessori theory and how it applies to adolescent education.
Colleagues will share their acquired knowledge and skills with one another resulting in the
knowledge being reinforced for the “teacher” and spread exponentially among the other
staff members.
School
Proposal
GCP – Professional Staff Promotion &
Reclassification
Human Resource Management:
Promotion and Reclassification
A change of assignment from one occupational classification to another may be requested
by the affected employee, may be recommended by the employee's administrator or
supervisor, or may be initiated by the superintendent and his staff. Approval of the
promotion by the superintendent and the Board shall be required.
Qualifications for promotion of certificated personnel shall be:
1. Master's degree, or master's degree and other professional preparation 2. Good
scholarship3. Satisfactory recommendations and appraisals of service 4. Good working
relations 5. Satisfactory experiences in certificated assignments 6. Reasonable length of
time in service in the Denver Public Schools
Policy
7. Professional growth and demonstrated potential 8. Ability to direct other employees
Responsibility of the employee An employee may initiate a request for change of
assignment ...
Principals and department heads periodically should submit to the executive director for
personnel services letters of commendation for persons who ought to be considered for
change of assignment. ...include references to scholastic background, professional growth,
parent and student relationships, and general fitness for assuming other and additional
responsibilities.
A change of assignment from one occupational classification to another may be requested
by the affected employee, or may be recommended by the employee's administrator or
Replacement supervisor. Approval of the promotion by the school principal shall be required.
Policy
Candidates for promotion at or above the level of a program director shall meet the
Page 19
following qualifications:
1. Must be highly qualified teachers who are Montessori trained in both elementary
and adolescent education.
2. Need to have completed or be willing to complete a Master’s level leadership
program.
3. Must demonstrate either in their DMHS position or in past positions they can
create a culture of respect, inclusivity, shared decision making, recursive learning,
and empowering staff to work at their highest level.
When assignment change decisions have been made, the principal shall submit notice to
the executive director for personnel services or the appropriate Human Resource official to
process the change in status.
School
Proposal
GDA – Support Staff Positions
Human Resource Management:
Hiring of Support Staff
All support staff positions in the school system shall be established initially by the Board.
Support staff members shall be employed for such time as the district is in need of or
desirous of the services of such employees...
The Board shall approve a statement of job requirements as presented by the
Policy
superintendent. This shall be in the form of a job description setting forth the qualifications
for the job, a detailed list of performance responsibilities and any required physical
capabilities.
Only the Board may abolish a position that it has created.
The school will use the same support staff positions as identified by the Board. Should
these positions prove to not properly reflect the need for support staff, the school principal
will identify additional support staff roles. Once these roles are identified, job descriptions
Replacement will be created. The school leader or her designee will then provide the job description to
the Office of Human Resources for the district so that the school leader can then move
Policy
forward with staffing the position. Further, should the board abolish a position that it has
created, DMHS retains the right to continue staffing the position in the historic way unless
it would be in conflict with state or federal laws that supersede innovation autonomies.
School
GDD: Support Staff Vacations
Calendar and Schedule
Proposal
Professional technical and nonaffiliated staff: Vacations and holidays for professional
technical and nonaffiliated staff members shall be those determined by the officially
adopted school calendar.
Policy
Facility managers: Facility managers shall be granted 15 days of paid vacation per year.
Those who have completed 15 years of continuous service…shall be granted an five
additional days of vacation for a total of 20 days. Holidays for facility managers shall be
those determined by the officially adopted school calendar for 245-day classified
employees.
Page 20
GDD will be followed with the following exception: Vacations and holidays for professional
Replacement
technical and nonaffiliated staff members shall be those determined by the DMHS school
Policy
calendar.
School
Proposal
GDF-R: Selection, Appointment, and Reappointment
of Full-time Classified Employees – Procedures
Human Resource Management:
Hiring,
The term "classified employee" …shall be deemed to include, each DPS employee assigned
to a full-time position listed in the salary and classification schedules for classified
employees as maintained by the Department of Human Resources. No position requiring
Policy
Department of Education certification or license shall be considered a classified position.
Employees on the administrative and managerial salary schedules are not subject to the
provisions of this policy.
DMHS will follow the district hiring process for Classified employees and select candidates
through the district recruitment and application processes; however, final hiring
determinations will be reserved by the school principal. Should the school principal
determine that the candidates for a position as provided through the district recruitment
and staffing process do not meet the expectations of the principal, the principal will have
Replacement the ability to not hire the position and re-post the position for new applicants, and pursue
additional recruitment activities as deemed necessary to fill the position appropriately.
Policy
If DMHS identifies a need for a position that does not exist in the district's current list of
classified positions, DMHS will create a profile for this position, provide the information to
the district's HR office, and use district systems to post the position and hire a candidate for
the position.
School
Proposal
Policy
Human Resources: Hiring and
Dismissal
A full-time classified employee shall serve a probationary period of two years on a full-time
basis…before attaining the status of continuing service. Any classified employee having
served as an employee in active service…for two complete years…and who has been
notified in writing shall have continuing service as a classified employee during efficient
performance of duties, good behavior and continuous service without the need for
recurring annual appointment…A classified employee who has resigned and who is
reappointed after the expiration of five years or more shall be reappointed on the
conditions applying to a classified employee employed for the first time.
All employees will be employed according to an annual contract.
GDI: Support Staff Probation, Tenure and Seniority
Annual contracts for the following academic year will generally be provided
to all staff who receive a rating on their end-of-year performance evaluation of "meets or
exceeds expectations" (or whatever the equivalent will be in any future evaluation system)
except for staff positions that may need to be restructured to meet the needs of the school
Replacement
in the following year. The school principal also reserves the right to offer a new annual
Policy
contract to a staff member before a final evaluation is completed in a situation where the
staff member has communicated a need to confirm employment for the following year due
to extenuating circumstances (such as another job offer or a potential move). In such
situations, the school principal will base the decision on information collected throughout
the current year and whether the staff member's performance at that time warrants a
rating of meets or exceeds expectations.
Page 21
School
Proposal
GDO: Evaluation of Support Staff
Human Resource Management:
Staff Evaluation
All classified employees in the Denver Public Schools shall be appraised throughout the first
two years of employment and at least annually thereafter. Transportation personnel shall
be appraised each six months during the first two years and each year during continued
employment. Buildings and grounds personnel shall receive an appraisal each six months
during the first year and annually thereafter. Operations employees, helpers and assistant
custodians shall be appraised after the first 30 and on a six-month sequence during the first
two years and then semi-annually throughout employment. Head custodians shall be
appraised once each year. Nonaffiliated and professional technical employees shall follow
Policy
the pattern of six months for appraisal during the first two years and annually thereafter.
Food services personnel shall be appraised once each year throughout continued
employment. Classified office personnel shall receive an evaluation each six months during
the first two years of employment and for two years after a change of job status. Appraisal
of facility managers shall be the responsibility of the principal or immediate supervisor with
input from area supervisors in accordance with Board-approved procedures.
Review The principal… shall review …and provide the employee with a copy Signatures
Classified employees' signatures on appraisal reports shall indicate only that they are
acquainted with the contents of the reports.
All classified employees that report directly to the school shall receive an annual appraisal
from the Principal or Principal's designee. The principal or her designee shall review the
results of the appraisal with each employee and provide the employee with a copy.
Replacement Classified employees' signatures on appraisal reports shall indicate only that they are
acquainted with the contents of the reports. If an employee wishes to make comments,
Policy:
they may do so on the reverse side of the form or by attaching an additional sheet to the
form. For performance review appraisals, the reports shall include a designation of
whether or not the employee is meeting expectations. P. 43 and 44 of the PSA.
School
Proposal
Policy
IC/ICA: School Year/School Calendar
Calendar & Schedule
Prior to the end of the school year, the Board of Education shall determine the length of
time during which district schools shall be in session during the next school year…All
calendars shall include the dates for all staff in-service programs scheduled for the coming
school year…Any change in the calendar except for emergency closings or other
unforeseen circumstances shall be preceded by adequate and timely notice of no less than
30 days.
Prior to the end of the school year, the school principal shall determine the following year's
school calendar that meets or exceeds the Board of Education's determination of the
length of time during which district schools shall be in session during the next school year.
All calendars shall include the dates for all staff in-service programs scheduled for the
Replacement coming school year. Any change in the calendar except for emergency closings or other
Policy:
unforeseen circumstances shall be preceded by adequate and timely notice of no less than
30 days. The school's calendar will be placed on its website prior to February 1 of the
previous year. A calendar for school year 2013/14 is posted on the school's website at
dmhs.dpsk12.org.
Page 22
School
Proposal
IE: Organization of Instruction
Education Program
The schools of the district shall be organized to present a unified program of instruction
and shall be operated as a single system under the direction of the superintendent.
The grouping and housing of instructional levels in school facilities shall be in accordance
Policy
with the P5-3-4 plan. Under this plan, preschool through the first five grades shall be the
elementary schools; middle schools shall contain grades 6, 7 and 8, and high schools shall
contain grades 9, 10, 11 and 12.
The organization of instruction for DMHS will be separate and distinct from the district's
organization. The model will be designed in accordance with the organization of instruction
Replacement
appropriate for a secondary Montessori school. Section III: Education Program of the DMHS
Policy:
performance application specifies the organization of instruction for the school including
specifics on grade levels and configuration.
Page 23
School
Proposal
Policy
IEA: Alternative Grade Level Organization in
Education Program
Neighborhood Schools (K-8 Policies)
All students may attend the neighborhood school serving their residence area or another
neighborhood school consistent with Policy JC and Policy Procedures JC-R or as otherwise
provided in district policy…
The Board recognizes that neighborhood schools with different (alternative) grade level
configurations and educational programs may be established through School Design (Policy
IF) and Policy Waiver Procedures (BGR-R… Resolution 2529 which states:… increased
parental and community support is fostered and enhanced by parents having the
opportunity …to select from among the numerous educational offerings of the district and
to participate in site-based governance.
1. .. enrollment in alternative grades is a choice…may not duplicate or be as extensive as
the educational program in neighborhood schools serving those grades. The affected
schools are responsible for maintaining a viable educational program for students in
alternative grades consistent with this policy.
…Schools with alternative grades that wish to participate in extra-curricular activities are
responsible for developing alternatives ...If an extra-curricular activity is not offered at the
school with alternative grade levels, students may participate in the extra-curricular activity
at another district …
3. Schools serving students in alternative grades are responsible for ensuring that students
in these grades are provided with the opportunity to achieve all district content…If a school
with an alternative grade level organization intends to grant diplomas, the high school
courses necessary to meet graduation requirements must be offered. In addition, such
schools must meet North Central Association accreditation requirements…5. Teachers
assigned to an alternative grade level must meet district and state education, certification,
and endorsement requirements for that grade level… Neighborhood school students in
grades identified in Policy IE have a priority for enrollment …9. Board of Education policies
that apply to students in a particular grade also apply to students in that grade in a
neighborhood school with an alternative grade level organization…10. Transportation is not
provided for students in alternative grades…12. The Board of Education may review fundraising
The organization of instruction for DMHS will be separate and distinct from the district's
organization. The model will be designed in accordance with the organization of instruction
appropriate for a secondary Montessori school. Section III: Education Program of the DMHS
performance application specifies the organization of instruction for the school including
specifics on grade levels and configuration. DMHS agrees that:
1. An understanding that enrollment in alternative grades is a choice. As such, the
educational program, including extra-curricular activities, may not duplicate or be as
Replacement
extensive as the educational program in neighborhood schools serving those grades. The
Policy:
affected schools are responsible for maintaining a viable educational program for students
in alternative grades consistent with this policy.
2. Participation in the Nuggets Prep League, the Denver Prep League, and athletic
competitions are offered at schools with alternative grades to the extent practicable.
Considerations for determining the offerings include incremental costs, facility
characteristics, the nature of the program, and the nature of the extra-curricular offerings.
Page 24
Schools with alternative grades that wish to participate in extra-curricular activities are
responsible for developing alternatives that make such participation viable and are subject
to the same conditions as other participating schools.
If an extra-curricular activity is not offered at the school with alternative grade levels,
students may participate in the extra-curricular activity at another district school consistent
with Department of Athletics rules.
3. Schools serving students in alternative grades are responsible for ensuring that students
in these grades are provided with the opportunity to achieve all district content standards
(e.g., first and second tier). Resources allocated through the district's resource allocation
methodology may be used for this purpose. Additional resources may not be provided by
the district.
If a school with an alternative grade level organization intends to grant diplomas, the high
school courses necessary to meet graduation requirements must be offered. In addition,
such schools must meet North Central Association accreditation requirements.
Other curricular offerings for students in alternative grade levels are based on the school's
educational program, facility considerations, and available resources.
4. District assessment requirements apply to all district students in affected grades
including those with alternative grade levels.
5. Teachers assigned to an alternative grade level must meet district and state education,
certification, and endorsement requirements for that grade level.
6. Opportunities to participate in district-organized staff development and activities related
to alternative grade levels will be based on the nature of the school's educational program.
7. Neighborhood school students in grades identified in Policy IE have a priority for
enrollment within the parameters agreed upon at the time of approval of the performance
school application. This priority is specified in the replacement language for policy JC-R.
8. Resources for a school with alternative grades will be allocated according to the formulas
for the grades identified in Policy IE (e.g., elementary schools serving grades 6, 7, or 8 are
allocated resources for these grades based on the elementary school formulas; a middle
school serving fifth graders would be allocated resources for this grade based on the
middle school formulas). The district does not provide additional resources for operating
expenses that are the result of establishing an alternative grade level organization.
9. Transportation is not provided for students in alternative grades unless otherwise
approved by the Board of Education.
10. Schools serving alternative grades are responsible for making necessary adjustments as
the district's educational program changes. Resources allocated through the district's
resource allocation methodology may be used for this purpose. Additional resources may
not be provided by the district for this purpose.
Page 25
11. The Board of Education may review fund-raising efforts to support educational
programming or extra-curricular activities for alternative grades. Such review will include
consideration of the extent to which the proposed fund-raising is consistent with
Resolution 2529 and whether or not the proposed fund-raising disadvantages other
students.
Principals of affected schools are responsible for reviewing this policy and its implications
with their supervisors. Principals, in turn, are responsible for distributing this policy and
explaining its implications to the parents of students considering enrollment in an alternate
grade level.
School
Proposal
Policy
IGA: Curriculum Development
Educational Program
Constant adaptation and development of the curriculum is necessary if the district is to
meet the needs of the students in its schools. As standards for student outcomes and
performance are adopted, the curriculum shall provide a program of instruction based on
and designed to enable students to meet the Board-adopted standards, which meet or
exceed state adopted standards. The Board expects its faculty and administration to
regularly evaluate the education program and to recommend modifications of practice and
changes in curriculum content as well as the addition of new courses to the instructional
program.
Denver Montessori will be using the Montessori curriculum for the instruction of students
in grades 6-12. This curriculum will be aligned to the Common Core State Standards and
the Colorado Academic Standards. The curricular framework is described in the
Performance School Application, Appendix C. The mapping is targeted for completion in
January 2013.
Replacement
Policy:
The curricular design approach will use the following schedule: 1. Unit plans for all subjects
and grades mapped to the “at a glance” level of CAS and CCSS standards = end of
December. 2. Development of all classes aligned to the course units = mid-January. 3.
Individual classes mapped back to CCSS and CAS = end of January 2013. Complete gap
analysis on any standards not mapped to individual lessons and develop new lessons that
map to these missing standards = mid-to-late February.
School
IGD: Curriculum Adoption
Educational Program
Proposal
The Board of Education is required by state statutes to determine the educational
programs to be carried on in the schools of the district and to prescribe the textbooks for
Policy
any course of instruction or study in such programs
The DPS Board recognizes the distinctiveness of the DMHS educational model and
therefore delegates curricular and educational material adoption/modification to the local
level with feedback and support to be provided by the DPS Departments of Elementary and
Replacement Secondary Education and School Reform and Innovation. DMHS will be authorized to use a
Policy:
Montessori curriculum for the instruction of students in grades 6-12. This curriculum must
be aligned to the Common Core State Standards and the Colorado Academic Standards.
The curricular framework is described in the Performance School Application, Appendix C.
The mapping is targeted for completion in January 2013.
Page 26
The curricular design approach will use the following schedule: 1. Unit plans for all subjects
and grades = end of November. 2. Development of all classes aligned to the course units =
early January. 3. Individual classes mapped back to CCSS and CAS = end of January 2013.
Complete gap analysis on any standards not mapped to individual lessons and develop new
lessons that map to these missing standards = mid-to-late February.
School
Proposal
Policy
The school principal will select the instructional materials used by the school after careful
consideration of Montessori best practices and recommendations of the school-based
instructional materials committee. The school principal will respond to any District
concerns regarding selected instructional materials by demonstrating the Montessori
pedagogical need and alignment to CAS and CCSS. For grades 10 – 12 Science, History and
Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum
and DPS approved textbooks unless as otherwise adopted through a separate curriculum
waiver process.
IIA: Instructional Materials (Textbooks or their
Educational Program
Equivalent Learning Materials)
I. Identification Phase
A. Establishment of Curriculum Committees, B. Textbook Fair, C. Identification of Textbooks
for Evaluation
II. Evaluation Phase, A. Textbook Analysis, B. Selections for Review
III. Review Phase: A. Parent Advisory Committee Review, B. Community Review, C. Board of
Education Review, D. Preparation of Textbook Evaluation Matrix and Documentation , E.
Board of Education Consideration for Adoption
IV. Purchase of Textbooks: A. All schools use adopted textbooks for the core subject areas
of mathematics, social studies, science, foreign language and language arts; B. Following
subject area adoption, schools purchase new textbooks for the next school year using
procedures developed by staff; and C. The Board of Education grants waivers for purchase
and use of non-adopted textbooks in core subject areas, except that non-adopted
textbooks may be purchased subject to approval of the Superintendent or his/her
designess, prior to the dates below.
IV. Purchase and Use of Supplemental Instructional Materials and Textbooks in Non-core
Subject Areas.
Page 27
Following approval of the DMHS curriculum, a school-based instructional materials
committee will be formed to manage the selection process for choosing instructional
materials that align to the Montessori educational model. The selection process will be
conducted in a transparent manner that follows purchasing best practices. As materials are
integrated into the DMHS curriculum, the school principal will evaluate the effectiveness of
instructional materials and seek feedback from teachers. Highlights of findings will be
communicated to OSRI to further district awareness of how materials are driving
education.
Replacement
The school principal will select the instructional materials used by the school after careful
Policy
consideration of Montessori best practices and recommendations of the school-based
instructional materials committee. The school principal will respond to any District
concerns regarding selected instructional materials by demonstrating the Montessori
pedagogical need and alignment to CAS and CCSS. For grades 10 – 12 Science, History and
Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum
and DPS approved textbooks unless as otherwise adopted through a separate curriculum
waiver process.
School
Proposal
Policy
Replacement
Policy
IIA-R: Instructional Materials
Education Program
I. Planning and Acquisition
A. In cooperation with their Collaborative Decision Making (CDM)
committee, each school will determine needs and prepare a three-year plan …C. assure
that the school meets or exceeds the district's course and grade level standards D. The
departments of Elementary and Secondary Education will review…Each school will maintain
a current inventory of textbooks
III. Each school…will enact measures to ensure that teachers return textbooks
A. Students are required to pay for or replace damaged or lost books. C. Until payment is
made, the student's grades, transcript, and diploma will be withheld
Following approval of the DMHS curriculum, a school-based instructional materials
committee will be formed to manage the selection process for choosing instructional
materials that align to the Montessori educational model. The selection process will be
conducted in a transparent manner that follows purchasing best practices. As materials are
integrated into the DMHS curriculum, the school principal will evaluate the effectiveness of
instructional materials and seek feedback from teachers. Highlights of findings will be
communicated to OSRI to further district awareness of how materials are driving
education.
The school principal will select the instructional materials used by the school after careful
consideration of Montessori best practices and recommendations of the school-based
instructional materials committee. The school principal will respond to any District
concerns regarding selected instructional materials by demonstrating the Montessori
pedagogical need and alignment to CAS and CCSS. For grades 10 – 12 Science, History and
Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum
and DPS approved textbooks unless otherwise adopted through a separate curriculum
waiver process.
Page 28
School
Proposal
Policy
Replacement
Policy
IJJ: Instructional Materials (Textbooks) Selection or
Educational Program
Adoption
Instructional materials will be adopted by the Board of Education based upon their
effectiveness in implementing the instructional program for which they are intended and
according to the following criteria:
1. The extent to which they are aligned with Denver Public Schools Standards for Success,
district goals, and adopted curricula;
2. The extent to which they meet a wide range of needs, interests, and student
performance levels;
3. The extent to which they support teaching practices known to positively impact student
learning; and
4. The extent to which they reflect diversity in such areas as ethnicity, gender, national
origin and handicapping conditions.
Spanish and English language materials shall be adopted at the same time, if practicable.
Schools shall use the current adopted instructional materials in each subject area, except as
otherwise provided by superintendent and/or designee.
Supplementary materials generally do not require adoption by the Board of Education.
Definitions:
The following definitions apply to the terms as used in this policy:
Instructional materials are the basic set of materials teachers use to guide the instructional
activities of a course of study and, thereby, reach their objectives. The basic set of
instructional materials for a course of study may be a single textbook or multiple books and
include such materials as workbooks, visual aids, videos, software, literature and resource
supplements, classroom libraries, and activity kits.
Supplementary materials are most often used for short term instruction to provide
extended or enriched learning opportunities to motivate individual and/or small groups of
students.
Procedures
The Superintendent or designee shall promulgate such procedures as may be needed for
the implementation of this policy.
Following approval of the DMHS curriculum, a school-based instructional materials
committee will be formed to manage the selection process for choosing instructional
materials that align to the Montessori educational model. The selection process will be
conducted in a transparent manner that follows purchasing best practices. As materials are
integrated into the DMHS curriculum, the school principal will evaluate the effectiveness of
instructional materials and seek feedback from teachers. Highlights of findings will be
communicated to OSRI to further district awareness of how materials are driving
education.
The school principal will select the instructional materials used by the school after careful
consideration of Montessori best practices and recommendations of the school-based
instructional materials committee. The school principal will respond to any District
concerns regarding selected instructional materials by demonstrating the Montessori
pedagogical need and alignment to CAS and CCSS. For grades 10 – 12 Science, History and
Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum
and DPS approved textbooks unless as otherwise adopted through a separate curriculum
waiver process.
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School
Proposal
IJJ-R: Instructional Materials (Textbooks) Selection
Educational Program
or Adoption Procedures
New textbooks in each subject area are considered for adoption on a rotating schedule.
Textbooks suggested for consideration are evaluated, rated and reviewed by curriculum
committees, teachers, parents and community before formal review and adoption by the
Board of Education. Spanish language textbooks are considered for adoption along with
English language textbooks in each subject area. Under special circumstances, textbooks
may be considered for adoption outside of the established cycle. The textbook selection
process is outlined below.I. Identification PhaseA. Establishment of Curriculum
Committees…B. Textbook Fair…C. Identification of Textbooks for Evaluation…II. Evaluation
PhaseA. Textbook AnalysisThe curriculum committees review and evaluate the textbooks
using a numerical ranking system to determine the extent to which they meet the criteria
below……B. Selections for ReviewDesignated administrative staff select textbooks for the
review phase based on the results of the evaluation phase.III. Review PhaseThe review
phase allows for additional input from Parent Advisory Committees, the community and
the Board of Education. Opportunities are provided for each group to examine
recommended textbooks and their evaluations as well as any other supporting
documentation.A. Parent Advisory Committee Review…B. Community Review…C. Board of
Policy
Education Review…D. Preparation of Textbook Evaluation Matrix and Documentation…E.
Board of Education Consideration for AdoptionThe Board of Education reviews the
textbooks and their attached evaluative materials, including:…IV. Purchase of TextbooksA.
All schools use adopted textbooks…B. Schools purchase new textbooks using procedures
developed by staff; andC. The Board of Education grants waivers for purchase and use of
non-adopted textbooks in core subject areas, except that non-adopted textbooks may be
purchased subject to approval of the Superintendent or his/her designess, prior to the
dates below.IV. Purchase and Use of Supplemental Instructional Materials and Textbooks in
Non-core Subject Areas.A. Supplemental instructional materials and non-adopted
textbooks for subject areas not defined as "core" may be purchased subject to the approval
of the principal. The principal considers such requests based on the extent to which the
textbook:1. Aligns with Denver Public Schools Standards for Success, Curriculum Matrix,
and District Goals;2. Provides assessment skills practice;…8. Makes available ancillary
materials to support instruction…B. Principals are encouraged to display…all adopted, nonadopted, and supplemental materials so that they may be perused by the school
community.
Following approval of the DMHS curriculum, a school-based instructional materials
committee will be formed to manage the selection process for choosing instructional
materials that align to the Montessori educational model. The selection process will be
conducted in a transparent manner that follows purchasing best practices. As materials are
integrated into the DMHS curriculum, the school principal will evaluate the effectiveness of
instructional materials and seek feedback from teachers. Highlights of findings will be
Replacement communicated to OSRI to further district awareness of how materials are driving
education.
Policy
The school principal will select the instructional materials used by the school after careful
consideration of Montessori best practices and recommendations of the school-based
instructional materials committee. The school principal will respond to any District
concerns regarding selected instructional materials by demonstrating the Montessori
pedagogical need and alignment to CAS and CCSS. For grades 10 – 12 Science, History and
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School
Proposal
Policy
Language Arts, 9th grade Earth Science, and 9th grade Civics, DMHS will use DPS curriculum
and DPS approved textbooks unless as otherwise adopted through a separate curriculum
waiver process.
IJOA: Field Trips / IJOA-R: Field Trips (Guidelines for
Educational Program
Extended Excursions)
Most educational excursions shall be carried out on school time to approved destinations
listed in the catalog for approved excursions. Excursions to destinations not listed in the
catalog may be arranged by following the accompanying procedures for field trips.
Sometimes these experiences in the field will last overnight or for even longer periods. The
accompanying procedures for extended excursions give guidance to teachers and principals
so that judicious decisions may be made at the local level concerning most such excursions.
When the proposed experience involves long, extended periods of time...principals shall
seek counsel, direction and approval from their lead principal who in turn may secure
approval from the superintendent or designee.
School buses shall be provided for teachers to take their classes on educational excursions
insofar as possible using bus allocations established for that school. When school buses are
not available, arrangements may be made to use public transportation or private
transportation. For all excursions requiring students transportation in school buses,
arrangements should be made through the department of transportation.
DMHS will follow the district field trip policies and procedures with two exceptions: The
school will design field trips that match the Montessori curriculum and therefore may be
outside of the district catalog. In such situations, DMHS will have autonomy in determining
Replacement the appropriateness of field trips, and the school principal will be responsible for approving
all school field trips. Second, if a situation exists where the school must pay the district for
Policy
transportation services, the school may choose to contract with another school
transportation provider if the cost estimate from the district is significantly higher that the
other school district's cost estimate.
School
IK- Student Academic Achievement
Education Program
Proposal
The Board’s vision is…In order to achieve this vision the board adopts the following core
beliefs which will govern district policy decisions…
The Board adopts an instructional reform theory for Denver that has the following essential
elements that will positively impact student achievement..
This is an integrated reform strategy that addresses three of DPS's greatest challenges-a
high mobility rate among our students and teachers, low academic preparedness of our
students, and lack of consistent and timely data…
Policy
Each student is expected to meet or exceed the District's academic content standards
before they transition from level to level and before they are eligible to graduate…The
school staff and students are directly responsible for student learning... The District content
standards are to be the focal point of classroom instruction…To fulfill this expectation, all
students will be provided challenging instructional programs. Student learning and
performance will be continuously monitored against the standards through the use of valid
and reliable measures...The Superintendent is directed to comply, modify and implement
the core belief and action plan as necessary.
Replacement Student progression in their mastery of curricular content will be monitored and
Policy
documented through a detailed junior and senior high portfolio. All record keeping will be
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maintained in a Student Electronic Portfolio, which will contain documentation of lessons
attended, student submitted work, teacher feedback, mastery level quizzes, cumulative
project, and overall unit assessment. The Performance School Application, Appendix C,
Sections B and C specify the alternative benchmark assessment program and the
graduation and promotion standards for the school. In addition, DMHS has provided
further policy definition in the attachment, DMHS Alignment with Graduation Standards,
and the relevant mapping to each of the core subject standards.
School
Proposal
IKB: Homework
Educational Program
Parents should expect their children to have regular homework assignments and should
question the lack of such assignments.
Elementary school: The amount, length and type of homework at the elementary school
level may vary…but the minimum amount assigned shall be as follows:
Kindergarten and grade 1- 10-15 minutes, one or two days per week Grade 2- 10-20
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minutes, two days per week Grade 3- 15-25 minutes, two days per week Grade 4- 15-30
minutes, two to three days per week Grade 5- 20-30 minutes, three to four days per week
Middle school: A minimum of five hours of homework per week
High school: The expected minimum amount of homework shall be 10 hours per week in
grades 9 through 12.
The school will implement a Montessori homework policy that is in alignment with the
Montessori educational philosophy. Homework will only be assigned as deemed necessary
at the school level. Students are given independent work time during the school day that
Replacement usually allows them to accomplish a majority of the school's work requirements. In
instances when work is not completed at school, students are expected to complete their
Policy
work by a specified deadline set by the teacher. As the students progress to higher grades,
the homework load will increase in order to appropriately prepare students for postacademic success.
IKE - Promotion, Retention, and Acceleration of
School
Students
Proposal
General Considerations
Grade retention or acceleration will be based on the best interests of the student and
his/her educational success.
Elementary and Middle School: Students will be retained or accelerated, if the following
criteria are met: 1. The parents and the school principal agree that grade retention or
acceleration is in the best interests of the student based on the general considerations
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above and is consistent with Policy Procedures IKE-R. 2. The student does not comply with
requirements for promotion that are established by the Superintendent
High School Grade levels will be determined based on credits earned as defined below:
Grade 9 (Freshman) Less than 60 credits Grade 10 (Sophomore) 60 to 120 credits Grade 11
(Junior) 121 to 170 credits Grade 12 (Senior) 171 to 240 credits
Student progression in their mastery of curricular content will be monitored and
documented through a detailed junior and senior high portfolio. The Performance School
Application, Appendix C, Sections B and C specify the alternative benchmark assessment
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program and the graduation and promotion standards for the school. In addition, DMHS
Policy
has provided further policy definition in the attachment, DMHS Alignment with Graduation
Standards, and the relevant mapping to each of the core subject standards.
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DMHS is designed to respect stages of adolescent development, and
promotion and retention criteria will reflect this value. Students will be expected
to be promoted within their established class. A key time for evaluation will
occur towards the end of the ninth grade year. If a student is demonstrating
significant gaps in academic achievement, social and/or emotional growth to the
level that they may not thrive in the high school environment, a conference will
be called between the student, their family, the principal and the student’s
advisor to determine if the student should spend an additional year in the junior
high. In high school, if a student is not on track to meet all DMHS graduation
requirements, the student, their family, the principal and the student’s advisor
will meet to create a plan in order for the student to graduate. One possible
outcome of that plan may be for the student to spend
an additional semester or year at DMHS until all graduation requirements are
met.
If a student has exceeded graduation requirements before the end of
their 12th grade year, that student will have the option to graduate early or
dually enroll in UCD, Metropolitan State, or another college that offers dual
enrollment. Again, a meeting will be called between the student, their family,
the principal and the student’s advisor to determine the best course of action
for that student.
School
Proposal
Policy
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Policy
School
Proposal
Policy
IKF: Graduation
Graduation and Promotion
Highly detailed. Specifies credit for general ed, etc.
Alternative graduation requirements are specified in the document, DMHS Alignment with
Graduation Standards.
JC-R: Pupil Assignment
Enrollment
Highly detailed. Specifies choice process for parents.
DMHS will participate in the School Choice process with the exception that enrollment
priority will be given according to the following schema:
1) Students who are currently attending Sandoval, Gilpin, Denison, or Lincoln
2) Students who have a sibling currently attending DMHS
3) Students who are the children of DMHS staff members
4) Denver residents who have attended Montessori elementary school
5) Non-Denver residents who have attended Montessori elementary school
6) Denver residents who have not attended Montessori elementary school
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7) Non-Denver residents who have not attended Montessori elementary school
Policy
Additionally, for all priorities stated above, neighborhood students will be granted seat
priority over non-neighborhood students. For example, if after applying priority 1, there are
more students than seats, then priority will be given to students who reside in the school
neighborhood area over students from other areas in the district.
NOTE: “Family Link” will be in effect at DMHS. This means that siblings who apply together
will be systematically linked, maximizing their opportunity to stay together.
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DMHS will continue to reach out to the Montessori community in an equitable manner to
create a diverse student body that is reflective of the DPS and the neighborhood student
body. If a situation arises where a noticeable demographic difference exists between the
school and the neighborhood, the school principal will work with the district in
implementing a plan that recruits more students from the neighborhood area while also
ensuring for their success in a Montessori program.
School
DCTA:
Calendar & Schedule
Proposal
Article 1-7 Definition of “School Year”
The term "school year" as used in these Articles shall mean the officially adopted school
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calendar.
Replacement The term "school year" as used in these Articles shall mean the officially adopted DMHS
Policy
school calendar.
School
Article 5-1-4: Teamwork among Teachers
Curriculum
Proposal
Teamwork among teachers and with the principals is an important component for
improving achievement. Teachers shall have a significant role in identifying and
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developing the instructional program.
Teamwork among teachers and with the principals is an important component for
Replacement improving achievement. Teachers shall have a significant role in identifying and
developing the instructional program as long as the primary focus is in alignment with the
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mission of the school as stated in the Performance School Application.
School
Article 5-4: School Leadership Team
Management
Proposal
Each school will have a School Leadership Team (SLT) consisting of the principal, the
association representative, a teacher appointed by the principal, and a minimum of 3
teacher representatives … elected annually by a majority of the faculty voting by secret
ballot
The SLT will make decisions by consensus. A consensus is either a unanimous decision or a
majority decision that the entire SLT, including the dissenters, will support.
Their responsibilities shall include: a. Collaborate in the development of the School
Policy
Improvement Plans; b. Review and collaborate on the design of and schedule for the
professional
development c. Review and collaborate on the implementation of the District’s
instructional
program …including prioritizing and sequencing activities within the work week;…f.
Collaborate to implement best instructional practices
Teachers will be active participants in the management of the school through the School
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Accountability Committee as it is outlined in district policy BDFH and in the Performance
Policy
School Application.
Professional Standards (Article 8): Sets Teacher
School
Calendar, Work Year, Work Week, Work Day, Class
·
Calendar & Schedule
Proposal
Size and Teaching Load
6 pages. Sections include: School leadership team, contract year, evening meetings, 40
hour work week, lunch periods, planning time, multi-school assignments, teaching loads,
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funding specialized service providers, non-teaching duties, lesson plans, class coverage,
emergency school closings, and teacher-in-charge status.
Replacement Provisions specified in Article 8 will not apply to the school. The school will create and
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School
Proposal
Policy
publish an annual calendar that shall be used for defining the contract year for teachers.
The teacher schedule is highlighted in pages 25 and 26 of the Performance School
Application.
Article 7 Grievance Policy
Human Resource Management
6 pages. Sections include: 1. Definitions, Purpose, Procedure (Level 1, Level 2, Level 3,
Mediation/arbitration), Rights of teachers to representation, Miscellaneous
The school shall maintain the following Grievance Policy:
7-1 Definitions.
7-1-1 A "grievance" shall mean a written complaint by a school staff member that there has
been a violation, a misinterpretation, or inequitable application of any of the provisions of
the School’s Employment Contract or the School’s Employee Handbook.
7-1-2 Unless provided otherwise in this Agreement, all administrative procedures, practices
and written personnel policies that affect staff are grievable.
7-1-3 The term "grievance" shall not apply to any matter as to which (1) the method of
review is prescribed by law, (2) the Board is without authority to act, or (3) a grievance is
specifically prohibited or limited by the terms of the Employment Contract or School
Handbook.
7-1-4 An "aggrieved person" is a school staff member asserting a grievance.
7-2 Purpose. The purpose of this grievance procedure is to secure equitable solutions at the
Replacement lowest possible administrative level to problems that may arise. To this end, grievance
proceedings will be kept informal and confidential and both parties will work toward a
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resolution to avoid litigation.
7-3 Procedure. Since it is important that grievances be processed as rapidly as possible, the
number of days indicated at each level is a maximum, and every effort should be made to
expedite the process. The time limits specified may, however, be extended by mutual
agreement.
Information. The School agrees to make available to the aggrieved person and the aggrieved
person’s representative, all pertinent information not privileged under law, in its possession
or control, and which is relevant to the issues raised by the grievance. The grievant agrees to
make available to the School and its representatives, all pertinent information not privileged
under law in its possession or control, and which is relevant to the issue raised by the
grievant.
Timing. No grievance shall be recognized by the District or the School unless it is presented
at the appropriate level within fifteen (15) school days after the aggrieved person knew, or
should have known, of the act or condition on which the grievance is based. No grievance
shall be recognized at Level Two unless it is filed with the Department of Human Resources
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within at least twenty (20) school days after the act or condition upon which it is based
occurred. Grievances not timely presented will be considered as waived.
7-3-1 Level One. A grievance first will be discussed with the aggrieved person's principal to
attempt to resolve the matter informally, at which time the aggrieved person (1) may discuss
the grievance personally, (2) may be accompanied by a District Human Resource
Representative, or (3) may request that the District Human Resource Representative act on
behalf of the aggrieved person. No written documentation of the grievance or administrative
response will be required if the grievance is settled at Level One.
7-3-2 If the aggrieved person is not satisfied with the results of the informal conference, the
aggrieved person may then file a grievance in writing on the proper form with the principal
or supervisor within seven (7) school days. The grievance must refer to the specific Articles
of the Employment Contract and/or School Handbook and explain how they were violated
and indicate the reason why the Level One decision is unsatisfactory. The principal shall
also have the opportunity to provide comment related to the Level One in writing. The
grievant shall send a copy of the written grievance and the principal response to the
Department of Human Resources. All known documentation related to the grievance must
be provided prior to the Level Two meeting.
7-3-3 Level Two. The Human Resources Director or Instructional Superintendent will go to
the school and meet with the teacher and principal to facilitate a resolution. Such meeting
will take place within seven (7) school days after receipt of the written grievance by the
Department of Human Resources. Any resolution determined by the Human Resources
Director or Instructional Superintendent will be considered final.
7-4 Miscellaneous. If the time limits for processing a grievance are not met by the
administrator responding to the grievance, the grievance may be moved to the next level at
the request of the aggrieved. The Department of Human Resources may take appropriate
action on whether to grant the grievant’s requested remedy based on its review of the
situation.
School
Proposal
Article 10 Teacher Evaluation: Describes the
Human Resource Management:
Evaluation Process for Teachers
Teacher Evaluation
12 page process, which includes: defining evaluators, documentation, records of teaching,
observations, interview data, written communication, sequence of evaluation, pre and post
Policy
observation conferences, evaluation data review conferences, performance ratings,
completion of evaluation, remediation, conducting a remediation plan, PD plans, special
evaluations, personnel performance evaluation council.
All teachers will receive annual performance evaluations. DMHS will use the LEAP
Replacement
framework. The evaluation and feedback process is specified in pages 42-44 of the
Policy
Performance School Application.
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School
Proposal
Committees (Articles 5, 13, 29): Development
Committee (5-4-1) and Personnel Committee (13-8)
Governance & Human Resource
Management: Leadership
Structure
Committees identified in these sections include:
- Instructional Issues Council
- IS Advisory Committee
Policy
- School Leadership Team
- Personnel Committee
- Task Force on School and District Climate
The school will be lead by a School Accountability Committee and will operate as the
Replacement Collaborative School Committee as established in district policy BDFH. Ad-hoc committees
created to address specific needs or concerns within the school will be created when
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appropriate either at the direction of the school principal or the SAC.
School
Article 11: Complaints Against
Human Resource Management
Proposal
Teachers/Administrative Leave/Corrective Action
11-2 Administrative Leave. If a principal decides to place a teacher on administrative leave
for…the principal or designee shall meet with the teacher to give specific allegation(s) and
the basic reason why the administrative leave for investigation is necessary, when possible.
11-2-1 The meeting shall take place at the end of the school day or whenever it is
appropriate.11-2-2 The principal shall provide the teacher a copy of the administrative
leave checklist and review it with the teacher. The teacher shall sign the form only as
acknowledgement of receipt..11-2-3 At the teacher’s request a meeting will be held within
three (3) school days...to give the teacher an opportunity to respond. The teacher may
have Association representation at the meeting. 11-2-4…If an investigation must extend
beyond seven (7) calendar days…the teacher and the Association will be notified by phone
calls…[with]…the reasons for the extension and the expected date of completion…11-2-5
Policy
During the investigation, the teacher…will…
receive full pay. 11-2-6 Following completion…the principal or designee shall…share the
results…and give the teacher an opportunity to respond…11-2-7 Administrative leave
should be considered as an option to be used only when necessary to protect the students
or staff or to conduct an appropriate investigation…There will be no record of the leave in a
teacher's personnel file…11-2-8 The Agreement Review Committee (ARC) will review on an
annual basis administrative leaves for the prior year to ensure that the above procedures
have been implemented appropriately.
11-3 Corrective Action. Before taking a corrective action against a teacher, the principal
shall investigate the situation, meet with the teacher and give the teacher an opportunity
to respond.
Complaints: When a person makes a written or verbal complaint against a teacher, the
principal or designee shall promptly notify the teacher of the complaint and the teacher
shall be given the opportunity to respond. The principal or designee shall investigate the
complaint and attempt to resolve the complaint informally if appropriate.
Replacement
If any record of the complaint, or its formal or informal resolution, is placed in the teacher's
Policy
files, the teacher shall have the right to file a written response within twenty (20) school
days.
Administrative Leave: If a principal decides to place a teacher on administrative leave for
the purpose of further investigation, the principal or designee shall meet with the teacher
Page 37
to give specific allegation(s) and the basic reason why the administrative leave for
investigation is necessary, when possible.
At the teacher’s request a meeting will be held within three (3) school days. The purpose of
the meeting is to give the teacher an opportunity to respond. The teacher may have his or
her own representation at the meeting.
Administrative leave should be considered as an option to be used only when necessary to
protect the students or staff or to conduct an appropriate investigation.
School
Proposal
Policy
Corrective action: If a principal or designee determines it may be necessary to take a
corrective action, the principal shall inform the teacher of his/her intent to consider
potential corrective action measures and allow the teacher the opportunity to have a
representative of their choosing present at the meeting.
Assignments, Schedules and Transfer (Article 13):
Human Resource Management:
Describes District and School Procedures for
Hiring & Staff Assignments
Transfer and Reassignment of Teachers
10 Pages. Sections include: Timelines with the HR process, Hiring through Personnel
Committee, Reduction in Building Staff (RIBS), Voluntary Transfers, In-Building Bidding,
Posting Vacancies, Applications, Selection Procedure, Assignments/Placements.
DMHS will work with the district HR office to post teaching positions through the district
website. From this posting, DMHS will engage in independent outreach efforts to recruit
candidates outside of the centralized recruitment channels.
Teachers shall be hired based on the following criteria: DMHS will create a rubric that
values Montessori training, NAMTA or other Montessori Adolescent training, Highly
qualified, teacher licensure, demonstrated ability to team teach, experience with
Montessori adolescent programs, and demonstrated understanding and ability to
implement a Montessori adolescent program. Initial hiring decisions will be made by the
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school principal. Subsequent hiring decisions will be made as the school’s “personnel
Policy
committee”, with final determination to be made by the school principal. The personnel
committee shall consist of volunteer representatives from all staffing areas that will be
affected by the new hire, such as the teaching team, the program director, special
education and support staff. All candidates must pass a DPS background check, which will
be conducted through the district HR process.
School
Proposal
Policy
The school will adhere to district salary schedules for all teachers but requires autonomy in
determining the years of experience in order to account for private and other school
experience.
Human Resource Management:
Article 14-1: Summer school teaching positions
Hiring & Staff Assignments
Summer School and Evening School. Summer and evening school programs shall be
provided flexibility of design and implementation following the guidelines set forth below.
14-1-1 Staffing. The purpose of all staffing procedures is to find the most suitable
candidates for the teaching positions needed to run the summer school.
14-1-1-1 Summer school teaching positions shall be posted.
14-1-1-2 Postings shall include the following basic components: descriptions of any
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teaching position that may be included in the summer school,
and an explanation of the selection process.
14-1-1-3 All teaching positions in summer school programs will be filled first by teachers
currently in the District.
In the event that Denver Montessori offers summer school classes, the school principal will
first work with a district HR representative to specify job descriptions and compensation
for the positions to be hired for. Summer school positions will first be shared internally and
staff will be encouraged to apply by a specified deadline. The school leaders will then
Replacement interview all internal candidates for the position and make offers to candidates that there
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is mutual consent for the position. After this internal hiring has been completed, the school
leader will work with a district HR representative to post an open position for the summer
school term. The school leader will be provided with all applications received and will have
the ability to offer positions to any qualified applicant that they deem would be the best fit
for the position.
School
Reduction in Force (RIF) (Article 20): Procedures for
Human Resource Management:
Proposal
Conducting Reduction in Force
Staffing
20-1 Reduction in Force…shall be done in compliance with federal and state statutes, any
existing court orders upon the District, and in a manner that will maintain the best
educational program for the District. 20-1-1 If the District anticipates a reduction in staff,
the Executive Director of Human Resources…shall consult with the Association…20-1-2
Normal attrition shall precede any reduction in force of regularly assigned teachers…20-1-3
Policy
Required staff reductions should be done by endorsement area in reverse order of being
hired as a teacher…20-1-5 Whenever possible, Reductions in Force will be limited to the
end of the semester or school year. Affected teachers shall receive thirty (30) days written
notice. 20-1-6 Upon the written request of the teacher identified for job reduction, the
administration shall investigate all possible assignments for which the teacher is eligible.
In the event that the school is required to implement a reduction in force process, it shall
be done in compliance with federal and state statutes, any existing court orders upon the
District, and in a manner that will maintain the DMHS educational program. RIF
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determinations will be made by the school principal as deemed appropriate to minimize
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the impact to the delivery of high quality educational services to students. Determinations
will be made in consultation with district staff to ensure compliance with state and federal
statutes.
Job Sharing and Half-Time (Article 25): Procedures
School
Human Resource Management:
for Arranging Job-Sharing Assignments and Half
Proposal
Staff Assignments
Time
25-1 Job sharing,…may be requested by…full-time equivalent non-probationary teachers
who wish to work only half-time…25-1-2 Teachers wishing to job share must find another
teacher who also wishes to job share…25-1-3…assignments, when possible, shall be for one
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(1) year at a time. 25-1-4 Salary, benefits, accrued service and other employment
entitlements shall be half their usual value... 25-1-5…the job sharing or half-time
assignments must be approved by the CSC
Job-Sharing: Job sharing, or converting from a full-time employee to a half-time employee,
may be requested by regularly assigned full-time equivalent teachers who wish to work
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only half time. Procedures for assignment to a job sharing or half-time position will be
Policy
available upon request from the Department of Human Resources.
-Application for a job sharing or half-time position must be made in writing to the
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Department of Human Resources by the published date.
-Teachers wishing to job share must find another teacher who also wishes to job share.
-Job share and half-time assignments, when possible, shall be for one (1) year at a time.
-Salary, benefits, accrued service and other employment entitlements shall be half their
usual value, as applicable.
-Job sharing or half-time assignment must be approved by the school leader
School
Article 32: Extra Duty Comp: Sets Rates for Extra
Human Resource Management:
Proposal
Duty Compensation
Compensation
Various tables that specify compensation levels for activities that include:
Policy
Substitute pay, Hourly rates, Activity salaries with steps and schedules
The School reserves the right to not provide additional compensation to exempt employees
for additional time that occurs during overnight and extended trips, after school meetings,
Replacement parent/teacher conferences, after school activities, school performances, events, or games,
Policy
evening meetings and professional development. If the school does give compensation for
such additional time, the compensation will be provided consistently to all teachers and
staff working such additional time.
School
Proposal
Colorado State Statutes:
Section 22-9-106: Local Board Duties Concerning
Performance Evaluations for Licensed Personnel
Human Resource Management:
Teacher Evaluations
All of the teacher and principal effectiveness legislation.
Policy
The school will have the authority to adapt LEAP or adopt an alternative evaluation system,
provided such system meets the standards of SENATE BILL 10-191 and is approved by the
District HR office. An alternative proposal will be provided prior to use in formally
evaluating staff.
Only the following individuals may serve as evaluators for DPMS: The school principal, the
school's program directors at the permission of the school principal, other professional
teacher evaluators through the LEAP Peer Observer program.
The school principal, as hired by the district, shall be allowed to evaluate professional staff
Replacement
members regardless of whether the administrator has an active administrative certificate.
Policy
No other individual will have de facto authorization to evaluate staff without the explicit
designation by the school principal. The school principal will continue to be evaluated by
the superintendent or his/her designee and will receive feedback on the quality of
evaluations being given at the school. The school principal will be responsible for
evaluation of other evaluators on campus, but may discuss evaluations with district staff as
well to ensure meaningful calibration of scores.
The policy will apply evenly to all teachers in the school. All teachers will receive at least
one formal evaluation each year. P. 43 of PSA.
Page 40
School
Proposal
Section 22-32-109(1)(f): Local Board Duties
Concerning Selection of Personnel and Pay
Human Resource Management:
Staff Hiring, Compensation
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
(f) (I) To employ all personnel required to maintain the operations and carry out the
educational program of the district and to fix and order paid their compensation...A board
of a district of innovation…may delegate the duty specified in this paragraph (f) to an
innovation school,
Replacement The principal, in consultation with the school leadership team, will select teaching staff
Policy
directly and rates of pay will be based on the district schedule.
School
Section 22-32-109(1)(cc):
Human Resource Management:
Proposal
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
Policy
Policy
(cc) To adopt a dress code policy for teachers and other school employees;
Replacement The principal, in consultation with the school leadership team, will adopt a dress code
Policy
policy for teachers and other school employees.
School
Section 22-32-109(1)(n)(I): Schedule and Calendar
Calendar and Schedule
Proposal
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
(n) (I) To determine, prior to the end of a school year, the length of time which the schools
of the district shall be in session during the next following school year, but in no event shall
said schools be scheduled to have fewer than [varies by grade level] hours of planned
teacher-pupil instruction
The principal, in consultation with the school leadership team, will determine prior to the
Replacement end of a school year, the length of time which the school shall be in session during the next
following school year, but in no event shall DMHS have fewer than the minimum hours set
Policy
by the district and state for public instruction.
School
Section 22-32-109 (1)(n)(II)(A): Actual Hours of
Calendar and Schedule
Proposal
Teacher-Pupil Instruction and Contact
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
Policy
(II) (A) The actual hours of teacher-pupil instruction and teacher-pupil contact specified in
subparagraph (I) of this paragraph (n) may be reduced to no fewer than one thousand fiftyPolicy
six hours for secondary school pupils, no fewer than nine hundred sixtyeight hours for
elementary school pupils, no fewer than four hundred thirty-five hours for half-day
kindergarten pupils, or no fewer than eight hundred seventy hours for full-day
kindergarten pupils, for parent-teacher conferences, staff in-service programs, and closing
deemed by the board to be necessary for the health, safety, or welfare of students.
Replacement The school leader, in consultation with the school leadership team, will determine prior to
Policy
the end of a school year, the length of time which the school shall be in session during the
Page 41
next following school year, but in no event shall DMHS have fewer than the minimum
hours set by the district and state for public instruction.
School
Proposal
Section 22-32-109 (1)(n)(II)(B): School Calendar
Calendar and Schedule
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
(B) Prior to the beginning of the school year, each district shall provide for the adoption of
a district calendar which is applicable to all schools within the district…A copy of the
Policy
calendar shall be provided to the parents or guardians of all children enrolled…Such
calendar shall include the dates for all staff in-service programs…[The] school
administration shall allow for public input from parents and teachers prior to scheduling
…staff in-service programs. Any change in the calendar…shall be preceded by adequate and
timely…of not less than thirty days.
The principal, in consultation with the school leadership team, will determine prior to the
end of a school year, the length of time which the school shall be in session during the next
Replacement following school year, but in no event shall DMHS have fewer than the minimum hours set
by the district and state for public instruction.
Policy
School
Proposal
The school calendar will replace the school’s need to follow the district calendar.
Section22-32-109 (1)(aa): Adopt Content Standards
Educational Program
and Plan for Implementation of Content Standards
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
Policy
(aa) To adopt content standards and a plan for implementation of such content
standards pursuant to the provisions of section 22-7-407;
The DPS Board delegates to DMHS the authority to develop a local plan for implementation
of the CCSS and the CAS in a way that aligns to the mission and vision of the school. All
Replacement substantial material changes to the district educational program must be communicated to
the district offices of Elementary and Secondary Education and School Reform and
Policy
Innovation for review. These offices are provided with final authority for determining
whether the changes will be approved by the district.
School
Section 22-32-109(1)(t): Determine Educational
Education Program
Proposal
Program and Prescribe Textbooks
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
Policy
(t) To determine the educational programs to be carried on in the schools of the district
and to prescribe the textbooks for any course of instruction or study in such programs;
The DPS Board delegates to DMHS the authority to develop a local plan for implementation
of the CCSS and the CAS in a way that aligns to the mission and vision of the school. All
Replacement substantial material changes to the district educational program must be communicated to
Policy
the district offices of Elementary and Secondary Education and School Reform and
Innovation for review. These offices are provided with final authority for determining
whether the changes will be approved by the district.
School
Section 22-32-109(1)(jj): Identify Areas in which the
Human Resource Management:
Page 42
Proposal
Principal/s Require Training or Development
Professional Development
22-32-109. Board of education - specific duties. (1) …each board of education shall have
and perform the following specific duties:
Policy
(jj) To identify any areas in which one or more of the principals of the schools of the school
district require further training or development. The board of education shall contract for
or otherwise assist the identified principals in participating in professional development
programs to assist the identified principals in improving their skills in the identified areas.
District will establish a supervisory role with the school principal and as part of this role,
Replacement will jointly develop a professional development plan that will be followed by the school
principal. This relationship, through the waiver, will be such that a personalized PD plan
Policy
that can be developed to allow for greater autonomy of the school leader.
Section 22-32-110(1)(h), C.R.S.: Local Board Powers
School
Human Resource Management:
Concerning Employment Termination of School
Proposal
Staff Dismissals
Personnel
22-32-110. Board of education - specific powers. (1) In addition to any other power granted
… each board of education of a school district shall have the following specific powers, to
be exercised in its judgment:
Policy
(h) To discharge or otherwise terminate the employment of any personnel. A board of a
district of innovation…may delegate the power specified in this paragraph (h) to an
innovation school
The principal will have the authority to discharge or otherwise terminate the employment
Replacement
of any personnel in accordance with dismissal policies outlined in the innovation plan (see
Policy
GDQD waiver language).
School
Proposal
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63- 201: Employment-License
Required-Exception
Human Resource Management:
Hiring and Teacher Qualifications
Paraphrasing - Must hire a teacher with a license. An alternative license is okay. Districts
are not required to hire administrators with the requisite license.
Policy will remain, but with recognition that the principal does the hiring. Additionally, refer
Replacement
to replacement policy for CFBA for replacement language that exempts the school from
Policy
needing to be licensed.
Policy
School
Proposal
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63-202, C.R.S.: Contracts in
Writing Duration Damage Provision
Human Resource Management:
Hiring, Contracts and Employment
Offer Letters
Contracts shall be in writing, amount of notice required by a teacher/principal who intends
to resign, when a position can be re-opened, penalties for resigning outside of the window,
Policy
no direct placement requirement, priority hiring preference for effective/satisfactory
teachers, management of displaced teachers, disclosure of why contracts were terminated.
All contracts will be in writing. DMHS will provide contract language to the district for
Replacement
feedback before any employment contracts are offered. Mutual terminations will be
Policy
negotiated between the teacher and the school principal and teachers must give notice at
Page 43
least 30 days prior to the date of termination (unless mutually agreed upon that the
termination date could be sooner). Teachers will be at-will employees of the school, but
will also receive an annual contract outlining the terms of employment. Contract renewals
for the following school year must be finalized no later than 60 days before the end of the
current school year.
The school principal has the authority to make employment offers to qualified candidates.
Termination of all staff will follow the dismissal procedures outline in GDQD. DMHS will not
provide first opportunity to interview rights to priority hiring pool candidates, but will still
consider them for employment. The school has the right to refuse direct assignment of
teachers from the district.
School
Proposal
Policy
Replacement
Policy
School
Proposal
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63-203, C.R.S.: Probationary
Teachers – Renewal and Nonrenewal of
Employment Contract
Human Resource Management:
Dismissals
Non-probationary status - how established, treatment of probationary teachers, time,
ability to not renew contracts,
DMHS will hire teachers with terms specified in an annual contract.
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63-206, C.R.S.: Transfer of
Teachers – Compensation
Human Resource Management:
Direct Placement of Teachers
Specifies that schools are not required to accept transfers from the Chief Admin Officer of a
district, but if they do, specifies the manner in which compensation should be handled.
School will have the authority to decide whether to accept transfers of any staff from the
Replacement district on a case-by-case basis. In such situations where transfers occur, the school
Policy
principal has the authority to determine the appropriate years of experience on the salary
schedule.
Policy
School
Proposal
Policy
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63- 301: Grounds for
Dismissal
Human Resource Management:
Dismissals
Specifies reasons for why a teacher could be dismissed.
All teachers will be employed using an annual contract. This contract can be non-renewed
at the end of the contract term for any reason.
Replacement
Policy
In all situations related to teacher dismissal except for non-renewal of annual contracts, a
teacher may only be dismissed for cause in accordance with the dismissal policies outlined
in the replacement policy for 22-63-302.
Page 44
School
Proposal
Policy
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63- 302: Procedures for
Dismissal of Teachers and Judicial Review
Human Resource Management:
Dismissals
Process for terminating a teacher through judicial review. Teacher can appeal for an
impartial hearing, appeal to court of appeals, appeal to supreme court. Instances when a
district can dismiss a teacher without cause is specified. Criminal convictions.
School will administer dismissal policies as specified below:
I. Dismissal Procedures For Teachers
-These procedures do not apply to non-renewal of annual contracts.
A. No teacher will be dismissed until he/she has been notified by one of his/her
supervisors of the supervisor's intent to recommend dismissal to the
Superintendent or his/her designee. The supervisor will inform the teacher of the
grounds for the recommended dismissal and will give the teacher a reasonable
opportunity to respond.
B. If the supervisor decides to proceed with the dismissal recommendation, the
supervisor will provide the teacher with written notice of the ground(s) for the
dismissal recommendation and the teacher may request a post-termination hearing
before an administrator (designated by the Superintendent or his/her designee) in
the Human Resources Department. The teacher must request the post-termination
hearing within three (3) scheduled working days of the last day of work.
Replacement 1. If the teacher does not request the post-termination hearing within three (3)
scheduled working days, the termination will be considered final. The
Policy
recommendation for dismissal of teachers who do not request a post-termination
hearing will be forwarded to the Superintendent or his/her designee for final
action. If the Superintendent or his/her designee does not uphold the supervisor's
recommendation for dismissal, then the teacher shall be entitled to back pay.
2. If the teacher makes a timely request for a post-termination hearing, then the
Human Resources administrator shall conduct the hearing within ten (10)
scheduled working days of the receipt of the request for hearing, unless
extraordinary circumstances require additional time.
i. The Human Resources administrator shall review the supervisor's decision in
order to determine if there are facts that demonstrate that any of the ground(s)
specified in the notice of dismissal recommendation provided the teacher are
present. The Human Resources administrator shall issue a decision in writing
affirming, modifying, or reversing the dismissal recommendation. The decision shall
be rendered within five (5) working days of the hearing, unless extraordinary
circumstances require additional time.
Page 45
ii. If the Human Resources administrator affirms the dismissal recommendation,
the recommendation will be forwarded to the Superintendent or his / her designee
for final action. If the Superintendent or his/her designee does not uphold the
recommendation for dismissal, the teacher shall be entitled to back pay.
School
Proposal
Teacher Employment, Compensation and Dismissal
Act of 1990 Section 22-63- 401: Teachers Subject to
Adopted Salary Schedule
Human Resource Management:
Compensation
Districts are required to pay teachers according to a schedule or according to a
performance policy. Salaries are not to be changed until the end of the year. Individual
teachers cannot have their salaries cut unless all teachers have salaries cut.
The school will use the district salary schedule for determining pay for teachers and staff;
however, they will have discretion on how the budget is impacted for paying staff (actuals
Replacement vs. averages). The school principal reserves the right to develop a supplemental
Policy
compensation system to reimburse employees for extra duty pay as it may arise for
activities that may include, but not necessarily be limited to coaching, tutoring, external
professional development or for performance incentive pay.
Policy
Page 46
Part III: Evidence of Support
Page 47
Evidence of Community Support for Innovation Status
As the founders of Denver Montessori Junior/Senior High School (DMHS) wrote and
compiled the School Performance Application, they sought out both the national and local
Montessori community to review and comment on every section. This community
expressed its support of the Application as noted in Appendix F, Evidence of Support
For this application for Innovation Status, the majority of the application is the Performance
School Application. All additional sections of the Request for Innovation Status have been
presented to this same group of community supporters. Please find below the evidence of
their support for Denver Montessori Junior/Senior High School’s application for innovation
Status. Also included is a letter of support from DMHS employee Carol Delong. Principal
Katy Myer’s evidence of support is evidenced by the cover letter she wrote for this
application for innovation status. Katy and Carol are currently the only two employees of
DMHS.
From: "Delong, Carol" <[email protected]>
Subject: request for innovation status
Date: December 19, 2012 11:38:59 AM MST
To: "'Katy Myers' ([email protected])" <[email protected]>
I, Carol Delong, Office Support for the Denver Montessori Junior/Senior High, support the
request for DMHS to have innovation status. I have worked at Gilpin Montessori Public
School for four years now and have seen such positive growth in our students as a result of
their Montessori education. It is very exciting that our students in Denver Public Schools
will now have an option to continue their Montessori education through high school.
Sincerely,
Carol Delong
Page 48
From: Vincent, Frank
Sent: Wednesday, December 19, 2012 1:59 PM
To: Katy Myers ([email protected]); Myers, Katy
Subject: Support for the Denver Montessori Junior/Senior High School
Katy,
I strongly support the Denver Montessori Junior/Senior High School’s request for
Innovation Status. I think it will allow this school to move forward in the fastest possible
manner to ensure the continuation of the Montessori program for our students in Denver
Montessori programs, whether public, charter, or private. I look forward to working with
this school to develop this groundbreaking model for school innovation that has been
shown to be exactly what students need in their middle and high school years.
Frank Vincent
Principal
Gilpin Montessori Public School
Page 49
On Dec 19, 2012, at 3:41 PM, [email protected] wrote:
Dear Denver Public Schools and Katy Myers,
I strongly endorse and support the Denver Montessori Junior/Senior High School's request
for Innovation Status.
The Denver Public Schools has strongly supported Montessori Education for over twenty
years.
It is exciting to provide parents and students with an opportunity to continue and complete
their public school education in a Montessori setting and the innovation status approach
will ensure successful completion.
Denver Public Schools is truly a national leader in the quest for innovative school design.
We have an amazing opportunity to demonstrate that adolescent Montessori programs can
work within the confines of District run schools.
Sincerely,
Dr. Martha M. Urioste
Former Mitchell Montessori Elementary Citywide Magnet School Principal
Former Denison Montessori Elementary Citywide Magnet School Principal
Montessori Consultant for Sandoval, Lincoln, and Gilpin Montessori Elementary Schools
Co-founder, President, and Board Member of Family Star 0-3 Montessori Education; two
sites
Page 50
On Dec 19, 2012, at 11:33 AM, Hannah Ewert-Krocker <[email protected]>
wrote:
Dear Katy,
I wanted to send you a quick email to let you know that as a graduate of the Hershey
Montessori Adolescent Farm Program in Huntsburg, Ohio, a resident of the City and County
of Denver, and the former High School Intern at Compass Montessori School in Golden, CO,
support Denver Montessori Junior/Senior High School’s request for Innovation Status.
Good luck!
Hannah Ewert-Krocker
1346 Downing St. Apt. 2
Denver, CO, 80218
440.313.5882
On Dec 19, 2012, at 10:51 AM, Kathryn Ross <[email protected]> wrote:
To Whom It May Concern:
I am writing to express strong support of the Denver Montessori Junior/High School's
request for Innovation Status within DPS. As president of the Colorado Montessori
Association, I know I speak for all our members when I say that we are excited to have the
opportunity for a Montessori junior/senior high school option in Colorado. Support for and
understanding of the Montessori education approach continues to grow in Colorado.
Approving DMHS as a school with Innovation Status will be a valuable step in this process.
Sincerely,
Kathryn Ross
-Kathryn Ross
President, Colorado Montessori Association
2500 Curtis St.
Denver, CO 80205
Page 51
On Dec 19, 2012, at 10:21 AM, Greg MacDonald <[email protected]>
wrote:
Dear Katy,
As a Director of Elementary Teacher Training in the Montessori movement, I am very pleased to
support Denver Montessori Junior/Senior High School’s request for Innovation Status.
Please let me know if there is anything else that I can do to support your work –
This is a wonderful project that will impact generations to come!
Greg MacDonald
Director of Elementary Training
Hershey Montessori Training Institute
10924 Magnolia Drive
Cleveland OH 44106
Telephone: 216-231-2651, ext. 306 (Office) 240-304-0275 (Cell)
e-mail: [email protected]
On Dec 19, 2012, at 10:16 AM, JUDITH ORION <[email protected]> wrote:
I, Judith Orion, Director of Training, The Montessori Institute, Denver, support Denver
Montessori Junior/Senior High School’s request for Innovation Status.
On Dec 19, 2012, at 1:46 PM, Laurie Ewert-Krocker <[email protected]> wrote:
Dear Katy,
Please make it known that as a National Consultant to Montessori Adolescent programs and
Co-Director of the AMI-NAMTA Orientation to Adolescent Studies Course, I fully support
the Denver Montessori Junior/Senior High School’s request for Innovation Status.
Please let me know how else I can help or support this endeavor.
Sincerely,
Laurie Ewert-Krocker
North American Montessori Teachers Association and
Montessori Development Partnerships
-Laurie Ewert-Krocker Hershey
Montessori School Adolescent
Program on the Farm
11530 Madison Rd.
Huntsburg, OH 44046
Page 52
From: Kristy Cash - HS Program Director [[email protected]]
Sent: Saturday, December 29, 2012 9:25 AM
To: Myers, Katy
Subject: Support Statement
As the program director of Compass Montessori School's secondary school program for the
past 13 years, I am absolutely thrilled with the enormous possibilities of Denver Montessori
Junior/Senior High School to be a powerful leader in the national movement for educational
innovation and change. Therefore, I would fully support Denver Montessori Junior/Senior
High School's request for Innovation Status.
Please feel free to contact me anytime with any questions. Thank you for your kind and
encouraging consideration.
-Kristy Cash, Program Director
Compass Montessori Secondary School
Website: www.compassmontessori.org
Phone: (303) 271-1977 x242
Fax:
(303) 271-1984
Statement Regarding Other Evidence of Support
The proposed innovation school is a new school, and thus, currently employs no teachers or
other staff members. All employees will have access to the innovation school’s plan prior to
being hired. Prior to being hired and upon acceptance of employment at the school, each
employee shall make a commitment that s/he supports and consents to the designation as an
innovation school.
Similarly, as a new school, the school has no school accountability committee (“SAC”). Included
in this plan, is a letter from the current administrators at the school, which outlines
administrative support and consent to the designation as an innovation school.
Page 53
Part IV: Curriculum Components
Page 54
DMHS Alignment with DPS Graduation Standards
October 2012
Denver Montessori Junior/Senior High School (DMHS) is an approved DPS
performance school that will open in August 2013. As part of the approval process,
DMHS agreed to provide evidence as to how they will meet or exceed DPS
Graduation Requirements. DMHS will meet all graduation requirements as stated in
the DPS Board Policy IKF. Explanation of how DMHS will meet these requirements is
included below.
Nearly all of DMHS classes will be taught through an integrated approach with
mastery level requirements for each subject area. For example, in the 6th, 7th , 8th
and 9th grade, Language Arts and History will be taught together as a Humanities
Class. Art will be integrated into this unit as well as music. Each unit will have stated
objectives for each subject area along with related required evidence of mastery for
each objective. All record keeping will be maintained in a Student Electronic
Portfolio, which will contain documentation of lessons attended, student submitted
work, teacher feedback, mastery level quizzes, cumulative project, and overall unit
assessment.
Because of this integrated approach and focus on mastery, DMHS will refer to units
in the graduation requirements versus semester hours. Each unit will equate to one
year’s instructional content, and a .5 unit will equal one semester of instructional
content.
In addition to DMHS classes, high school juniors and seniors will also have the
option to obtain dual credit through either attendance at a local college or university
or through vetted and approved accredited on-line university level course work.
Students will be responsible for fees associated with college credit. DMHS will assist
students in the application process, navigating the college or university and
applying for scholarships and financial aid.
In addition to the DPS high school graduation requirements, DMHS will require
community service / service learning versus allowing it to be optional. DMHS will
also strongly encourage all students to apply to three colleges / universities /
technical college or other similar post secondary options.
Following are requirements as outlined by DPS Board Policy IKF and the DMHS
response to each requirement.
Page 55
REQUIRED UNITS OF STUDY
Requirement:
THE PERSONAL EDUCATION PLAN
Each student who enters a Denver Public Schools high school will develop a
personal education plan (P.E.P.). This plan will set his/her intended course of study
as he/she begins his/her journey toward graduation. The student and an academic
adviser (this may be a teacher, counselor, dean administrator or other professional
school staff member) will review and amend the P.E.P. each semester, prior to the
development of a new class schedule (for students attending the 8th grade in the
Denver Public Schools, the P.E.P. will be initiated during the spring semester of the
8th grade year). Schools may opt for an "advisement" class to provide for the P.E.P.
This process will not only provide clear information and a focus on the future for the
student, but also bring a new purpose to the important articulation between middle
school and high school staff members.
Response:
Every student at DMHS will have a personal education plan (P.E.P). Beginning in 8th
grade, students will design their plan with assistance from their academic advisor.
The P.E.P will be reviewed at every student/advisor/family conference and
amended as agreed by that team.
Requirement:
General Course of Study
Twenty-four (24) units of study (240 semester hours) shall be required in grades 9,
10, 11, and 12 for students to graduate from high school and receive a high school
diploma.
Response:
DMHS students will receive a minimum of twenty-four (24) units of study.
Completion of a unit of study will be determined by assessments that demonstrate
mastery of that particular course of study.
Requirement:
1. Language Arts
A minimum of forty semester hours (4 units) shall be earned including ten semester
hours (1 unit) of Introduction to Literature and Composition 1 & 2 (9th Grade), ten
semester hours (1 unit) of American Literature 1 & 2 (10th Grade), ten semester
hours (1 unit) of upper division writing academic elective or world literature, and
ten semester hours (1 unit) of other language arts.
Page 56
Response:
9th Grade:
Ninth grade students will receive 1 unit of Literature and Composition1&2 that will
be integrated as part of the thematic humanities course of study.
10th, 11th and 12th:
Over a three-year cycle, students will be required to take 1 unit of American
Literature 1 & 2, 1 unit of upper division writing academic elective or world
literature, and 1 unit of other Language Arts.
American Literature will be offered every other year to insure that students meet
this requirement. American Literature will be integrated with U.S. History.
Each year, an AP component will be offered in Language Arts.
Requirement:
2. Social Studies
Thirty semester hours (3 units) shall be earned: ten semester hours (1 unit) in U.S.
History, five semester hours (.5 units) in Civics, and fifteen semester hours (1.5
units) of other Social Studies are required.
Response:
9th Grade:
Ninth grade students at DMHS will receive .5 units of Civics. Ninth grade students
will also receive .5 units of Social Studies. Social Studies will be integrated with
Language Arts and delivered as an overall thematic humanities course of study.
10th, 11th and 12th.
Over a three-year cycle, student will be required to take 1 unit of U.S. History and a
minimum 1 unit of other Social Studies.
U.S. history will be offered every other year to insure that students meet this
requirement. U.S. History will be integrated with American Literature. During these
years, DMHS will also offer A.P. U.S. History.
On the alternate years, DMHS will offer 1 unit of World History.
Requirement:
3. Science
Page 57
Thirty semester hours (3 units) shall be earned: Students will be required to
complete 30 semester hours of science credit, 20 semester hours (2 units) must
come from Earth Science, Biology, Chemistry, or Physics.
Response:
9th Grade:
Ninth grade students will receive .5 units of Earth Science. Ninth grade students will
also receive .5 units of Health and Human Development.
10th, 11th and 12th
During a three-year cycle, students will be required to take a total of 1. 5 units of
Biology and Chemistry. DMHS will offer Biology (1 unit), Chemistry (1 unit) and
Environmental Science (1 unit). DMHS will offer A.P. Environmental Science as well
as A.P. Biology.
Requirement:
4. Mathematics
Forty semester hours (4 units) shall be earned. Ten semester hours (1 unit) of
Algebra I or its integrated equivalent (9th Grade), ten semester hours (1 unit) of
Geometry or its integrated equivalent (10th Grade), ten semester hours (1 unit) of
Algebra II or the integrated equivalent, and ten semester hours (1 unit) of higher
math from an approved course list are required. Except that the high school Algebra
requirement will be waived for a student who successfully completes one year of
algebra in middle school. However, such students will still be required to complete
forty semester hours (4 units) of mathematics in high school, including ten semester
hours (1 unit) of Geometry and 10 semester hours of Algebra II (1 unit). In no case,
will students receive high school credit for courses completed in middle school.
Response:
9th Grade:
Students will earn 1 unit of math based on the individual student’s Math placement.
Students will work at the level of Algebra I unless they have already demonstrated
mastery in Algebra I.
The DMHS High School Math Curriculum is composed of three elements. The first
element is subject lessons through Khan Academy. Khan Academy is an on-line
program that provides detailed lessons starting with addition and proceeding
through Calculus. Each subject area has extensive on-line lessons that fully cover the
identified subject. The second element is Exeter Math, which is the curriculum
delivered at Phillips Exeter Academy. Exeter Math is delivered via real-world
problem solving, seminar and group work. The third element is a highly qualified
Page 58
secondary Math teacher who will provide individualized assistance to students as
they progress through the Khan curricular map. The math teacher will also
participate in the Exeter groups providing group instruction as needed.
Credit will be awarded based on the following criteria: Students have completed a
full unit of study such as Algebra I. Students will have participated in an Exeter
study group for and average of no less than one hour per week. Students have
turned in a completed math album that shows evidence of work for each Khan unit
of study and their weekly Exeter group problem solving exercises.
Most students will already be placed on the Khan curriculum map from their DMHS
work in 8th grade. Students new to DMHS will take an on-line evaluative math
assessment (currently identified as the STAR Assessment but subject to change as
on-line assessments continue to evolve and improve) to determine placement on the
curriculum map. Students will work individually through the Khan curriculum map,
and they will have the opportunity to accelerate or remediate based on their success
level with placement.
10th, 11th and 12th
Over the three-year cycle, students will complete 3 units of math. Unless they have
already demonstrated mastery, studies will include Algebra II and Geometry and
continue through pre-calculus and calculus.
The DMHS High School Math Curriculum is composed of three elements. The first
element is subject lessons through Khan Academy. Khan Academy is an on-line
program that provides detailed lessons starting with addition and proceeding
through Calculus. Each subject area has extensive on-line lessons that fully cover the
identified subject. The second element is Exeter Math, which is the curriculum
delivered at Phillips Exeter Academy. Exeter Math is delivered via real-world
problem solving, seminar and group work. The third element is a highly qualified
secondary Math teacher who will provide individualized assistance to students as
they progress through the Khan curricular map. The math teacher will also
participate in the Exeter groups providing group instruction as needed.
Credit will be awarded based on the following criteria: Students have completed a
full unit of study such as Geometry. Students will have participated in an Exeter
study group for and average of no less than one hour per week. Students have
turned in a completed math album that shows evidence of work for each Khan unit
of study and their weekly Exeter group problem solving exercises.
Most students will already be placed on the Khan curriculum map from their
previous DMHS work. Students new to DMHS will take an on-line evaluative math
assessment (currently identified as the STAR Assessment but subject to change as
on-line assessments continue to evolve and improve) to determine placement on the
curriculum map. Students will have the opportunity to accelerate or remediate
based on their success level with placement. Advanced students will have the
Page 59
opportunity to take advanced trigonometry or calculus via on-line college or
university curriculum or through Metropolitan State University.
Requirement:
5. Physical Education/Dance, Citywide Marching Band, ROTC, or DPS Athletics
Ten semester hours (1 unit) of Physical Education or Dance shall be earned or an
equivalent shall exempt the student from this requirement. Equivalents shall
include: Citywide Marching Band, ROTC, DPS Athletics.
Athletic sports that are sanctioned by the Denver Public Schools Board of Education
and meet the criteria below may exempt a student from the physical education
graduation requirement. No grade or credit will be given for athletic participation
and such exemptions will not reduce the total number of hours required to earn a
diploma. Both semesters of the physical education requirement may be exempted
by athletic participation.
Criteria governing physical education exemptions:
a. The student must maintain academic eligibility for the entire season.
b. One full sport season is required to exempt a student from five semester hours (5
units) of P.E. requirement,
c. A student must be a high school freshman, sophomore, or junior to qualify for the
exemption. Seniors who have not yet met the physical education requirement are
not allowed to take this exemption and must enroll in a physical education course.
d. The waiver must be requested in the same semester that the sport s played.
(Rationale: this aligns the criteria of the Board policy and with the guidelines
provided on the Criteria for Athletic Exemption form that is located on page 23 of
the High School Procedures Guide. Provides clarification.)
d. The waiver must be requested in the same semester that the sport is played.
Response:
9th – 12th grade
DMHS students will be required to complete 1 unit of Physical Education / Dance,
Citywide Marching Band, ROTC, or DPS Athletics in compliance with requirement.
DMHS will have a competitive Ultimate Frisbee team that will include after-school
practices and games.
Requirement:
6. Electives: Ninety semester hours (9 units) shall be earned.
Academic Electives
Forty semester hours (4 units) shall be earned. Ten semester hours (1 unit) shall be
earned from an approved electives list. Another ten semester hours (1 unit) of fine
arts (Music, Art, Drama) or Career Technical Education (CTE) must be earned.
Page 60
Response:
9th Grade:
Ninth grade students will be required to take 1 unit of Spanish. Spanish will be
delivered via a highly qualified Spanish Teacher using the TPRS curriculum.
Students will also complete .5 units of art, drama or music.
10th, 11th, 12th
Students will be required to complete 1 unit of Spanish. Spanish will be delivered via
a highly qualified Spanish Teacher using the TPRS curriculum. Students will also
complete a minimum of .5 units of art, drama or music.
If a student elects not to continue foreign language instruction, they will be required
to complete 1 more unit of an academic elective in order to meet the 4 unit
requirement for academic electives.
Requirement:
Other Electives
Student must earn 50 semester hours of electives, of which 20 semester hours may
be community service and service learning.
Response:
DMHS will offer a variety of electives to insure students have the opportunity to
meet this graduation requirement. Electives will include drama, art, music, Ultimate
Frisbee, Social Justice, cooking, craft work, and Micro-economy.
Requirement:
Community-Based experienceWithin the 240 semester hours (24 units) required for a diploma, a minimum of 220
semester hours (22 units) shall be earned in classroom-based instruction. Students
may, therefore, earn and apply a maximum of twenty semester hours (2 units) of
community service and/or service learning experience, approved by the school,
toward graduation requirements. These experiences may include, but are not
limited to, field or service experiences, work experiences, volunteering with
community organizations, and internships.
Response:
9th Grade:
Students may have the opportunity to apply for a community service opportunity.
Credit will be awarded based on the number of semester hours worked. Twenty
completed hours worked will be equal to a .5 unit of Community Service.
Page 61
10th, 11th and 12th Grade:
Students will be required to participate in either a Community Service or Service
Learning experience for a minimum of two hours per academic week. The schedule
is designed to allow students to complete this requirement on Wednesday
afternoons. Students may elect to complete their service during other hours in the
week with advisor approval.
Requirement:
General Course of Study Additional Information
At least four years (eight semesters) of attendance is required for students to
complete grades 9, 10, 11, and 12 except that:
* students with a 3.0 GPA who have completed all core curriculum/elective
requirements and 240 credit hours (24 units) and all required assessments may
graduate in seven semesters
* students with a 3.5 GPA who have completed all core curriculum/elective
requirements and 240 credit hours (24 units) and all required assessments may
graduate in six semesters.
* students with an Individual Education Program who are working towards a
general course of study may earn up to 40 semester hours (4 units) in Special
Education modified classes in only one core subject area. In addition, they may earn
up to twenty semester hours (2 units) of Special Education modified credit in world
language classes.
Achieving Personal Excellence (APEX) Requirements COURSE OF STUDY
Provided that the high school has approval by the Superintendent or his designee,
students will be awarded an ASCENT diploma if they meet all of the requirements in
one through five in the general course of study, earn 35 hours of elective credit, and
meet the requirements to earn an Associate of Arts (A.A.), Associate of Science (A.S.),
or Associate of Applied Science (A.A.S.) Degree from a community college or a
certificate of career and technical education.
Combined General Course of Study
The combined General Course of Study requirements are the same as those for the
General Course of Study, except that students with an Individual Education Program
may earn up to 140 semester hours (14 units) in Special Education modified courses
in the core subject areas and world language classes.
Two hundred and forty semester hours (24 units) will be required in grades 9, 10,
11, and 12, and/or through the first semester in which the student's twenty-first
(21st) birthday falls, from courses approved by the school principal and determined
by the staffing team. Transcripts will reflect differences in program content. The
content areas and work study requirements are as listed below. Numbers of units
are stated as minimums:
1. Language Arts 3.0 Units
Page 62
2. Social Studies 2.0 Units
3. Science 1.0 Unit
4. Mathematics 2.0 Units
5. Physical Education/ Dance, Citywide Marching Band, or ROTC 1.0 Unit (unless
otherwise specified by IEP)
6. Electives
1.0 Unit in vocations and/or Transition Classes - Required
8.0 Units (may include work experience)
7. Work Experience and Study 6.0 Units of work experience earned in Special
Education-coordinated work experience. Vocations/Transitions course must be
taken and passed as a prerequisite or in conjunction with work experience/study
1. Language Arts 3.0 Units
2. Social Studies 2.0 Units
3. Science 1.0 Unit
4. Mathematics 2.0 Units
5. Physical Education/ Dance, Citywide Marching Band, or ROTC 1.0 Unit (unless
otherwise specified by IEP)
6. Electives 1.0 Unit in vocations and/or Transition Classes - Required
8.0 Units (may include work experience)
7. Work Experience and Study 6.0 Units of work experience earned in Special
Education-coordinated work experience. Vocations/Transitions course must be
taken and passed as a prerequisite or in conjunction with work experience/study
Designated Course of Study Requirements:
The designated course of study will substitute for the curriculum/content standard
approved by the Board of Education. In making determinations for earning a
diploma, assessment instruments will be selected and administered so as to best
ensure that when an assessment is administered to a student with impaired
sensory, manual, or speaking skills, the test results accurately reflect the student's
aptitude or achievement level rather than reflecting the student's impaired sensory,
manual, or speaking skills.
1. Students with severe and profound disabling conditions that interfere with their
ability to meet the requirements for either of the above courses of study and have
satisfied the requirements of an Individualized Education Program shall graduate
with a high school diploma.
2. Students may attend school in grades 9, 10, 11, and 12, and/or through the
semester in which the student's twenty-first (21st) birthday falls, as determined by
the IEP.
Transfer Students
A transfer student from outside the Denver Public Schools must meet the
requirements to receive a diploma from the Denver Public Schools. All graduation
requirements must be met prior to graduation, including attendance in the Denver
Public Schools for at least two semesters, with a minimum of 50 semester hours (5
units) of credit earned.
Page 63
Certificate of Attendance
Students who attend school regularly but do not meet the course of study
requirements in any of the three courses of study areas may be awarded a
Certificate of Attendance.
Response:
DMHS agrees with these requirements.
Page 64
Denver Montessori Junior/Senior High School: Grades 6 - 8 Math Curriculum Alignment to the Common Core State Standards
Credit
CCSS
CCSS Category
CCSS Sub-Category
Khan Academy Work - Videos:
6th Grade Math
6.EE.1
Expressions and
Equations
Write and evaluate numerical expressions
involving whole-number exponents.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Dividing Monomials
Dividing polynomials 1
Dividing polynomials with remainders
Evaluating exponential expressions
Evaluating exponential expressions 2
Exponent Properties 1
Exponent Properties 2
Exponent Properties 3
...and 16 more ...
Dividing real numbers with different signs
Equation Special Cases
Evaluating an expression with multiple variables
Evaluating exponential expressions 2
Multi-step equations 1
Multi-step equations 2
Multiplying real number application
Simplifying Expressions with Exponents
...and 5 more ...
Khan Academy Work - Exercises:
• Exponent rules
• Positive and zero exponents
• Dividing Monomials
MM: Algebra, Bead Chains, Base work
(e.g. Base 2, Base 9), Binomial/Trinomial
Cubes, Command Cards
• Evaluating expressions in 2 variables
• Evaluating expressions in one variable
• Writing expressions
MM: Algebra, Fact Families, Algebraic
Decanomial, Story of the Kings, Cubing
Materials, Colored Counting Bars,
Binomial Squares and Trinomial Squares,
Bead Cabinet, Bead Bars
• Writing expressions
MM: Algebra
6th Grade Math
6.EE.2
Expressions and
Equations
Write, read, and evaluate expressions in
which letters stand for numbers.
6th Grade Math
6.EE.2.a
Expressions and
Equations
Apply and extend previous understandings
of arithmetic to algebraic expressions
Expressions and
Equations
• Terms coefficients and exponents in a polynomial • Writing expressions
Identify parts of an expression using
mathematical terms (sum, term, product,
factor, quotient, coefficient); view one or
more parts of an expression as a single
entity. For example, describe the expression
2 (8 + 7) as a product of two factors; view
(8 + 7) as both a single entity and a sum of
two terms.
6th Grade Math
6th Grade Math
6.EE.2.b
6.EE.2.c
Expressions and
Equations
Evaluate expressions at specific values of
their variables. Include expressions that
arise from formulas used in real-world
problems. Perform arithmetic operations,
including those involving whole-number
exponents, in the conventional order when
there are no parentheses to specify a
particular order (Order of Operations). For
example, use the formulas V = s3 and A = 6
s2 to find the volume and surface area of a
cube with sides of length s = 1/2.
Occupations Work: 6,7,8 /
Montessori Materials
• Application problems with equation in one
variable
• Applying Radical Equations 2
• Evaluating expressions in one variable
• Evaluating expressions in 2 variables
• Direct Variation Application
• Properties of numbers 2
• Dividing Monomials
• Solving equations in terms of a variable
• Dividing polynomials 1
• Writing expressions
• Dividing polynomials with remainders
• Writing expressions 2
MM: Algebra, Fact Families, Algebraic
Decanomial, Story of the Kings, Cubing
Materials, Colored Counting Bars,
Binomial Squares and Trinomial Squares,
Bead Cabinet, Bead Bars.
MM: Algebra, Fact Families, Algebraic
Decanomial, Story of the Kings, Cubing
Materials, Colored Counting Bars,
Binomial Squares and Trinomial Squares,
Bead Cabinet, Bead Bars.
• Dividing real numbers with different signs
• Evaluate a formula using substitution
• ...and 43 more ...
Apply the properties of operations to
• Equation Special Cases
• Combining like terms with distribution
• Fractional Exponent Expressions 1
• Distributive property
MM: Algebra, Fact Families, Algebraic
Decanomial, Story of the Kings, Cubing
Materials, Colored Counting Bars,
Page 65
6th Grade Math
6.EE.3
Expressions and
Equations
generate equivalent expressions. For
example, apply the distributive property to
the expression 3 (2 + x) to produce the
equivalent expression 6 + 3x; apply the
distributive property to the expression 24x
+ 18y to produce the equivalent expression
6 (4x + 3y); apply properties of operations
to y + y + y to produce the equivalent
expression 3y.
• Fractional Exponent Expressions 2
• Distributive property with variables
• Fractional Exponent Expressions 3
• Expressions with unknown variables
• Inductive Reasoning 3
• Writing expressions 2
Binomial Squares and Trinomial Squares,
Bead Cabinet, Bead Bars.
• Multi-step equations 2
• Solving Equations with the Distributive Property
• The Distributive Property
• ...and 1 more ...
6th Grade Math
6th Grade Math
6th Grade Math
6th Grade Math
6th Grade Math
6.EE.4
6.EE.5
6.EE.6
6.EE.7
6.EE.8
Constructive Triangles, Geometric Insets
Cabinet, Pattern Blocks, Bead Bars,
Golden Beads, Decanomial
Expressions and
Equations
Identify when two expressions are
equivalent (i.e., when the two expressions
name the same number regardless of which
value is substituted into them). For
example, the expressions y + y + y and 3y
are equivalent because they name the same
number regardless of which number y
stands for.
Expressions and
Equations
• Algebra: Solving Inequalities
• Algebraic Word Problem
• Equation Special Cases
• Equations of Sequence Patterns
• Graphing Inequalities
• Graphing Inequalities 2
• Simple Equations
• Solving systems by substitution 1
• ...and 3 more ...
• Algebraic Word Problem
• Application problems with equation in one
variable
Use variables to represent numbers and
write expressions when solving a real-world • Averages
or mathematical problem; understand that a • Equations of Sequence Patterns
variable can represent an unknown number, • Evaluate a formula using substitution
or, depending on the purpose at hand, any • Example of Solving for a Variable
number in a specified set.
• Extraneous Solutions to Rational Equations
• Multiplying real number application
• ...and 6 more ...
• Multiplying and Dividing Monomials 1
Solve real-world and mathematical
problems by writing and solving equations
of the form x + p = q and px = q for cases in • Multiplying and Dividing Monomials 2
which p, q and x are all nonnegative
rational numbers.
• Multiplying and Dividing Monomials 3
• Absolute Inequalities 2
Write an inequality of the form x > c or x < • Absolute Value Inequalities
c to represent a constraint or condition in a • Absolute value inequalities example 3
• Algebra: Solving Inequalities
real-world or mathematical problem.
Recognize that inequalities of the form x > • Compound Inequalities 3
c or x < c have infinitely many solutions;
• Compound Inequalities 4
represent solutions of such inequalities on • Compund Inequalities
number line diagrams.
• Compund Inequalities 2
• ...and 14 more ...
• Deductive Reasoning 1
Use variables to represent two quantities in
Occupations Unit 1 and 2
Understand solving an equation or
inequality as a process of answering a
question: which values from a specified set,
if any, make the equation or inequality
true? Use substitution to determine whether
a given number in a specified set makes an
equation or inequality true.
Expressions and
Equations
Expressions and
Equations
Expressions and
Equations
• Midpoint of a segment
• Writing expressions
Occupations Unit 1 and 2
• Addition and subtraction word problems
MM: Word Problems, Occupations Unit 1
and 2
• Multiplication and division word
problems 2
• Inequalities on a number line
Occupations Unit 1 and 2
• Identifying linear relationships
Occupations Unit 1 and 2
Page 66
6th Grade Math
6th Grade Math
6th Grade Math
6th Grade Math
6.EE.9
6.G.1
6.G.2
6.G.3
6th Grade Math
6.G.4
6th Grade Math
6.RP.1
6th Grade Math
6.RP.2
Expressions and
Equations
a real-world problem that change in
relationship to one another; write an
equation to express one quantity, thought of
as the dependent variable, in terms of the
other quantity, thought of as the
independent variable. Analyze the
relationship between the dependent and
independent variables using graphs and
tables, and relate these to the equation. For
example, in a problem involving motion at
constant speed, list and graph ordered pairs
of distances and times, and write the
equation d = 65t to represent the
relationship between distance and time.
Geometry
Find the area of right triangles, other
triangles, special quadrilaterals, and
polygons by composing into rectangles or
decomposing into triangles and other
shapes; apply these techniques in the
context of solving real-world and
mathematical problems.
Geometry
Find the volume of a right rectangular prism
with fractional edge lengths by packing it
with unit cubes of the appropriate unit
fraction edge lengths, and show that
the volume is the same as would be found
by multiplying the edge lengths of the
prism. Apply the formulas V = l w h and V
= b h to find volumes of right rectangular
prisms with fractional edge lengths in the
context of solving real-world and
mathematical problems.
Geometry
Draw polygons in the coordinate plane given
coordinates for the vertices; use coordinates
to find the length of a side joining points
with the same first coordinate or the same
second coordinate. Apply these techniques
in the context of solving real- world and
mathematical problems.
• Direct Inverse and Joint Variation
• Reading line charts 1
• Direct Variation Application
• Reading tables 1
• Evaluate a formula using substitution
• Reading tables 2
• Inverse Variation Application
• Multiplying real number application
• Proportionality Constant for Direct Variation
• Solving systems by graphing
• ...and 1 more ...
• Area and Perimeter
• Area of Diagonal Generated Triangles of
Rectangle are Equal
• Heron's Formula
• Rearrange formulas to isolate specific variables
• Rhombus Diagonals
• Area of parallelograms
• Area of squares and rectangles
•
•
•
•
•
Area of trapezoids, rhombi, and kites
Geometry 1
Heron's formula
Perimeter of squares and rectangles
Solid geometry
• The Coordinate Plane
Represent three-dimensional figures using •
nets made up of rectangles and triangles,
and use the nets to find the surface area of
Geometry
these figures. Apply these techniques in the
context of solving real-world and
mathematical problems.
•
Ratios and Proportional Understand ratio concepts and use ratio
•
Relationships
reasoning to solve problems
•
•
Ratios and Proportional Understand ratio concepts and use ratio
•
Relationships
reasoning to solve problems
•
•
Occupations Unit 1/ MM: Geometry:
Geometric Insets, Yellow Area Materials,
Stick Box
MM: Geometry: Volume Cubes, Volume
Containers, Five Yellow Prisms
Occupations Unit 1
Applying Radical Equations 2
MM: Geometry: Geometric Solids,
Volume Boxes.
Introduction to Ratios (new HD version)
Ratios as Fractions in Simplest Form
Simplifying Rates and Ratios
Finding Unit Prices
Finding Unit Rates
Introduction to Ratios (new HD version)
Another Take on the Rate Problem
MM: Ratio and Proportion
• Expressing ratios as fractions
MM: Ratio and Proportion. Occupations
Unit 2
MM: Ratio and Proportion. Occupations
Page 67
6th Grade Math
6th Grade Math
6th Grade Math
6th Grade Math
6.RP.3
Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by
Ratios and Proportional
reasoning about tables of equivalent ratios,
Relationships
tape diagrams, double number line
diagrams, or equations.
6.RP.3.a
Make tables of equivalent ratios relating
quantities with whole-number
Ratios and Proportional measurements, find missing values in the
Relationships
tables, and plot the pairs of values on the
coordinate plane. Use tables to compare
ratios.
6.RP.3.b
Solve unit rate problems including those
involving unit pricing and constant speed.
Ratios and Proportional For example, if it took 7 hours to mow 4
Relationships
lawns, then at that rate, how many lawns
could be mowed in 35 hours? At what rate
were lawns being mowed?
6.RP.3.c
6th Grade Math
6.RP.3.d
6th Grade Math
6.SP.1
6th Grade Math
6th Grade Math
6.SP.2
6.SP.3
Find a percent of a quantity as a rate per
100 (e.g., 30% of a quantity means 30/100
Ratios and Proportional
times the quantity); solve problems
Relationships
involving finding the whole, given a part
and the percent.
•
•
•
•
•
•
•
•
Unit 2
Finding Unit Prices
Finding Unit Rates
Introduction to Ratios
Rate Problem Involving Rational Equations
Ratio and Proportion
Scale and Indirect Measurement
Systems and rate problems
...and 1 more ...
MM: Ratio and Proportion. Occupations
Unit 2
• Another Take on the Rate Problem
• Rate problems 0.5
• Rate Problem Involving Rational Equations
• Rate problems 1
• Systems and rate problems
• Ratio word problems
MM: Word Problems, Ratio and
Proportion. Occupations Unit 2
• Systems and rate problems 2
• Systems and rate problems 3
•
•
•
•
Describing the Meaning of Percent
Describing the Meaning of Percent 2
Percent and decimals
Percent Problems
• Solving Percent Problems 2
• Solving Percent Problems 3
• Taking percentages
• Adding different units for weight
• Application problems involving units of weight
• Comparing Celsius and Farenheit temperature
Use ratio reasoning to convert measurement scales
• Conversion between metric units
Ratios and Proportional units; manipulate and transform units
Relationships
appropriately when multiplying or dividing • Converting Farenheit to Celsius
quantities.
• Converting Gallons to quarts pints and cups
• Converting pounds to ounces
• Converting units of length
• ...and 4 more ...
• Statistics: The Average
Develop understanding of statistical
Statistics and
variability
Probability
• Average or Central Tendency: Arithmetic Mean,
Median, and Mode
Understand that a set of data collected to
• Central Limit Theorem
answer a statistical question has a
Statistics and
• Sampling Distribution of the Sample Mean
distribution which can be described by its
Probability
• Sampling Distribution of the Sample Mean 2
center, spread, and overall shape.
• Standard Error of the Mean
• Statistics: The Average
• Average or Central Tendency: Arithmetic Mean,
Median, and Mode
Recognize that a measure of center for a
• Statistics: Alternate Variance Formulas
numerical data set summarizes all of its
Statistics and
values with a single number, while a
• Statistics: Sample Variance
Probability
measure of variation describes how its
• Statistics: Sample vs. Population Mean
•
•
•
•
Converting decimals to percents
Converting percents to decimals
Discount tax and tip word problems
Markup and commission word problems
MM: Centesimal Protractor, Fraction
Circles, Geometric Cabinet, Word
Problems. Occupations Unit 2.
MM: Ratio and Proportion, Word
Problems. Occupations Unit 2
Integrated Humanities: Population Study
• Exploring standard deviation 1
Integrated Humanities: Population Study,
Occupations Unit 2: Yield
• Mean median and mode
Integrated Humanities: Population Study,
Occupations Unit 2: Yield
Page 68
values vary with a single number.
6th Grade Math
6.SP.4
Statistics and
Probability
Display numerical data in plots on a
number line, including dot plots,
histograms, and box plots.
6th Grade Math
6.SP.5
Statistics and
Probability
Summarize numerical data sets in relation
to their context, such as by:
6th Grade Math
6.SP.5.a
Statistics and
Probability
Reporting the number of observations.
6th Grade Math
6.SP.5.b
Statistics and
Probability
6th Grade Math
6th Grade Math
6.SP.5.c
6.SP.5.d
Statistics and
Probability
Statistics and
Probability
•
•
•
•
•
•
•
•
•
•
•
•
Statistics: The Average
Statistics: Variance of a Population
Box-and-whisker Plot
Central Limit Theorem
Histograms
Sampling Distribution of the Sample Mean
Sampling Distribution of the Sample Mean 2
Standard Error of the Mean
Statistics: Alternate Variance Formulas
Statistics: Sample Variance
...and 1 more ...
•
•
•
•
•
Creating bar charts 1
Reading bar charts 1
Reading bar charts 2
Reading bar charts 3
Reading stem and leaf plots
• Mean median and mode
• Central Limit Theorem
• Mean median and mode
• Statistics: Sample Variance
• Statistics: Standard Deviation
• Mean median and mode
Describing the nature of the attribute under •
investigation, including how it was
measured and its units of measurement.
• Average or Central Tendency: Arithmetic Mean, • Mean median and mode
Median, and Mode
• Central Limit Theorem
• ck12.org Exercise: Standard Normal Distribution
and the Empirical Rule
Giving quantitative measures of center
• ck12.org Normal Distribution Problems:
(median and/or mean) and variability
Empirical Rule
(interquartile range and/or mean absolute
deviation), as well as describing any overall • ck12.org Normal Distribution Problems:
pattern and any striking deviations from the Qualitative sense of normal distributions
overall pattern with reference to the context • ck12.org Normal Distribution Problems: z-score
in which the data were gathered.
Relating the choice of measures of center
and variability to the shape of the data
distribution and the context in which the
data were gathered.
6th Grade Math
6.NS.1
The Number System
Apply and extend previous understandings
of multiplication and division to divide
fractions by fractions
6th Grade Math
6.NS.2
The Number System
Fluently divide multi-digit numbers using
the standard algorithm
• ck12.org: More Empirical Rule and Z-score
practice
• Law of Large Numbers
• ...and 8 more ...
• Mean median and mode
• Central Limit Theorem
• ck12.org Exercise: Standard Normal Distribution
and the Empirical Rule
• ck12.org Normal Distribution Problems:
Empirical Rule
• ck12.org Normal Distribution Problems:
Qualitative sense of normal distributions
• ck12.org Normal Distribution Problems: z-score
•
•
•
•
•
•
•
•
•
Introduction to the Normal Distribution
Normal Distribution Excel Exercise
Sampling Distribution of the Sample Mean
...and 2 more ...
Dividing fractions
Dividing Mixed Numbers
Dividing Mixed Numbers and Fractions
Reciprocal of a Mixed Number
Level 4 division
• Dividing fractions
• Dividing fractions 0.5
• Dividing fractions word problems
Integrated Humanities: Population Study,
Occupations Unit 2: Yield, MM: Graphs
and Charts
•
Occupations Unit 2: Yield
Occupations Unit 2: Yield
Integrated Humanities: Population Study,
Occupations Unit 2: Yield, MM: Graphs
and Charts
Integrated Humanities: Population Study,
Occupations Unit 2: Yield, MM: Graphs
and Charts
MM: Fraction Circles, Fraction Operation
Boards, Fraction Skittles
• Addition and subtraction word problems MM: Racks and Tubes, Division Boards
Page 69
6th Grade Math
6th Grade Math
6th Grade Math
6.NS.3
6.NS.4
6.NS.5
The Number System
The Number System
The Number System
6th Grade Math
6.NS.6
The Number System
6th Grade Math
6.NS.6.a
The Number System
6th Grade Math
6.NS.6.b
The Number System
6th Grade Math
6th Grade Math
6.NS.6.c
6.NS.7
The Number System
The Number System
•
•
•
Fluently add, subtract, multiply, and divide •
multi-digit decimals using the standard
•
algorithm for each operation.
•
•
•
•
•
•
•
Compute fluently with multi-digit numbers •
•
and find common factors and multiples
•
•
•
•
Understand that positive and negative
numbers are used together to describe
quantities having opposite directions or
values (e.g., temperature above/below zero, •
elevation above/below sea level,
credits/debits, positive/negative electric
charge); use positive and negative numbers
to represent quantities in real-world
contexts, explaining the mean of 0 in each
situation.
Understand a rational number as a point on
the number line. Extend number line
diagrams and coordinate axes familiar from
previous grades to represent points on the
line and in the plane with negative number
coordinates.
Apply and extend previous understandings
of numbers to the system of rational
n
Uunm
debresrtsand signs of numbers in ordered
pairs as indicating locations in quadrants of
the coordinate plane; recognize that when
Adding Decimals
Dividing decimal
Dividing Decimals
Dividing Decimals 2.1
Dividing real numbers with different signs
Dividing Whole Numbers and Applications 1
Dividing Whole Numbers and Applications 2
Dividing Whole Numbers and Applications 3
...and 11 more ...
Comparing Fractions
Comparing Fractions 2
Finding Factors of a Number
Fractions in lowest terms
Greatest Common Divisor
Least Common Multiple
The Distributive Property
The Distributive Property 2
Negative Numbers Introduction
Opposite of a given number
•
•
•
Find and position integers and other
rational numbers on a horizontal or vertical •
number line diagram; find and position
•
pairs of integers and other rational numbers •
on a coordinate plane.
•
•
•
•
•
Understand ordering and absolute value of •
rational numbers.
•
Multi-digit division
4-digit addition with carrying
4-digit subtraction with borrowing
Adding decimals 2
Dividing decimals
Multi-digit division
Multi-digit multiplication
Multiplying decimals
Subtracting decimals
• Divisibility
• Divisibility 0.5
• Divisibility tests
• Greatest common divisor
• LCM and GCD word problems
• Least common multiple
• Prime numbers
• The fundamental theorem of arithmetic
• Adding and subtracting negative
numbers
MM: Yellow Decimal Board, Decimal
Checkerboard, Decimal Checkerboard
Squares, Centesimal Protractor
MM: Peg Board, Sieve of Erathostenes,
Factor Trees.
MM: Positive/Negative Snake Game,
Number Line, Temperature Measurement
• Adding negative numbers
• Negative number word problems
• Integers and Rational Numbers
• Number Sets
• Number Sets 1
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Number Sets 2
Number Sets 3
Points on a number line
Quadrants of Coordinate Plane
Integers and Rational Numbers
Opposite of a given number
Quadrants of Coordinate Plane
Absolute Value Inequalities
Compound Inequalities 3
Compound Inequalities 4
Compund Inequalities
Compund Inequalities 2
Inequalities on a number line
Integers and Rational Numbers
Locate integers on a number line
...and 11 more ...
Absolute Value 1
Absolute Value and Number Lines
Absolute Value of Integers
Application of addition of real numbers
• Number line 2
• Points lines and planes
MM: Negative Snake Game, World
Problems, Graphing
• Ordering negative numbers
MM: Number Lines, Graphing
• Graphing points
• Points on the coordinate plane
• Ordering negative numbers
MM: Graphing
• Comparing absolute values
• Finding absolute values
• Ordering numbers
MM: Graphing
MM: Number Line, Graphing
Page 70
6th Grade Math
6.NS.7.a
The Number System
Apply and extend previous understandings
of numbers to the system of rational
numbers
6th Grade Math
6.NS.7.b
The Number System
Apply and extend previous understandings
of numbers to the system of rational
numbers
6th Grade Math
6.NS.7.c
The Number System
Apply and extend previous understandings
of numbers to the system of rational
numbers
6th Grade Math
6.NS.7.d
The Number System
Apply and extend previous understandings
of numbers to the system of rational
numbers
Solve real-world and mathematical
problems by graphing points in all four
quadrants of the coordinate plane. Include
use of coordinates and absolute value to
find distances between points with the same
first coordinate or the same second
coordinate.
6th Grade Math
6.NS.8
The Number System
Credit
CCSS
CCSS Category
7th Grade Math
7th Grade Math
7th Grade Math
7.EE.1
Expressions and
Equations
7.EE.2
Expressions and
Equations
7.EE.3
Expressions and
Equations
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
CCSS Sub-Category
• Comparing absolute values
• Finding absolute values
• Inequalities on a number line
MM: Number Line, Graphing
•
•
•
•
•
•
•
Comparing absolute values
Finding absolute values
Ordering numbers
Comparing absolute values
Finding absolute values
Ordering negative numbers
Ordering numbers
MM: Number Line, Graphing. Occupations
1: GIS Mapping.
•
•
•
•
Comparing absolute values
Finding absolute values
Ordering numbers
Graphing points
MM: Number Line, Graphing. Occupations
1: GIS Mapping.
Khan Academy Work - Videos:
•
•
•
Apply properties of operations as strategies •
to add, subtract, factor, and expand linear
•
expressions with rational coefficients.
Ordering Numeric Expressions
Absolute Inequalities 2
Absolute Value and Number Lines
Absolute Value Inequalities
Absolute value inequalities example 3
Compound Inequalities 3
Compound Inequalities 4
Compund Inequalities
Compund Inequalities 2
...and 7 more ...
Absolute Value and Number Lines
Negative Numbers Introduction
Ordering Numeric Expressions
Absolute Inequalities 2
Absolute Value 1
Absolute Value and Number Lines
Absolute Value Equation Example 2
Absolute Value Equations
Absolute Value Equations 1
Absolute Value Inequalities
Absolute value inequalities example 3
...and 3 more ...
Absolute Value Inequalities
•
•
•
•
•
Khan Academy Work - Exercises:
Algebra: Linear Equations 4
Equations 2
Equations 3
Multiplying Monomials
•
•
•
•
Multiplying Monomials by Polynomials
• One-step equations with mult
Opposite of a Polynomial
Simple Equations
The Distributive Property
...and 1 more ...
Growing by a percentage
Combining like terms
Expressions with unknown variables
One step equations
One step equations 0.5
• Writing expressions 2
Use properties of operations to generate
equivalent expressions
Solve multi-step real-life and mathematical
• Basic Rate Problem
•
problems posed with positive and negative
• Representing a number as a decimal, percent, and
rational numbers in any form (whole
fraction
numbers fractions and decimals) using
MM: Number Line, Graphing. Occupations
1: GIS Mapping.
Occupations 1: GIS Mapping, Occupations
2: Yield, Integrated Humanities 1:
Population Study
Occupations Work: 6,7,8 /
Montessori Materials
MM: Algebra, Fact Families, Algebraic
Decanomial, Story of the Kings, Cubing
Materials, Colored Counting Bars,
Binomial Squares and Trinomial Squares,
Bead Cabinet, Bead Bars,
MM: Algebra
MM: Word Problems, Occupations Unit 1
and 2
Page 71
7th Grade Math
7th Grade Math
7th Grade Math
7.EE.4
7.EE.4.a
7.EE.4.b
• Representing a number as a decimal, percent, and
tools strategically. Apply properties of
fraction 2
operations to calculate with numbers in any
• Absolute Value Inequalities
• Application problems with equation in one
variable
Use variables to represent quantities in a
• Compound Inequalities 3
real-world or mathematical problem, and
• Compound Inequalities 4
construct simple equations and inequalities
• Compund Inequalities
to solve problems by reasoning about the
• Compund Inequalities 2
quantities.
• Equations and Inequalities
• Evaluate a formula using substitution
• ...and 18 more ...
Solve word problems leading to equations • Algebraic Word Problem
• Application problems with equation in one
of the form px + q = r and p(x + q) = r,
variable
where p, q, and r are specific rational
• Converting within the metric system
numbers. Solve equations of these forms
fluently. Compare an algebraic solution to • Equations 2
an arithmetic solution, identifying the
• Equations 3
sequence of the operations used in each
• Example of Solving for a Variable
approach. For example, the perimeter of a • Extraneous Solutions to Rational Equations
rectangle is 54 cm. Its length is 6 cm. What • Multiplying and Dividing Monomials 1
is its width?
• ...and 7 more ...
• Absolute Value Inequalities
•
MM: Word Problems, Occupations Unit 1
and 2
• Age word problems
• Reading tables 2
MM: Algebra, Word Problems,
Occupations Unit 1 and 2
•
MM: Algebra, Word Problems,
Occupations Unit 1 and 2
•
Geometry
Solve problems involving scale drawings of • Polynomials1
geometric figures, including computing
actual lengths and areas from a scale
drawing and reproducing a scale drawing at
a different scale.
MM: Geometry, Solids, Area of Plane
Figures, Geometric Construction.
Occupations Unit 1.
• Congruency postulates
Geometry
Draw (freehand, with ruler and protractor, •
and with technology) geometric shapes with
given conditions. Focus on constructing
triangles from three measures of angles or
sides, noticing when the conditions
determine a unique triangle, more than one
triangle, or no triangle.
MM: Geometry, Solids, Area of Plane
Figures, Geometric Construction,
Constructive Triangles, Occupations Unit
1.
Expressions and
Equations
Expressions and
Equations
Expressions and
Equations
Solve word problems leading to inequalities
of the form px + q > r or px + q < r, where
p, q, and r are specific rational numbers.
Graph the solution set of the inequality and
interpret it in the context of the problem.
For example: As a salesperson, you are paid
$50 per week plus $3 per sale. This week
you want your pay to be at least $100.
Write an inequality for the number of sales
you need to make, and describe the
solutions.
• Algebra: Solving Inequalities
• Compound Inequalities 3
• Compound Inequalities 4
• Compund Inequalities
• Compund Inequalities 2
• Graphing linear inequalities in two variables 2
• Inequalities
• ...and 6 more ...
Geometry
7th Grade Math
7th Grade Math
7.G.1
7.G.2
Page 72
7th Grade Math
7th Grade Math
7.G.3
7.G.4
Geometry
Geometry
Describe the two-dimensional figures that
result from slicing three-dimensional
figures, as in plane sections of right
rectangular prisms and right rectangular
pyramids.
• Applying Radical Equations 3
• Area of a circle
Know the formulas for the area and
• Circles: Radius, Diameter and Circumference
circumference of a circle and use them to
• Polynomials1
solve problems; give an informal derivation
of the relationship between the
circumference and area of a circle.
•
•
•
•
•
7th Grade Math
7.G.5
7th Grade Math
7.G.6
7th Grade Math
7.RP.1
7th Grade Math
7th Grade Math
7.RP.2
7.RP.2.a
Geometry
Geometry
Angle Game (part 2)
Angles (part 2)
Similar triangles
Similar triangles (part 2)
The Angle Game
Use facts about supplementary,
complementary, vertical, and adjacent
angles in a multi-step problem to write and
solve simple equations for an unknown
angle in a figure.
Solve real-world and mathematical
problems involving area, volume and
surface area of two- and three-dimensional
objects composed of triangles,
quadrilaterals, polygons, cubes, and right
prisms.
• 2003 AIME II Problem 7
• Heron's Formula
• Performing arithmetic calculations on units of
volume
• Polynomials1
• Simplifying Expressions with Exponents 3
• Solid Geometry Volume
• Solving application problems involving units of
volume
• Solving Quadratic Equations by Factoring 3
Compute unit rates associated with ratios of
Ratios and Proportional
• Basic Rate Problem
fractions, including ratios of lengths, areas
Relationships
• Systems and rate problems
and other quantities measured in like or
• Find an Unknown in a Proportion
• Find an Unknown in a Proportion 2
• Mixture problems 1
Ratios and Proportional Recognize and represent proportional
• Mixture problems 2
Relationships
relationships between quantities.
• Mixture problems 3
• Proportionality
• Understanding Proportions
• Understanding Proportions
Decide whether two quantities are in a
proportional relationship, e.g., by testing for
Ratios and Proportional
equivalent ratios in a table or graphing on a
Relationships
coordinate plane and observing whether the
graph is a straight line through the origin.
•
MM: Geometry, Solids, Area of Plane
Figures, Geometric Construction,
• Area of a circle
• Areas of circles and sectors
• Circles and arcs
• Geometry 1
• Radius diameter and circumference
• Shaded areas
• Alternate exterior angles 2
• Alternate interior angles
• Alternate interior angles 2
• Angle addition postulate
• Angles 1
• Angles of a polygon
• Complementary and supplementary
angles
• Complementary angles
• Congruent angles
• Corresponding angles 2
• Exploring angle pairs
• Parallel lines 2
• Supplementary angles
• Vertical angles 2
• Heron's formula
MM: Geometry, The Circle, Area of a
Circle, Circumference of a Circle.
• Units
• Proportions 1
• Proportions 2
MM: Ratio and Proportion, Word
Problems. Occupations Unit 1 and 2.
MM: Ratio and Proportion, Word
Problems, Occupations Unit 1 and 2.
• Graphing points and naming quadrants
MM: Ratio and Proportion. Graphing.
MM: Geometry, Angles, Variety of
Angles, Measurement of an Angle, Adding
and Subtracting Angles using the
Montessori Protractor.
MM: Geometry: Solids, Volume, Volume
Cubes, Triangles, Constructive Triangles,
Geometric Plates. Occupations Unit 1 and
2.
• Proportions 1
• Proportions 2
Page 73
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7.RP.2.b
7.RP.2.c
7.RP.2.d
7.RP.3
7.SP.1
7.SP.2
• Finding Unit Rates
Identify the constant of proportionality (unit
• Mixture problems 1
Ratios and Proportional rate) in tables, graphs, equations, diagrams,
• Mixture problems 2
Relationships
and verbal descriptions of proportional
• Mixture problems 3
relationships.
• Proportionality
• Age word problems 1
Represent proportional relationships by
• Age word problems 2
equations. For example, if total cost t is
• Age word problems 3
Ratios and Proportional proportional to the number n of items
Relationships
purchased at a constant price p, the
• Mixture problems 1
relationship between the total cost and the • Mixture problems 2
number of items can be expressed as t = pn. • Mixture problems 3
Explain what a point (x, y) on the graph of •
a proportional relationship means in terms
Ratios and Proportional
of the situation, with special attention to the
Relationships
points (0, 0) and (1, r) where r is the unit
rate.
• Advanced ratio problems
• Alternate Solution to Ratio Problem (HD
Version)
Use proportional relationships to solve
• Another Percent Word Problem
multistep ratio and percent problems.
Ratios and Proportional Examples: simple interest, tax, markups and • Growing by a percentage
Relationships
markdowns, gratuities and commissions,
• Introduction to interest
fees, percent increase and decrease, percent • Mixture problems 1
error.
• Mixture problems 2
• Mixture problems 3
• ...and 5 more ...
Statistics and
Probability
Statistics and
Probability
•
MM: Ratio and Proportion. Graphing.
•
MM: Ratio and Proportion. Occupations
Unit 2.
•
MM: Ratio and Proportion. Occupations
Unit 2.
• Percentage word problems 1
• Percentage word problems 2
MM: Ratio and Proportion. Word
Problems. Occupations Unit 2.
• Central Limit Theorem
• Variance
• Confidence Interval Example
• Law of Large Numbers
• Margin of Error 1
• Margin of Error 2
• Sampling Distribution of the Sample Mean
• Sampling Distribution of the Sample Mean 2
• Statistics: Sample Variance
• ...and 3 more ...
• Central Limit Theorem
•
Use data from a random sample to draw
• ck12.org Normal Distribution Problems:
inferences about a population with an
Qualitative sense of normal distributions
unknown characteristic of interest. Generate • ck12.org Normal Distribution Problems: z-score
multiple samples (or simulated samples) of
the same size to gauge the variation in
• ck12.org: More Empirical Rule and Z-score
estimates or predictions. For example,
practice
estimate the mean word length in a book by
• Clarification of Confidence Interval of Difference
randomly sampling words from the book;
of Means
predict the winner of a school election
• Confidence Interval Example
based on randomly sampled survey data.
• Confidence Interval of Difference of Means
Gauge how far off the estimate or
• Introduction to the Normal Distribution
prediction might be.
• ...and 7 more ...
•
• ANOVA 1 - Calculating SST (Total Sum of
Informally assess the degree of visual
overlap of two numerical data distributions Squares)
• ANOVA 2 - Calculating SSW and SSB (Total
with similar variabilities, measuring the
Sum of Squares Within and Between).avi
difference between the centers by
Understand that statistics can be used to
gain information about a population by
examining a sample of the population;
generalizations about a population from a
sample are valid only if the sample is
representative of that population.
Understand that random sampling tends to
produce representative samples and support
valid inferences.
Integrated Thematics: Population Study.
MM: Word Problems. Occupations Unit 1
and 2.
Integrated Thematic Units 1 and 2:
Compare and Contrast.
Page 74
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7.SP.3
7.SP.4
7.SP.5
7.SP.6
7.SP.7
7.SP.7.a
Statistics and
Probability
expressing it as a multiple of a measure of
variability. For example, the mean height of
players on the basketball team is 10 cm
greater than the mean height of players on
the soccer team, about twice the variability
(mean absolute deviation) on either team;
on a dot plot, the separation between the
two distributions of heights is noticeable.
Statistics and
Probability
Use measures of center and measures of
variability for numerical data from random
samples to draw informal comparative
inferences about two populations. For
example, decide whether the words in a
chapter of a seventh-grade science book are
generally longer than the words in a chapter
of a fourth-grade science book.
Statistics and
Probability
Understand that the probability of a chance
event is a number between 0 and 1 that
expresses the likelihood of the event
occurring. Larger numbers indicate greater
likelihood. A probability near 0 indicates an
unlikely event, a probability around 1/2
indicates an event that is neither unlikely
nor likely, and a probability near 1 indicates
a likely event.
Statistics and
Probability
Approximate the probability of a chance
event by collecting data on the chance
process that produces it and observing its
long-run relative frequency, and predict the
approximate relative frequency given the
probability. For example, when rolling a
number cube 600 times, predict that a 3 or 6
would be rolled roughly 200 times, but
probably not exactly 200 times.
Statistics and
Probability
Statistics and
Probability
Develop a probability model and use it to
find probabilities of events. Compare
probabilities from a model to observed
frequencies; if the agreement is not good,
explain possible sources of the discrepancy.
Develop a uniform probability model by
assigning equal probability to all outcomes,
and use the model to determine
probabilities of events. For example, if a
student is selected at random from a class,
find the probability that Jane will be
selected and the probability that a girl will
• ANOVA 3 -Hypothesis Test with F-Statistic
• Clarification of Confidence Interval of Difference
of Means
• Comparing Population Proportions 1
• Comparing Population Proportions 2
• Confidence Interval of Difference of Means
• Hypothesis Test Comparing Population
Proportions
• ANOVA 1 - Calculating SST (Total Sum of
Squares)
• ANOVA 2 - Calculating SSW and SSB (Total
Sum of Squares Within and Between).avi
• ANOVA 3 -Hypothesis Test with F-Statistic
• Clarification of Confidence Interval of Difference
of Means
• Comparing Population Proportions 1
• Comparing Population Proportions 2
• Confidence Interval of Difference of Means
• Hypothesis Test Comparing Population
Proportions
• Dependent Probability Example 2
• Events and Outcomes 1
• Events and Outcomes 2
• Events and Outcomes 3
• Probability (part 2)
• Probability (part 3)
• Probability (part 4)
• Probability (part 5)
• ...and 2 more ...
• Dependent Probability Example 2
• Events and Outcomes 1
• Events and Outcomes 2
• Events and Outcomes 3
• Independent Events 3
• Probability (part 2)
• Probability (part 3)
• Probability (part 4)
• ...and 4 more ...
• Dependent Probability Example 2
• Events and Outcomes 1
• Events and Outcomes 2
• Events and Outcomes 3
• Probability (part 2)
• Probability (part 3)
• Probability (part 4)
• Probability (part 5)
• ...and 4 more ...
• Events and Outcomes 1
• Events and Outcomes 2
• Events and Outcomes 3
• Probability (part 2)
• Probability (part 3)
• Probability (part 5)
•
Integrated Thematic Units 1 and 2:
Compare and Contrast.
• Probability 1
MM: Yellow Decimal Board, Occupations
Unit 1.
• Probability 1
•
• Probability 1
Occupations Unit 1.
• Probability 1
•
Page 75
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7.SP.7.b
7.SP.8
7.SP.8.a
Statistics and
Probability
Statistics and
Probability
Statistics and
Probability
7.SP.8.b
Statistics and
Probability
7.SP.8.c
Statistics and
Probability
7.NS.1
The Number System
•
•
•
•
•
•
•
•
•
•
•
•
•
Find probabilities of compound events
•
using organized lists, tables, tree diagrams, •
and simulation.
•
•
•
•
•
•
•
Understand that, just as with simple events,
•
the probability of a compound event is the
•
fraction of outcomes in the sample space
•
for which the compound event occurs.
•
•
•
•
•
•
•
Investigate chance processes and develop,
•
use, and evaluate probability models
•
•
•
•
Design and use a simulation to generate
•
frequencies for compound events. For
•
example, use random digits as a simulation
•
tool to approximate the answer to the
•
question: If 40% of donors have type A
•
blood what is the probability that it will
be selected
Develop a probability model (which may
not be uniform) by observing frequencies in
data generated from a chance process. For
example, find the approximate probability
that a spinning penny will land heads up or
that a tossed paper cup will land open-end
down. Do the outcomes for the spinning
penny appear to be equally likely based on
the observed frequencies?
Apply and extend previous understandings
of addition and subtraction to add and
subtract rational numbers; represent
addition and subtraction on a horizontal or
vertical number line diagram.
•
•
•
•
•
•
Probability 1 Module Examples
Dependent Probability Example 2
Events and Outcomes 1
Events and Outcomes 2
Events and Outcomes 3
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
...and 4 more ...
Dependent Probability Example 2
Events and Outcomes 2
Events and Outcomes 3
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
Probability (part 6)
...and 1 more ...
Dependent Probability Example 2
Events and Outcomes 2
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
Probability (part 6)
Probability (part 7)
...and 1 more ...
Dependent Probability Example 2
Events and Outcomes 2
Independent Events 2
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
Probability (part 6)
...and 1 more ...
Independent Events 2
Introduction to Random Variables
Probability (part 4)
Probability (part 5)
Sampling Distribution Example Problem
Absolute Inequalities 2
Absolute Value Inequalities
Absolute value inequalities example 3
Adding and subtracting fractions
Addition of Rational Numbers
Subraction of Rational Numbers
• Probability 1
•
•
Occupations Unit 1 and 2.
•
Occupations Unit 1 and 2.
•
•
•
Occupations 1 and 2
•
MM: Positive/Negative Snake Game,
Number Line, Decimal Fractions, Yellow
Decimal Board, Decimal Chequer Board,
Centesimal Frame, Graphing.
Page 76
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7th Grade Math
7.NS.1.a
7.NS.1.b
7.NS.1.c
7.NS.1.d
7.NS.2
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MM: Number Line, Signed Numbers.
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Apply and extend previous understandings •
of operations with fractions to add, subtract, •
multiply, and divide rational numbers
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Adding and subtracting real numbers
Adding and subtracting real numbers application
Adding integers with different signs
Adding real numbers with different signs
Application of addition of real numbers
Subtracting Real Numbers
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Absolute Value Equations
Absolute Value Equations 2
Absolute Value Inequalities
Adding and subtracting real numbers
Adding and subtracting real numbers application
Adding integers with different signs
Adding real numbers with different signs
Adding/Subtracting negative numbers
...and 3 more ...
Adding and subtracting fractions
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MM: Number Line, Signed Numbers.
The Number System
Describe situations in which opposite
quantities combine to make 0. For example,
a hydrogen atom has 0 charge because its
two constituents are oppositely charged.
The Number System
Understand p + q as the number located a
distance |q| from p, in the positive or
negative direction depending on whether q
is positive or negative. Show that a number
and its opposite have a sum of 0 (are
additive inverses). Interpret sums of
rational numbers by describing real-world
The Number System
The Number System
The Number System
Apply properties of operations as strategies
to add and subtract rational numbers.
Apply and extend previous understandings
of multiplication and division and of
fractions to multiply and divide rational
numbers.
7th Grade Math
7.NS.2.a
The Number System
Apply and extend previous understandings
of operations with fractions to add, subtract,
multiply, and divide rational numbers
7th Grade Math
7.NS.2.b
The Number System
Apply and extend previous understandings
of operations with fractions to add, subtract,
multiply and divide rational numbers
7th Grade Math
7th Grade Math
7.NS.2.c
7.NS.2.d
The Number System
Apply properties of operations as strategies
to multiply and divide rational numbers.
The Number System
Convert a rational number to a decimal
using long division; know that the decimal
form of a rational number terminates in 0s
or eventually repeats.
• Dividing fractions
• Dividing real numbers with different signs
• Division of Rational Numbers
• Fractional Exponent Expressions 1
• Fractional Exponent Expressions 2
• Fractional Exponent Expressions 3
• Multiplication of Rational Numbers
• Multiplying Fractions
• ...and 2 more ...
• Fractional Exponent Expressions 1
• Fractional Exponent Expressions 2
• Fractional Exponent Expressions 3
• Multiplying and dividing negative numbers
• Multiplying negative real numbers
• Multiplying real number application
• Dividing real numbers with different signs
• Multiplying and dividing negative numbers
• Dividing fractions
• Dividing real numbers with different signs
• Fractional Exponent Expressions 1
• Fractional Exponent Expressions 2
• Fractional Exponent Expressions 3
• Multiplying Fractions
• Multiplying negative real numbers
• Multiplying real number application
• Representing a number as a decimal, percent, and
fraction 2
• Multiplying and dividing negative
numbers
MM: Number Line, Signed Numbers,
Decimal Fractions, Yellow Decimal Board,
Decimal Chequer Board, Centesimal
Frame, Graphing.
MM: Adding and Subtracting Fractions,
Signed Numbers, Decimal Fractions,
Yellow Decimal Board, Decimal Chequer
Board, Centesimal Frame
MM: Signed Numbers, Fraction Circles,
Fraction Operation Boards, Fraction
Skittles
• Multiplying and dividing negative
numbers
MM: Signed Numbers
• Multiplying and dividing negative
numbers
• Multiplying and dividing negative
numbers
MM: Signed Numbers
• Multiplying and dividing negative
numbers
Group Division with Stamp Game.
MM: Signed Numbers
Page 77
7th Grade Math
7.NS.3
The Number System
Credit
CCSS
CCSS Category
8th Grade Math
8th Grade Math
8th Grade Math
8th Grade Math
8th Grade Math
8.EE.1
8.EE.2
8.EE.3
8.EE.4
8.EE.5
Expressions and
Equations
Expressions and
Equations
Expressions and
Equations
Expressions and
Equations
Expressions and
Equations
• Fractional Exponent Expressions 1
Solve real-world and mathematical
problems involving the four operations with • Fractional Exponent Expressions 2
rational numbers.1
• Fractional Exponent Expressions 3
CCSS Sub-Category
Khan Academy Work - Videos:
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Work with radicals and integer exponents
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Use square root and cube root symbols to
represent solutions to equations of the form •
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x2 = p and x3 = p, where p is a positive
rational number. Evaluate square roots of
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small perfect squares and cube roots of
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small perfect cubes. Know that _2 is
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irrational.
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Dividing Monomials
Evaluating exponential expressions
Evaluating exponential expressions 2
Exponent Properties 1
Exponent Properties 2
Exponent Properties 3
Exponent Properties 4
Exponent Properties 5
...and 13 more ...
Applying Radical Equations 2
Simplifying Expressions with Exponents
Simplifying Expressions with Exponents 2
Simplifying Expressions with Exponents 3
Solving Radical Equations 3
Square Roots and Real Numbers
Understanding Square Roots
Scientific Notation
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Scientific notation 1
Scientific notation 2
Scientific notation 3
Scientific Notation Examples
Scientific Notation
Scientific notation 1
Scientific notation 2
Scientific notation 3
Scientific Notation Examples
Scientific Notation I
Calculus: Derivatives 1 (new HD version)
Calculus: Derivatives 2 (new HD version)
Converting to slope-intercept form
Graphical Slope of a Line
Slope Example
Slope of a line
Slope of a Line 2
Slope of a Line 3
Work with radicals and integer exponents
Perform operations with numbers expressed
in scientific notation, including problems
where both decimal and scientific notation
are used. Use scientific notation and choose
units of appropriate size for measurements
of very large or very small quantities (e.g.,
use millimeters per year for seafloor
Graph proportional relationships,
interpreting the unit rate as the slope of the
graph. Compare two different proportional
relationships represented in different ways.
For example, compare a distance-time
graph to a distance-time equation to
determine which of two moving objects has
greater speed.
• Average word problems
Khan Academy Work - Exercises:
MM: Word Problems, Occupations Unit 1
and 2
Occupations Work: 6,7,8 /
Montessori Materials
• Exponent rules
• Fractional exponents
• Negative fractional exponents
MM: Squaring and Cubing. Powers of
Numbers
• Cube roots
• Estimating square roots
• Square roots
MM: Cube Root, Square Root.
• Multiplying and dividing scientific
notation
• Scientific notation
• Scientific notation intuition
MM: Powers of Numbers
• Multiplying and dividing scientific
notation
MM: Powers of Numbers
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MM: Graphing. Occupations Unit 1 and 2.
Integrated Humanities Units 1 and 2:
Compare and Contrast.
Page 78
• Algebra: Equation of a line
8th Grade Math
8th Grade Math
8th Grade Math
8.EE.6
8.EE.7
8.EE.7.a
Expressions and
Equations
Expressions and
Equations
Solve linear equations in one variable.
Expressions and
Equations
Give examples of linear equations in one
variable with one solution, infinitely many
solutions, or no solutions. Show which of
these possibilities is the case by
successively transforming the given
equation into simpler forms, until an
equivalent equation of the form x = a, a = a,
or a = b results (where a and b are different
numbers).
8th Grade Math
8.EE.7.b
Expressions and
Equations
8th Grade Math
8.EE.8
Expressions and
Equations
8th Grade Math
8.EE.8.a
Use similar triangles to explain why the
slope m is the same between any two
distinct points on a non-vertical line in the
coordinate plane; derive the equation y =
mx for a line through the origin and the
equation y = mx + b for a line intercepting
the vertical axis at b.
Expressions and
Equations
Solve linear equations with rational number
coefficients, including equations whose
solutions require expanding expressions
using the distributive property and
collecting like terms.
Analyze and solve pairs of simultaneous
linear equations.
Understand that solutions to a system of
two linear equations in two variables
correspond to points of intersection of their
graphs, because points of intersection
satisfy both equations simultaneously.
Solve systems of two linear equations in
• Algebra: graphing lines 1
• Algebra: Slope
• Algebra: Slope 2
• Algebra: Slope 3
• Algebra: Slope and Y-intercept intuition
• Equation of a line 1
• Equation of a line 3
• ...and 6 more ...
• Absolute Value Equation Example 2
• Absolute Value Equations 1
• Application problem with graph
• Evaluate a formula using substitution
• Graphing using X and Y intercepts
• Plotting (x,y) relationships
• Solving Equations 1
• Solving Equations 2
• ...and 2 more ...
• Absolute Value Equation Example 2
• Absolute Value Equations 1
• Absolute value inequalities example 3
• Application problems with equation in one
variable
• Evaluate a formula using substitution
• Graphing using X and Y intercepts
• Multiplying real number application
• Solving systems by graphing 3
• Algebra: Linear Equations 4
• Algebraic Word Problem
• Example of Solving for a Variable
• Factoring and the Distributive Property
• Factoring and the Distributive Property 2
• Factoring and the Distributive Property 3
• Multi-step equations 2
• Solving Equations 2
• ...and 2 more ...
• Addition Elimination Method 3
• Converting to slope-intercept form
• systems of equations
• Addition Elimination Method 3
• Addition Elimination Method 4
• Consistent and Inconsistent Systems
• Graphical Systems Application Problem
• Independent and Dependent Systems
• Solving Linear Systems by Graphing
• Solving systems by graphing
• Solving systems by graphing 2
• ...and 6 more ...
• Addition Elimination Method 1
• Addition Elimination Method 2
• Converting between point-slope and
slope-intercept
• Converting between slope-intercept and
standard form
• Equations of parallel and perpendicular
lines
• Finding the equation of a line
• Identifying slope of a line
• Line graph intuition
• Solving for the y-intercept
MM: Algebra, Graphing.
• 2-step equations
MM: Algebra, Graphing
• 2-step equations
• One-step equations with mult
MM: Algebra, Graphing
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MM: Distributive Laws, Introduction to
Algebra, Word Problems, Binomial Cube,
Trinomial Cube.
2-step equations
Expressions with unknown variables 2
One-step equations with mult
Solving equations in terms of a variable
• Systems of equations
MM: Algebra, Graphing
• Systems of equations
MM: Algebra, Graphing
• Systems of equations
MM: Algebra, Graphing.
Page 79
8th Grade Math
8th Grade Math
8th Grade Math
8th Grade Math
8th Grade Math
8th Grade Math
8.EE.8.b
8.EE.8.c
8.F.1
8.F.2
8.F.3
8.F.4
Expressions and
Equations
Expressions and
Equations
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Solve real-world and mathematical
problems leading to two linear equations in •
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two variables. For example, given
coordinates for two pairs of points,
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determine whether the line through the first •
pair of points intersects the line through the •
second pair.
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two variables algebraically, and estimate
solutions by graphing the equations. Solve
simple cases by inspection. For example, 3x
+ 2y = 5 and 3x + 2y = 6 have no solution
because 3x + 2y cannot simultaneously be 5
and 6.
Functions
Understand that a function is a rule that
assigns to each input exactly one output.
The graph of a function is the set of ordered
pairs consisting of an input and the
corresponding output.1
Functions
Compare properties of two functions each
represented in a different way
(algebraically, graphically, numerically in
tables, or by verbal descriptions). For
example, given a linear function
represented by a table of values and a linear
function represented by an algebraic
expression, determine which function has
the greater rate of change.
Functions
Functions
Interpret the equation y = mx + b as
defining a linear function, whose graph is a
straight line; give examples of functions
that are not linear. For example, the
function A = s^2 giving the area of a square
as a function of its side length is not linear
because its graph contains the points (1,1),
(2,4) and (3,9), which are not on a straight
line.
Construct a function to model a linear
relationship between two quantities.
Determine the rate of change and initial
value of the function from a description of a
relationship or from two (x, y) values,
including reading these from a table or from
a graph Interpret the rate of change and
Addition Elimination Method 3
Addition Elimination Method 4
Consistent and Inconsistent Systems
Converting to slope-intercept form
Graphical Systems Application Problem
Independent and Dependent Systems
...and 15 more ...
Converting to slope-intercept form
Point-slope and standard form
Solving systems by elimination
Solving systems by elimination 2
Solving systems by elimination 3
Solving systems by graphing
Solving systems by graphing 2
Solving systems by graphing 3
...and 4 more ...
• Systems of equations
Occupations Unit 1.
• Application problem with graph
• Ordered pair solutions to linear equations MM: Algebra
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• Understanding function notation
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Direct Variation 1
Domain and Range 2
Functional Relationships 1
Functions as Graphs
Introduction to functions
Slope of a Line 3
Testing if a relationship is a function
...and 1 more ...
• Evaluating expressions with function
notation
Basic Linear Function
Converting to slope-intercept form
Equation of a line 1
Equation of a line 2
Equation of a line 3
Exploring linear relationships
Graphing a line in slope intercept form
Graphing linear inequalities in two variables 2
...and 5 more ...
Application problem with graph
Basic Linear Function
Calculus BC 2008 2 a
Direct Variation 1
Exploring linear relationships
Linear Equations in Slope Intercept Form
Application problem with graph
MM: Algebra
• Ordered pair solutions to linear equations MM: Algebra
• Ordered pair solutions to linear equations MM: Algebra, Occupation Unit 1
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MM: Algebra, Graphing, Occupations Unit
Page 80
8th Grade Math
8.F.5
Functions
8th Grade Math
8.G.1
Geometry
8th Grade Math
8.G.1.a
Geometry
8th Grade Math
8.G.1.b
Geometry
8th Grade Math
8.G.1.c
Geometry
8th Grade Math
8.G.2
Geometry
8th Grade Math
8.G.3
Geometry
8th Grade Math
8.G.4
Geometry
8th Grade Math
8.G.5
Geometry
8th Grade Math
8.G.6
Geometry
8th Grade Math
8th Grade Math
8th Grade Math
8.G.7
8.G.8
8.G.9
Geometry
Geometry
Geometry
Describe qualitatively the functional
relationship between two quantities by
analyzing a graph (e.g., where the function
is increasing or decreasing, linear or
nonlinear). Sketch a graph that exhibits the
qualitative features of a function that has
been described verbally.
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Verify experimentally the properties of
rotations, reflections, and translations:
Lines are taken to lines, and line segments
to line segments of the same length.
Angles are taken to angles of the same
measure.
Parallel lines are taken to parallel lines.
Understand that a two-dimensional figure is
congruent to another if the second can be
obtained from the first by a sequence of
Describe the effect of dilations, translations,
rotations, and reflections on twodimensional figures using coordinates.
Understand that a two-dimensional figure is
similar to another if the second can be
obtained from the first by a sequence of
rotations, reflections, translations, and
dilations; given two similar twodi
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Usmeeinsfioornmaal lfiagrugruem
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Parallel lines 1
Congruent triangles 1
Congruent triangles 2
Shifting and reflecting functions
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MM: Constructive Triangles, Geometric
Cabinet, Blue Triangles.
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Similar triangles 1
Similar triangles 2
Similar triangles review
Solving similar triangles 1
Solving similar triangles 2
Angles 2
Congruent triangles 1
Congruent triangles 2
MM: Constructive Triangles, Geometric
Cabinet, Blue Triangles
•
• Similar triangles
• Angle Game (part 2)
• Angles (part 3)
• Angles formed between transversals and parallel
lines
• Angles of parallel lines 2
• Similar triangles
• Similar triangles (part 2)
• The Angle Game
• Triangle Medians and Centroids
• Pythagorean Theorem II
Explain a proof of the Pythagorean
• The Pythagorean Theorem
Theorem and its converse.
• Visual Pythagorean Theorem Proof
• 30-60-90 Triangles II
• Basic Trigonometry
Apply the Pythagorean Theorem to
• Pythagorean Theorem
determine unknown side lengths in right
• Pythagorean Theorem 1
triangles in real-world and mathematical
• Pythagorean Theorem 2
problems in two and three dimensions.
• Pythagorean Theorem 3
• The Pythagorean Theorem
• Distance Formula
Apply the Pythagorean Theorem to find the
• Polar Coordinates 1
distance between two points in a coordinate
• Polar Coordinates 2
system.
• The Pythagorean Theorem
• Applying Radical Equations 3
Know the formulas for the volumes of
• Cylinder Volume and Surface Area
cones, cylinders, and spheres and use them
• Introduction to rate-of-change problems
to solve real-world and mathematical
• Multiplying and Dividing Monomials 2
problems
about the angle sum and exterior angle of
triangles, about the angles created when
parallel lines are cut by a transversal, and
the angle-angle criterion for similarity of
triangles. For example, arrange three copies
of the same triangle so that the sum of the
three angles appears to form a line, and give
an argument in terms of transversals why
this is so.
1 and 2.
Calculus: Derivatives 1 (new HD version)
Converting to slope-intercept form
Direct Variation 1
Equation of a line 1
Exploring linear relationships
Exploring nonlinear relationships
Functional Relationships 1
...and 7 more ...
MM: Angles, Constructive Triangles,
Geometric Cabinet, Blue Triangles.
• Pythagorean theorem
MM: Theorems, Pythagoras Geometric
Plates I, II and III.
• Special right triangles
MM: Theorems, Pythagoras Geometric
Plates I, II, and III. Occupations (Design
and Planning).
• Distance between point and line
• Distance formula
MM: Theorems, Pythagoras Geometric
Plates I, II, and III. Occupations (Design
and Planning).
•
MM: Solids, Volume
Page 81
• Multiplying Polynomials 3
Statistics and Probability
8th Grade Math
8th Grade Math
8th Grade Math
8th Grade Math
8.SP.1
8.SP.2
8.SP.3
8.SP.4
Statistics and
Probability
Statistics and
Probability
Construct and interpret scatter plots for
bivariate measurement data to investigate
patterns of association between two
quantities. Describe patterns such as
clustering, outliers, positive or negative
association, linear association, and
nonlinear association.
Know that straight lines are widely used to
model relationships between two
quantitative variables. For scatter plots that
suggest a linear association, informally fit a
straight line, and informally assess the
model fit by judging the closeness of the
data points to the line.
Statistics and
Probability
Use the equation of a linear model to solve
problems in the context of bivariate
measurement data, interpreting the slope
and intercept. For example, in a linear
model for a biology experiment, interpret a
slope of 1.5 cm/hr as meaning that an
additional hour of sunlight each day is
associated with an additional 1.5cm in
mature plant height.
Statistics and
Probability
Understand that patterns of association can
also be seen in bivariate categorical data by
displaying frequencies and relative
frequencies in a two-way table. Construct
and interpret a two-way table summarizing
data on two categorical variables collected
from the same subjects. Use relative
frequencies calculated for rows or columns
to describe possible association between the
two variables. For example, collect data
from students in your class on whether or
not they have a curfew on school nights and
whether or not they have assigned chores at
home. Is there evidence that those who
have a curfew also tend to have chores?
• Law of Large Numbers
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• Calculating R-Squared
• Covariance and the Regression Line
• Fitting a Line to Data
• Proof (Part 1) Minimizing Squared Error to
Regression Line
• Proof (Part 3) Minimizing Squared Error to
Regression Line
• Proof (Part 4) Minimizing Squared Error to
Regression Line
• R-Squared or Coefficient of Determination
• Second Regression Example
• ...and 1 more ...
• Calculating R-Squared
• Covariance and the Regression Line
• Fitting a Line to Data
• Proof (Part 1) Minimizing Squared Error to
Regression Line
• Proof (Part 3) Minimizing Squared Error to
Regression Line
• Proof (Part 4) Minimizing Squared Error to
Regression Line
• R-Squared or Coefficient of Determination
• Second Regression Example
• ...and 1 more ...
• Contingency Table Chi-Square Test
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Integrated Humanities 1 and 2, Compare
and Contrast.
Know that numbers that are not rational are • Number Sets
called irrational. Understand informally that
• Converting 1-digit repeating decimals to MM: Fractions, Yellow Decimal Board
fractions
Page 82
8th Grade Math
8.NS.1
The Number System
8th Grade Math
8.NS.2
The Number System
• Number Sets 1
rational numbers show that the decimal
expansion repeats eventually, and convert a
• Number Sets 3
de
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•
numbers to compare the size v`of irrational
numbers, locate them approximately on a
number line diagram, and estimate the
value of expressions (e g 2) For
• Converting multi-digit repeating
decimals to fractions
• Converting 1-digit repeating decimals to MM: Fractions, Yellow Decimal Board
fractions
• Converting multi-digit repeating
decimals to fractions
Page 83
Denver Montessori Junior/Senior High School: Grades 9 - 12 Math Curriculum Alignment to the Common Core State Standards
Credit
CCSS
Algebra 1
9-12.A-APR.1
Algebra 1
9-12.A-APR.3
Algebra 1
9-12.A-APR.5
Algebra 1
Algebra 1
Algebra 1
Algebra 1
Algebra 1
Algebra 1
9-12.A-APR.6
9-12.A-CED.1
9-12.A-CED.2
9-12.A-CED.3
9-12.A-CED.4
9-12.A-REI.1
CCSS Category
CCSS Sub-Category
Understand that polynomials form a system
analogous to the integers, namely, they are closed
Arithmetic with Polynomials and Rational
under the operations of addition, subtraction, and
Expressions
multiplication; add, subtract, and multiply
polynomials.
Identify zeros of polynomials when suitable
Arithmetic with Polynomials and Rationalfactorizations are available, and use the zeros to
Expressions
construct a rough graph of the function defined by
the polynomial.
Arithmetic with Polynomials and Rational
Use polynomial identities to solve problems
Expressions
Rewrite simple rational expressions in different
forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
Arithmetic with Polynomials and Rationa where a(x), b(x), q(x), and r(x) are polynomials
Expressions
with the degree of r(x) less than the degree of b(x),
using inspection, long division, or, for the more
complicated examples, a computer algebra system.
Creating Equations*
Creating Equations*
Creating Equations*
Creating Equations*
Reasoning with Equations and
Inequalities
Khan Academy Work - Videos:
Khan Academy Work - Exercises
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•
•
•
•
•
•
•
Adding and Subtracting Polynomials 1
Adding and Subtracting Polynomials 2
Adding and Subtracting Polynomials 3
Adding Polynomials
Addition and Subtraction of Polynomials
Dividing Monomials
Dividing multivariable polynomial with monomial
Dividing polynomials 1
• Adding and subtracting polynomials
• Multiplying polynomials
• Polynomial Equations in Factored Form
Exeter Work: 9-12
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
• Binomial Theorem (part 1)
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Create equations and inequalities in one variable
•
and use them to solve problems. Include equations •
arising from linear and quadratic functions, and
•
simple rational and exponential functions.
Exeter MAT 11T / 120 / 130 :
Algebra
Multiplying and Dividing Rational Expressions 2
Multiplying and Dividing Rational Expressions 3
Simplifying Rational Expressions 1
Simplifying Rational Expressions 2
Simplifying Rational Expressions 3
Exeter MAT 11T / 120 / 130 :
Algebra
• Multiplying expressions 0.5
• Multiplying expressions 1
Compound Inequalities 3
Compound Inequalities 4
Compund Inequalities
Compund Inequalities 2
...and 21 more ...
Exeter MAT 11T / 120 / 130 :
Algebra
• Graphing linear inequalities
• Multi-step linear inequalities
• One step inequalities
• Graphs of Linear Equations
Create equations in two or more variables to
• Mixture problems 1
represent relationships between quantities; graph
• Mixture problems 2
equations on coordinate axes with labels and scales.
Represent constraints by equations or inequalities, •
and by systems of equations and/or inequalities, and •
interpret solutions as viable or nonviable options in •
a modeling context. For example, represent
•
inequalities describing nutritional and cost
•
constraints on combinations of different foods.
•
Create equations that describe numbers or
•
relationship
Compound Inequalities 3
Compound Inequalities 4
Compund Inequalities
Compund Inequalities 2
Multi-Step Inequalities
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•
Explain each step in solving a simple equation as
following from the equality of numbers asserted at •
the previous step, starting from the assumption that •
the original equation has a solution. Construct a
•
viable argument to justify a solution method.
•
•
Mixture problems 1
Mixture problems 2
Mixture problems 3
Solving Equations 1
Solving Equations 2
Exeter MAT 11T / 120 / 130 :
Algebra
• Evaluating expressions with function notation
Exeter MAT 11T / 120 / 130 :
Algebra
• Compound inequalities
Proportionality
Rearrange formulas to isolate specific variables
• Solving equations in terms of a variable
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Solving Equations with the Distributive Property
Solving equations with the distributive property 2
Solving factored equations
...and 1 more ...
• Significant figures
• Solving equations in terms of a variable
Algebra 1
9-12.A-REI.10
Reasoning with Equations and
Inequalities
• Graphing linear inequalities in two variables 2
Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which
• Graphing using X and Y intercepts
could be a line).
Exeter MAT 11T / 120 / 130 :
Algebra
Page 84
Algebra 1
Algebra 1
Algebra 1
9-12.A-REI.11
9-12.A-REI.12
9-12.A-REI.2
Reasoning with Equations and
Inequalities
Reasoning with Equations and
Inequalities
Reasoning with Equations and
Inequalities
Explain why the x-coordinates of the points where •
the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) =
g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of
values, or find successive approximations. Include
cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and
logarithmic functions._
•
•
•
•
Graph the solutions to a linear inequality in two
variables as a halfplane (excluding the boundary in •
•
the case of a strict inequality), and graph the
solution set to a system of linear inequalities in two •
variables as the intersection of the corresponding
•
half-planes.
Solve simple rational and radical equations in one
variable, and give examples showing how
extraneous solutions may arise.
Solving Linear Systems by Graphing
Exeter MAT 11T / 120 / 130 :
Algebra
Graphical System of Inequalities
Graphing Inequalities
Graphing Inequalities 2
Graphing linear inequalities in two variables 2
Graphing systems of inequalities
Graphing systems of inequalities 2
Graphing systems of inequalities 3
System of Inequalities Application
Exeter MAT 11T / 120 / 130 :
Algebra
• Graphing and solving linear inequalities
• Graphing and solving systems of inequalities
• Graphing systems of inequalities
• Radical Equation Examples
• Simplifying Radical Expressions 2
• Simplifying Radical Expressions 3
Exeter MAT 11T / 120 / 130 :
Algebra
• Equations with variables on both sides
•
•
•
•
•
•
•
•
•
Compound Inequalities
Compound Inequalities 3
Compound Inequalities 4
Compund Inequalities
Compund Inequalities 2
Equations and Inequalities
Equations with Variables on Both Sides
Example of Solving for a Variable
...and 21 more ...
Algebra 1
9-12.A-REI.3
Reasoning with Equations and
Inequalities
Solve linear equations and inequalities in one
variable, including equations with coefficients
represented by letters.
Algebra 1
9-12.A-REI.4.b
Reasoning with Equations and
Inequalities
Solve equations and inequalities in one variable
Algebra 1
9-12.A-REI.5
Reasoning with Equations and
Inequalities
Prove that, given a system of two equations in two • Solving Systems of Equations by Elimination
variables, replacing one equation by the sum of that
equation and a multiple of the other produces a
• systems of equations
system with the same solutions.
Algebra 1
9-12.A-REI.6
Reasoning with Equations and
Inequalities
• Graphical Systems Application Problem
Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs • Graphings Systems of Equations
of linear equations in two variables.
Seeing Structure in Expressions
Interpret expressions that represent a quantity in
terms of its context.
Exeter MAT 11T / 120 / 130 :
Algebra
• Multi-step equations
Algebra 1
9-12.A-SSE.1
Algebra 1
9-12.A-SSE.1.a
Seeing Structure in Expressions
Algebra 1
9-12.A-SSE.1.b
Seeing Structure in Expressions
• Factor by Grouping and Factoring Completely
Algebra 1
9-12.A-SSE.2
Seeing Structure in Expressions
Interpret the structure of expressions
Algebra 1
9-12.A-SSE.3
Seeing Structure in Expressions
Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression.
Exeter MAT 11T / 120 / 130 :
Algebra
• Graphing linear inequalities
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
•
•
Interpret parts of an expression, such as terms,
•
•
factors, and coefficients.
•
Interpret complicated expressions by viewing one or •
more of their parts as a single entity. For example,
interpret P(1+r)^n as the product of P and a factor
not depending on P.
Exeter MAT 11T / 120 / 130 :
Algebra
Algebraic Expression Least Common Multiple
Factor expressions by grouping
Factoring and the Distributive Property
Factoring and the Distributive Property 2
Factoring and the Distributive Property 3
Algebraic Expression Least Common Multiple
• Factor expressions by grouping
•
•
•
•
•
•
Adding and Subtracting Rational Expressions
Dividing and Simplifying Rational Expressions
Factor by Grouping and Factoring Completely
Factor expressions by grouping
...and 28 more ...
Adding and Subtracting Rational Expressions
• Factor expressions by grouping
• Exponent Properties Involving Products
Use the properties of exponents to transform
expressions for exponential functions. For example • Exponent Properties Involving Quotients
th
i 1 15^t
b
itt
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Page 85
Algebra 1
9-12.A-SSE.3.c
Seeing Structure in Expressions
Algebra 1
9-12.A-SSE.4
Seeing Structure in Expressions
Algebra 1
9-12.F-BF.1.a
Building Functions
Algebra 1
9-12.F-BF.2
Building Functions
Algebra 1
9-12.F-BF.3
Building Functions
Algebra 1
9-12.F-BF.4
Building Functions
Algebra 1
9-12.F-BF.4.a
Building Functions
Algebra 1
9-12.F-BF.4.b
Building Functions
Algebra 1
9-12.F-BF.4.c
Building Functions
Algebra 1
9-12.F-BF.4.d
Building Functions
Algebra 1
9-12.F-IF.1
Interpreting Functions
the expression 1.15^t can be rewritten as
• Zero, Negative, and Fractional Exponents
(1.15^1/12)^12t _ 1.012^12t to reveal the
approximate equivalent monthly interest rate if the
annual rate is 15%.
9-12.F-IF.2
Interpreting Functions
Algebra 1
9-12.F-IF.3
Interpreting Functions
Algebra 1
9-12.F-IF.4
Interpreting Functions
• Simplifying expressions with exponents
Derive the formula for the sum of a finite geometric • Sequences and Series (part 1)
series (when the common ratio is not 1), and use the
formula to solve problems. For example, calculate
mortgage payments.
Determine an explicit expression, a recursive
process, or steps for calculation from a context.
•
•
Write arithmetic and geometric sequences both
•
recursively and with an explicit formula, use them
•
to model situations, and translate between the two
•
forms.
•
•
Identify the effect on the graph of replacing f(x) by •
•
f(x) + k, k f(x), f(kx), and f(x + k) for specific
•
values of k (both positive and negative); find the
value of k given the graphs. Experiment with cases •
and illustrate an explanation of the effects on the
•
graph using technology. Include recognizing even
and odd functions from their graphs and algebraic
expressions for them.
•
•
•
•
•
•
Build new functions from existing functions
•
•
Verify by composition that one function is the
•
inverse of another.
•
Read values of an inverse function from a graph or •
a table, given that the function has an inverse.
Produce an invertible function from a non-invertible •
function by restricting the domain.
•
•
Understand that a function from one set (called the
domain) to another set (called the range) assigns to •
each element of the domain exactly one element of
the range. If f is a function and x is an element of its
•
domain, then f(x) denotes the output of f
Find inverse functions.
Exeter MAT 11T / 120 / 130 :
Algebra
Equations of Sequence Patterns
Finding the 100th Term in a Sequence
Inductive Reasoning 2
Patterns in Sequences 1
Patterns in Sequences 2
Sequences and Series (part 1)
U12_L1_T3_we1 Inductive Reasoning 1
Algebra: graphing lines 1
Algebra: Slope and Y-intercept intuition
Connection between even and odd numbers and functions
Graphs of Square Root Functions
Recognizing Odd and Even Functions
• Even and odd functions
• Line graph intuition
• Shifting and reflecting functions
Function Inverse Example 1
Function Inverses Example 2
Function Inverses Example 3
Introduction to Function Inverses
Function Inverse Example 1
Function Inverses Example 2
Function Inverses Example 3
Introduction to Function Inverses
Function Inverse Example 1
Introduction to Function Inverses
Introduction to Function Inverses
Function Inverses Example 2
Function Inverses Example 3
Domain and Range 1
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Introduction to functions
• Understanding function notation
• Domain of a function
Use function notation, evaluate functions for inputs • Multiplying and Dividing Rational Expressions 1
in their domains, and interpret statements that use • Simplifying Rational Expressions 3
function notation in terms of a context.
• Domain of a function
• Range of a function
• Sequences and Series (part 1)
Recognize that sequences are functions, sometimes
defined recursively, whose domain is a subset of the
integers. For example, the Fibonacci sequence is
• Sequences and series (part 2)
defined recursively by f(0) = f(1) = 1, f(n+1) = f(n)
+ f(n-1) for n _ 1.
•
For a function that models a relationship between
two quantities, interpret key features of graphs and •
tables in terms of the quantities, and sketch graphs
showing key features given a verbal description of
•
the relationship. Key features include: intercepts;
intervals where the function is increasing,
decreasing, positive, or negative; relative maximums•
and minimums; symmetries; end behavior; an
Exeter MAT 11T / 120 / 130 :
Algebra
Domain and Range 2
corresponding to the input x. The graph of f is the
graph of the equation y = f(x).
Algebra 1
• Exponent rules
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 210/220/230:
Integrated Mathematics
Equation of a line 1
Functional Relationships 1
Functions (Part III)
Exeter MAT 11T / 120 / 130 :
Algebra
Graphing a line in slope intercept form
Page 86
periodicity.
• Testing if a relationship is a function
• Domain and Range 1
Algebra 1
9-12.F-IF.5
Interpreting Functions
Algebra 1
9-12.F-IF.6
Interpreting Functions
Algebra 1
9-12.F-IF.7
Interpreting Functions
Algebra 1
9-12.F-IF.7.a
Interpreting Functions
Algebra 1
9-12.F-IF.7.b
Interpreting Functions
Algebra 1
9-12.F-IF.8
Interpreting Functions
Algebra 1
9-12.F-IF.8.a
Interpreting Functions
Algebra 1
9-12.F-IF.8.b
Interpreting Functions
Algebra 1
9-12.F-IF.9
Interpreting Functions
Algebra 1
9-12.F-LE.1
Linear, Quadratic, and Exponential
Models
Algebra 1
9-12.F-LE.1.a
Linear, Quadratic, and Exponential
Models
Algebra 1
9-12.F-LE.1.b
Linear, Quadratic, and Exponential
Models
Algebra 1
9-12.F-LE.2
Linear, Quadratic, and Exponential
Models
Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it • Domain and Range of a Function
describes. For example, if the function h(n) gives
the number of person-hours it takes to assemble n • Simplifying Rational Expressions 2
engines in a factory, then the positive integers
would be an appropriate domain for the function. • Simplifying Rational Expressions 3
Exeter MAT 210/220/230:
Integrated Mathematics
• Basic Rate Problem
Calculate and interpret the average rate of change
of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of
• Slope and Rate of Change
change from a graph.
Graph functions expressed symbolically and show • Functional Relationships 1
key features of the graph, by hand in simple cases • Graphing a line in slope intercept form
• Converting to slope-intercept form
• Graphical Systems Application Problem
Graph linear and quadratic functions and show
• Graphing a line in slope intercept form
intercepts, maxima, and minima.
• Graphings Systems of Equations
• Graphs of Linear Equations
• Absolute Value Equations
Graph square root, cube root, and piecewise• Functions as Graphs
defined functions, including step functions and
• Functions Part 2
absolute value functions.
• Graphs of Square Root Functions
• Functions (part 4)
Write a function defined by an expression in
different but equivalent forms to reveal and explain
different properties of the function.
• Factor by Grouping and Factoring Completely
• Graphs of Quadratic Functions
Use the process of factoring and completing the
square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and
interpret these in terms of a context.
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 210/220/230:
Integrated Mathematics
•
•
•
•
Factoring polynomials 1
Factoring polynomials 2
Factoring polynomials by grouping
Factoring polynomials with two variables
• Exponent Rules 1
Use the properties of exponents to interpret
expressions for exponential functions. For example,
identify percent rate of change in functions such as • Exponent Rules 2
y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y =
(1.2)^t/10, and classify them as representing
• Exponent Rules 3
exponential growth or decay.
Compare properties of two functions each
represented in a different way (algebraically,
graphically, numerically in tables, or by verbal
descriptions). For example, given a graph of one
quadratic function and an algebraic expression for
another, say which has the larger maximum.
Distinguish between situations that can be modeled •
with linear functions and with exponential functions.
•
Prove that linear functions grow by equal
differences over equal intervals, and that
exponential functions grow by equal factors over
equal intervals.
•
Recognize situations in which one quantity changes •
at a constant rate per unit interval relative to
•
another.
•
•
•
•
Construct linear and exponential functions,
including arithmetic and geometric sequences, given•
a graph, a description of a relationship, or two input-•
output pairs (include reading these from a table).
Exeter MAT 11T / 120 / 130 :
Algebra
Linear, Quadratic, and Exponential Models
Exeter MAT 11T / 120 / 130 :
Algebra
Linear, Quadratic, and Exponential Models
Exeter MAT 11T / 120 / 130 :
Algebra
Direct Variation Models
Slope Example
Systems and rate problems
Systems and rate problems 2
Systems and rate problems 3
Graphing Using Intercepts
Graphs of Linear Equations
Slope Example
Word Problem Solving 4
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
• Point slope form
• Slope intercept form
Page 87
Algebra 1
Algebra 1
9-12.F-LE.3
9-12.G-CO.1
Linear, Quadratic, and Exponential
Models
Congruence
• Linear, Quadratic, and Exponential Models
Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more
generally) as a polynomial function.
• Perpendicular Line Slope
Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment,
• Perpendicular Lines
based on the undefined notions of point, line,
distance along a line, and distance around a circular
arc.
Algebra 1
9-12.G-GPE.5
Expressing Geometric Properties with
Equations
• Perpendicular Line Slope
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
• Perpendicular Lines
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a
• Perpendicular lines 2
given point).
Algebra 1
9-12.G-GPE.6
Expressing Geometric Properties with
Equations
Find the point on a directed line segment between
two given points that partitions the segment in a
given ratio.
Algebra 1
9-12.G-SRT.1.a
Similarity, Right Triangles, and
Trigonometry
Algebra 1
9-12.G-SRT.1.b
Similarity, Right Triangles, and
Trigonometry
A dilation takes a line not passing through the
center of the dilation to a parallel line, and leaves a
line passing through the center unchanged.
The dilation of a line segment is longer or shorter in
the ratio given by the scale factor.
Use units as a way to understand problems and to
guide the solution of multi-step problems; choose
and interpret units consistently in formulas; choose
and interpret the scale and the origin in graphs and
data displays.
Algebra 1
9-12.N-Q.1
Quantities
Algebra 1
9-12.N-Q.2
Quantities
Define appropriate quantities for the purpose of
descriptive modeling.
Quantities
Choose a level of accuracy appropriate to
limitations on measurement when reporting
quantities.
Algebra 1
Algebra 1
9-12.N-Q.3
9-12.N-RN.1
The Real Number System
Explain how the definition of the meaning of
rational exponents follows from extending the
properties of integer exponents to those values,
allowing for a notation for radicals in terms of
rational exponents. For example, we define 5^1/3 to
be the cube root of 5 because we want (5^1/3)^3 =
5^(1/3)3 to hold, so (5^1/3) must equal 5.
Algebra 1
9-12.N-RN.2
9-12.N-RN.3
Algebra 1
9-12.S-ID.7
Geometry
9-12.A-APR.4
The Real Number System
The Real Number System
• Equations of parallel and perpendicular lines
Exeter MAT 210/220/230:
Integrated Mathematics
• Midpoint formula
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
•
•
•
•
•
Mixture problems 1
Mixture problems 2
Mixture problems 3
Speed translation
Unit conversion
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
•
•
•
•
•
•
Addition and Subtraction with Significant Figures
More on Significant Figures
Multiplying and Dividing with Significant Figures
Pure Numbers and Significant Digits
Significant Figures
Level 3 exponents
Exeter MAT 11T / 120 / 130 :
Algebra
• Radical Expressions with Higher Roots
• Simplifying Radical Expressions 2
Exeter MAT 11T / 120 / 130 :
Algebra
• Simplifying Radical Expressions 3
• Simplifying Radical Expressions1
• Solving Radical Equations 2
Adding and Subtracting Polynomials 1
Adding and Subtracting Polynomials 2
Adding and Subtracting Polynomials 3
Exponent Rules 1
Exponent Rules 2
Rewrite expressions involving radicals and rational
• Exponent Rules 3
exponents using the properties of exponents.
• Exponent Rules Part 1
• ...and 19 more ...
Explain why the sum or product of two rational
numbers is rational; that the sum of a rational
number and an irrational number is irrational; and
that the product of a nonzero rational number and
an irrational number is irrational.
Exeter MAT 210/220/230:
Integrated Mathematics
• Midpoint Formula
•
•
•
•
•
Algebra 1
Exeter MAT 11T / 120 / 130 :
Algebra
• Simplifying radicals
Exeter MAT 11T / 120 / 130 :
Algebra
•
•
•
•
Adding and subtracting radicals
Multiplying radicals
Simplifying radicals
Square roots
• Square Roots and Real Numbers
Exeter MAT 11T / 120 / 130 :
Algebra
• Square roots
Interpret the slope (rate of change) and the
Interpreting Categorical and Quantitative
intercept (constant term) of a linear model in the
Data
context of the data.
• Graphing a line in slope intercept form
• Slope Example
• Slope of a line
Arithmetic with Polynomials and Rational
Use polynomial identities to solve problems
Expressions
• Deductive Reasoning 3
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Page 88
Interpret the structure of expressions
• Deductive Reasoning 2
Exeter MAT 11T / 120 / 130 :
Algebra
Geometry
9-12.A-SSE.2
Seeing Structure in Expressions
Geometry
9-12.G-C.1
Circles
Prove that all circles are similar.
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Geometry
9-12.G-C.2
Circles
• Area of Inscribed Equilateral Triangle (some basic trig used)
Identify and describe relationships among inscribed • Inscribed and Central Angles
angles, radii, and chords. Include the relationship
• Right Triangles Inscribed in Circles (Proof)
between central, inscribed, and circumscribed
angles; inscribed angles on a diameter are right
• Inscribed angles 1
angles; the radius of a circle is perpendicular to the
• Inscribed angles 2
tangent where the radius intersects the circle.
• Inscribed angles 3
Geometry
9-12.G-C.3
Circles
•
Construct the inscribed and circumscribed circles of
•
a triangle, and prove properties of angles for a
•
quadrilateral inscribed in a circle.
•
Geometry
9-12.G-C.4
Circles
Geometry
9-12.G-C.5
Circles
Geometry
9-12.G-CO.1
Congruence
Geometry
9-12.G-CO.10
Congruence
Prove geometric theorems
Congruence
Prove theorems about parallelograms. Theorems
include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent
diagonals.
9-12.G-CO.11
Exeter MAT 210/220/230:
Integrated Mathematics
Construct a tangent line from a point outside a
given circle to the circle.
Derive using similarity the fact that the length of the
arc intercepted by an angle is proportional to the
radius, and define the radian measure of the angle as
the constant of proportionality; derive the formula
for the area of a sector.
Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line,
distance along a line, and distance around a circular
arc.
Geometry
2003 AIME II Problem 7
Area of Diagonal Generated Triangles of Rectangle are Equal
Area of Inscribed Equilateral Triangle (some basic trig used)
Inscribed and Central Angles
Exeter MAT 210/220/230:
Integrated Mathematics
•
•
•
•
•
•
•
•
•
•
•
•
Circles: Radius, Diameter and Circumference
Introduction to angles (old)
Parallel Line Equation
Parallel Lines
Parallel Lines 2
Parallel lines 3
...and 1 more ...
Area of Diagonal Generated Triangles of Rectangle are Equal
Heron's Formula
Part 1 of Proof of Heron's Formula
Part 2 of the Proof of Heron's Formula
Triangle Medians and Centroids (2D Proof)
• Basic triangle proofs
• Wrong statements in triangle proofs
• Rhombus Diagonals
• Basic triangle proofs
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Wrong statements in triangle proofs
• Angle bisector theorem
Geometry
9-12.G-CO.12
Congruence
Geometry
9-12.G-CO.13
Congruence
Geometry
9-12.G-CO.2
Congruence
Geometry
9-12.G-CO.3
Congruence
Make formal geometric constructions with a variety
of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an
angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a
point not on the line.
• 2003 AIME II Problem 7
Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe
transformations as functions that take points in the
plane as inputs and give other points as outputs.
Compare transformations that preserve distance and
angle to those that do not (e.g., translation versus
horizontal stretch).
Given a rectangle, parallelogram, trapezoid, or
regular polygon, describe the rotations and
reflections that carry it onto itself.
• Heron's formula
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Quadrilateral types
Exeter MAT 210/220/230:
Integrated Mathematics
Page 89
Geometry
9-12.G-CO.4
Congruence
Develop definitions of rotations, reflections, and
translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
Congruence
Given a geometric figure and a rotation, reflection,
or translation, draw the transformed figure using,
e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations
that will carry a given figure onto another.
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Congruency postulates
Geometry
9-12.G-CO.5
Geometry
9-12.G-CO.6
Congruence
Use geometric descriptions of rigid motions to
transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures,
use the definition of congruence in terms of rigid
motions to decide if they are congruent.
Geometry
9-12.G-CO.7
Congruence
Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent if
and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
Geometry
9-12.G-CO.8
Congruence
Explain how the criteria for triangle congruence
(ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
• Congruency postulates
Exeter MAT 210/220/230:
Integrated Mathematics
• Angles of parallel lines 2
•
•
•
•
•
•
•
•
•
•
•
Prove geometric theorems
Alternate exterior angles
Alternate exterior angles 2
Alternate interior angles 2
Congruency postulates
Corresponding angles
Parallel lines 1
Same side exterior angles
Same side exterior angles 2
Same side interior angles
Same side interior angles 2
Vertical angles
Exeter MAT 210/220/230:
Integrated Mathematics
Geometry
9-12.G-CO.9
Congruence
Geometry
9-12.G-GMD.1
Geometric Measurement and Dimension
Geometry
9-12.G-GMD.2
Geometric Measurement and Dimension
Geometry
9-12.G-GMD.3
Geometry
9-12.G-GMD.4
Geometric Measurement and Dimension
Identify the shapes of two-dimensional crosssections of three-dimensional objects, and identify
three-dimensional objects generated by rotations of
two-dimensional objects.
Exeter MAT 210/220/230:
Integrated Mathematics
Geometry
9-12.G-GPE.1
Expressing Geometric Properties with
Equations
Derive the equation of a circle of given center and
radius using the Pythagorean Theorem; complete
the square to find the center and radius of a circle
given by an equation.
Exeter MAT 210/220/230:
Integrated Mathematics
Explain volume formulas and use them to solve
problems
Explain volume formulas and use them to solve
problems
Use volume formulas for cylinders, pyramids,
Geometric Measurement and Dimension
cones, and spheres to solve problems._
• Cylinder Volume and Surface Area
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Applying Radical Equations 3
• Cylinder Volume and Surface Area
• Multiplying and Dividing Monomials 2
Exeter MAT 210/220/230:
Integrated Mathematics
• Focus and Directrix of a Parabola 2
• Parabola Focus and Directrix 1
Geometry
Geometry
9-12.G-GPE.2
9-12.G-GPE.3
Expressing Geometric Properties with
Equations
Derive the equation of a parabola given a focus and
directrix.
Expressing Geometric Properties with
Equations
Derive the equations of ellipses and hyperbolas
given the foci, using the fact that the sum or
difference of distances from the foci is constant.
• Parabola intuition 1
• Parabola intuition 2
• Parabola intuition 3
• Foci of a Hyperbola
• Foci of an Ellipse
• Proof: Hyperbola Foci
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Page 90
9-12.G-GPE.4
Expressing Geometric Properties with
Equations
9-12.G-GPE.5
Expressing Geometric Properties with
Equations
9-12.G-GPE.5
Expressing Geometric Properties with
Equations
Geometry
9-12.G-GPE.5
Expressing Geometric Properties with
Equations
Geometry
9-12.G-GPE.5
Expressing Geometric Properties with
Equations
Geometry
9-12.G-GPE.7
Expressing Geometric Properties with
Equations
Geometry
9-12.G-MG.1
Modeling with Geometry
Geometry
9-12.G-MG.2
Modeling with Geometry
Geometry
9-12.G-MG.3
Modeling with Geometry
Geometry
9-12.G-SRT.1
Similarity, Right Triangles, and
Trigonometry
Geometry
Geometry
Geometry
Geometry
9-12.G-SRT.2
Similarity, Right Triangles, and
Trigonometry
Use coordinates to prove simple geometric
theorems algebraically. For example, prove or
disprove that a figure defined by four given points
in the coordinate plane is a rectangle; prove or
disprove that the point (1, _3) lies on the circle
centered at the origin and containing the point (0,
2).
•
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a
given point).
•
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a
given point).
•
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a
given point).
•
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric •
problems (e.g., find the equation of a line parallel or •
Use coordinates to compute perimeters of polygons •
and areas of triangles and rectangles, e.g., using the
distance formula._
Use geometric shapes, their measures, and their
properties to describe objects (e.g., modeling a tree
trunk or a human torso as a cylinder)._
Apply concepts of density based on area and
volume in modeling situations (e.g., persons per
square mile, BTUs per cubic foot)._
Exeter MAT 210/220/230:
Integrated Mathematics
Equations of Parallel and Perpendicular Lines
Exeter MAT 210/220/230:
Integrated Mathematics
Parallel Line Equation
Exeter MAT 210/220/230:
Integrated Mathematics
Parallel Lines
Exeter MAT 210/220/230:
Integrated Mathematics
Parallel Lines 2
Parallel lines 3
...and 1 more ...
Distance Formula
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Apply geometric methods to solve design problems
(e.g., designing an object or structure to satisfy
physical constraints or minimize cost; working with
typographic grid systems based on ratios)._
Verify experimentally the properties of dilations
given by a center and a scale factor:
Given two figures, use the definition of similarity in
terms of similarity transformations to decide if they
are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Similar triangles 1
Exeter MAT 210/220/230:
Integrated Mathematics
• Similar triangles 2
Geometry
9-12.G-SRT.2
Similarity, Right Triangles, and
Trigonometry
9-12.G-SRT.3
Similarity, Right Triangles, and
Trigonometry
Geometry
9-12.G-SRT.4
Similarity, Right Triangles, and
Trigonometry
Geometry
9-12.G-SRT.5
Similarity, Right Triangles, and
Trigonometry
Geometry
Given two figures, use the definition of similarity in
terms of similarity transformations to decide if they
are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
Use the properties of similarity transformations to
establish the AA criterion for two triangles to be
similar.
Prove theorems about triangles. Theorems include: • Visual Pythagorean Theorem Proof
a line parallel to one side of a triangle divides the
other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle
similarity.
Use congruence and similarity criteria for triangles
to solve problems and to prove relationships in
geometric figures.
• Basic Trigonometry
Understand that by similarity, side ratios in right
i
l
i
f h
l
i
h
i
l
• Similar triangles review
• Solving similar triangles 1
Exeter MAT 210/220/230:
Integrated Mathematics
• Solving similar triangles 2
•
•
•
•
•
Similar triangles 1
Similar triangles 2
Similar triangles review
Solving similar triangles 1
Solving similar triangles 2
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Triangle angles 1
Exeter MAT 210/220/230:
Integrated Mathematics
Page 91
Geometry
9-12.G-SRT.6
Geometry
9-12.G-SRT.7
Geometry
9-12.G-SRT.8
Geometry
9-12.N-RN.2
Geometry
9-12.S-CP.1
Geometry
Similarity, Right Triangles, and
Trigonometry
triangles are properties of the angles in the triangle, • Basic Trigonometry II
leading to definitions of trigonometric ratios for
acute angles.
Similarity, Right Triangles, and
Trigonometry
Explain and use the relationship between the sine
and cosine of complementary angles.
• Trigonometry 0.5
• Trigonometry 1
• 30-60-90 Triangles II
Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied
• 45-45-90 Triangles
problems._
Rewrite expressions involving radicals and rational • Deductive Reasoning 2
The Real Number System
exponents using the properties of exponents.
Conditional Probability & the Rules of Understand independence and conditional
Probability
probability and use them to interpret data
Similarity, Right Triangles, and
Trigonometry
9-12.S-CP.2
Understand that two events A and B are
independent if the probability of A and B occurring
Conditional Probability & the Rules of
together is the product of their probabilities, and
Probability
use this characterization to determine if they are
independent.
9-12.S-CP.3
Understand the conditional probability of A given B
as P(A and B)/P(B), and interpret independence of
Conditional Probability & the Rules of A and B as saying that the conditional probability of
Probability
A given B is the same as the probability of A, and
the conditional probability of B given A is the same
as the probability of B.
9-12.S-CP.5
Recognize and explain the concepts of conditional
probability and independence in everyday language
Conditional Probability & the Rules of and everyday situations. For example, compare the
Probability
chance of having lung cancer if you are a smoker
with the chance of being a smoker if you have lung
cancer.
• Triangle angles 1
• Trigonometry 0.5
• Conditional statements
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT40S: Introduction to
Statistics
• Conditional statements
• Logical arguments and deductive reasoning
Exeter MAT40S: Introduction to
Statistics
• Conditional statements and truth value
Geometry
Geometry
Algebra 2
9-12.A-SSE.3.a
Seeing Structure in Expressions
Algebra 2
9-12.A-SSE.3.b
Seeing Structure in Expressions
Algebra 2
9-12.A-SSE.3.c
Seeing Structure in Expressions
• Logical arguments and deductive reasoning
Exeter MAT40S: Introduction to
Statistics
• Conditional statements and truth value
Exeter MAT40S: Introduction to
Statistics
•
•
Factor a quadratic expression to reveal the zeros of •
the function it defines.
•
•
•
•
•
•
Complete the square in a quadratic expression to
reveal the maximum or minimum value of the
•
function it defines.
•
•
•
•
Use the properties of exponents to transform
expressions for exponential functions. For example •
the expression 1.15^t can be rewritten as
•
(1.15^1/12)^12t _ 1.012^12t to reveal the
approximate equivalent monthly interest rate if the •
annual rate is 15%.
•
Applications Problem Factoring Quadratics
Factoring Quadratic Expressions
Factoring Special Products
Quadratic Formula 3
Solving a quadratic by factoring
...and 2 more ...
Completing the square
Completing the Square 1
Completing the Square 2
Completing the Square 3
Completing the Square 4
Quadratic Functions 2
Solving Quadratic Equations by Completing the Square
Exponential Decay Functions
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exponential Growth
Interest (part 2)
Introduction to compound interest and e
Exeter MAT 11T / 120 / 130 :
Algebra
Introduction to interest
• Geometric Sequences (Introduction)
Algebra 2
9-12.A-SSE.4
Seeing Structure in Expressions
Algebra 2
9-12.F-BF.1
Building Functions
Algebra 2
9-12.F-BF.1.b
Building Functions
Derive the formula for the sum of a finite geometric
series (when the common ratio is not 1), and use the
formula to solve problems. For example, calculate • Geometric series sum to figure out mortgage payments
mortgage payments.
Write a function that describes a relationship
between two quantities._
• Exponential Growth
Combine standard function types using arithmetic
operations. For example, build a function that
models the temperature of a cooling body by adding
a constant function to a decaying exponential, and
relate these functions to the model.
Compose functions. For example, if T(y) is the
temperature in the atmosphere as a function of
Exeter MAT 210/220/230:
Integrated Mathematics
• Exponential Growth
Exeter MAT 210/220/230:
Integrated Mathematics
• Parametric Equations 1
Page 92
Algebra 2
Algebra 2
9-12.F-BF.1.c
9-12.F-BF.5
Building Functions
Building Functions
Algebra 2
9-12.F-IF.4
Interpreting Functions
Algebra 2
9-12.F-IF.6
Interpreting Functions
Algebra 2
9-12.F-IF.7.a
Interpreting Functions
Algebra 2
9-12.F-IF.7.c
Interpreting Functions
Algebra 2
9-12.F-IF.7.d
Interpreting Functions
Algebra 2
9-12.F-IF.8.a
Interpreting Functions
Algebra 2
9-12.F-IF.8.b
Interpreting Functions
Algebra 2
9-12.F-LE.1
Linear, Quadratic, and Exponential
Models
Algebra 2
9-12.F-LE.1.a
Linear, Quadratic, and Exponential
Models
Algebra 2
9-12.F-LE.1.c
Linear, Quadratic, and Exponential
Models
p
p
height, and h(t) is the height of a weather balloon as • Parametric Equations 2
a function of time, then T(h(t)) is the temperature at
the location of the weather balloon as a function of • Parametric Equations 3
time.
• Introduction to logarithm properties
Understand the inverse relationship between
• Introduction to logarithm properties (part 2)
exponents and logarithms and use this relationship
• Introduction to Logarithms
to solve problems involving logarithms and
exponents.
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
• Operations with logarithms
• Parametric Equations 1
For a function that models a relationship between
two quantities, interpret key features of graphs and
tables in terms of the quantities, and sketch graphs
showing key features given a verbal description of
the relationship. Key features include: intercepts;
• ...and 3 more ...
intervals where the function is increasing,
decreasing, positive, or negative; relative maximum
and minimums; symmetries; end behavior; and
periodicity._
Calculate and interpret the average rate of change •
of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of
change from a graph._
•
•
•
Graph linear and quadratic functions and show
intercepts, maxima, and minima.
Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing
end behavior.
•
Graph rational functions, identifying zeros and
asymptotes when suitable factorizations are
•
available, and showing end behavior.
•
•
•
•
Use the process of factoring and completing the
•
square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and
interpret these in terms of a context.
Parametric Equations 1
Exeter MAT 210/220/230:
Integrated Mathematics
Applying Quadratic Functions 1
Applying Quadratic Functions 3
...and 12 more ...
• Graphing parabolas in all forms
• Graphing parabolas in standard form
• Graphing parabolas in vertex form
• Graphing parabolas in all forms
• Graphing parabolas in standard form
• Graphing parabolas in vertex form
A Third Example of Graphing a Rational Function
Another Rational Function Graph Example
Asymptotes of Rational Functions
Factoring Quadratic Expressions
Factoring Special Products
Quadratic Functions 2
Solving Quadratic Equations by Completing the Square
• Factoring difference of squares 1
• Factoring difference of squares 2
• Factoring difference of squares 3
• Solving quadratics by taking the square root
Exponential Decay Functions
•
Use the properties of exponents to interpret
expressions for exponential functions. For example,
identify percent rate of change in functions such as • Exponential Growth
y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y =
(1.2)^t/10, and classify them as representing
• Exponential Growth Functions
exponential growth or decay.
Distinguish between situations that can be modeled •
with linear functions and with exponential functions.•
•
Prove that linear functions grow by equal
differences over equal intervals, and that
exponential functions grow by equal factors over
equal intervals.
•
Recognize situations in which a quantity grows or
decays by a constant percent rate per unit interval •
relative to another.
•
Exeter MAT 210/220/230:
Integrated Mathematics
Identifying Exponential Models
Identifying Quadratic Models
Identifying Exponential Models
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
Exponential Decay Functions
Exponential Growth Functions
Geometric Sequences (Introduction)
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
• Geometric Sequences (Introduction)
Algebra 2
9-12.F-LE.2
Linear, Quadratic, and Exponential
Models
Construct linear and exponential functions,
including arithmetic and geometric sequences, given• Geometric series sum to figure out mortgage payments
a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).
• Word Problem Solving- Exponential Growth and Decay
Exeter MAT 11T / 120 / 130 :
Algebra
Page 93
Algebra 2
9-12.F-LE.4
Linear, Quadratic, and Exponential
Models
Algebra 2
9-12.F-LE.5
Linear, Quadratic, and Exponential
Models
Algebra 2
9-12.G-GPE.1
Expressing Geometric Properties with
Equations
Algebra 2
9-12.G-GPE.2
Expressing Geometric Properties with
Equations
Algebra 2
9-12.G-GPE.3
Expressing Geometric Properties with
Equations
Algebra 2
Algebra 2
9-12.N-CN.1
9-12.N-CN.2
The Complex Number System
The Complex Number System
For exponential models, express as a logarithm the
solution to ab^ct = d where a, c, and d are numbers
and the base b is 2, 10, or e; evaluate the logarithm
using technology.
Interpret the parameters in a linear or exponential • Parametric Equations 1
function in terms of a context.
Derive the equation of a circle of given center and • Conic Sections: Intro to Circles
radius using the Pythagorean Theorem; complete
the square to find the center and radius of a circle
given by an equation.
Derive the equation of a parabola given a focus and
directrix.
• Conic Sections: Hyperbolas 2
• Conic Sections: Hyperbolas 3
Derive the equations of ellipses and hyperbolas
• Conic Sections: Intro to Ellipses
given the foci, using the fact that the sum or
• Conic Sections: Intro to Hyperbolas
difference of distances from the foci is constant.
Perform arithmetic operations with complex
numbers
Perform arithmetic operations with complex
numbers
• Solving logarithms
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
•
•
•
•
Equation of a circle in factored form
Equation of a circle in non-factored form
Recognizing conic sections
Vertex of a parabola
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 11T / 120 / 130 :
Algebra
Exeter MAT 11T / 120 / 130 :
Algebra
• Equation of a hyperbola
• Equation of an ellipse
• Basic Complex Analysis
• Complex Numbers (part 1)
• Introduction to i and Imaginary Numbers
• Imaginary unit powers
•
•
•
•
•
•
•
Associative Law of Multiplication
Associative property for multiplication
Basic Complex Analysis
Commutative Law of Addition
Commutative Law of Multiplication
Commutative Property for Addition
Complex Numbers (part 1)
• Adding and subtracting complex numbers
• Multiplying complex numbers
Algebra 2
9-12.N-CN.3
The Complex Number System
•
Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex •
numbers.
•
Represent complex numbers on the complex plane
in rectangular and polar form (including real and
imaginary numbers), and explain why the
•
rectangular and polar forms of a given complex
number represent the same number.
Algebra 2
9-12.N-CN.4
The Complex Number System
Algebra 2
9-12.N-CN.5
The Complex Number System
Represent complex numbers and their operations on
the complex plane
Algebra 2
9-12.N-CN.6
The Complex Number System
Calculate the distance between numbers in the
complex plane as the modulus of the difference, and
the midpoint of a segment as the average of the
numbers at its endpoints.
Complex Conjugates
Complex Numbers (part 2)
• Dividing complex numbers
Basic Complex Analysis
Exponential form to find complex roots
• Basic Complex Analysis
Algebra 2
9-12.N-CN.7
The Complex Number System
• Absolute value of complex numbers
• The complex plane
•
•
•
•
Solve quadratic equations with real coefficients that
•
have complex solutions.
•
•
•
Applications Problem Factoring Quadratics
Applying Quadratic Functions 1
Applying Quadratic Functions 2
Applying Quadratic Functions 3
Evaluating a polynomial at a given value
Non-Linear Systems of Equations 1
Non-Linear Systems of Equations 2
...and 13 more ...
• Quadratic formula
Algebra 2
9-12.N-CN.8
The Complex Number System
Use complex numbers in polynomial identities and
equations
Algebra 2
9-12.N-CN.9
The Complex Number System
Know the Fundamental Theorem of Algebra; show
that it is true for quadratic polynomials.
Algebra 2
9-12.N-VM.1
Vector and Matrix Quantities
Recognize vector quantities as having both
magnitude and direction. Represent vector
quantities by directed line segments, and use
magnitudes (e.g., v, |v|, ||v||, v).
• Gradient 1
appropriate
symbols
• Line Integrals
and for
Vector Fields
vectors and their
Page 94
• Gradient of a scalar field
Exeter MAT 210/220/230:
Integrated Mathematics
magnitudes (e.g., v, |v|, ||v||, v).
• Line Integrals and Vector Fields
Page 94
Algebra 2
9-12.N-VM.10
Vector and Matrix Quantities
• Identity property of 0
Understand that the zero and identity matrices play
a role in matrix addition and multiplication similar
to the role of 0 and 1 in the real numbers. The
• Identity Property of 1
determinant of a square matrix is nonzero if and
only if the matrix has a multiplicative inverse.
Algebra 2
9-12.N-VM.11
Vector and Matrix Quantities
Multiply a vector (regarded as a matrix with one
column) by a matrix of suitable dimensions to
produce another vector. Work with matrices as
transformations of vectors.
Algebra 2
9-12.N-VM.12
Vector and Matrix Quantities
Algebra 2
9-12.N-VM.2
Vector and Matrix Quantities
Algebra 2
9-12.N-VM.4
Vector and Matrix Quantities
Add and subtract vectors.
Algebra 2
9-12.N-VM.4.a
Vector and Matrix Quantities
Add vectors end-to-end, component-wise, and by
the parallelogram rule. Understand that the
magnitude of a sum of two vectors is typically not
the sum of the magnitudes.
Algebra 2
9-12.N-VM.4.b
Vector and Matrix Quantities
Given two vectors in magnitude and direction form,
determine the magnitude and direction of their sum.
Algebra 2
9-12.N-VM.4.c
Vector and Matrix Quantities
Perform operations on vectors
Exeter MAT 210/220/230:
Integrated Mathematics
Algebra 2
9-12.N-VM.5
Vector and Matrix Quantities
Multiply a vector by a scalar.
Exeter MAT 210/220/230:
Integrated Mathematics
Algebra 2
9-12.N-VM.5.a
Vector and Matrix Quantities
Algebra 2
9-12.N-VM.5.b
Vector and Matrix Quantities
Algebra 2
9-12.N-VM.6
Vector and Matrix Quantities
Algebra 2
9-12.N-VM.7
Vector and Matrix Quantities
Algebra 2
9-12.N-VM.8
Algebra 2
9-12.N-VM.9
Algebra 2
9-12.S-ID.2
9-12.S-ID.6.a
Trigonometry
9-12.A-REI.4
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
• Adding vectors
Exeter MAT 210/220/230:
Integrated Mathematics
• Adding vectors
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Add, subtract, and multiply matrices of appropriate
dimensions.
Understand that, unlike multiplication of numbers,
matrix multiplication for square matrices is not a
Vector and Matrix Quantities
commutative operation, but still satisfies the
associative and distributive properties.
Use statistics appropriate to the shape of the data
Interpreting Categorical and Quantitative distribution to compare center (median, mean) and
Data
spread (interquartile range, standard deviation) of
two or more different data sets.
Fit a function to the data; use functions fitted to
data to solve problems in the context of the data.
Interpreting Categorical and Quantitative
Use given functions or choose a function suggested
Data
by the context. Emphasize linear, quadratic, and
exponential models.
Solve quadratic equations in one variable.
Trigonometry
9-12.F-BF.4
Building Functions
Find inverse functions.
Trigonometry
9-12.F-BF.4.a
Building Functions
Build new functions from existing functions
Trigonometry
9-12.F-BF.4.b
Building Functions
Verify by composition that one function is the
inverse of another.
Exeter MAT 210/220/230:
Integrated Mathematics
• Scaling vectors
Represent scalar multiplication graphically by
scaling vectors and possibly reversing their
direction; perform scalar multiplication componentwise, e.g., as c(vx, vy) = (cvx, cvy).
Compute the magnitude of a scalar multiple cv
using ||cv|| = |c|v. Compute the direction of cv
knowing that when |c|v _ 0, the direction of cv is
either along v (for c > 0) or against v (for c < 0).
Use matrices to represent and manipulate data, e.g.,
to represent payoffs or incidence relationships in a
network.
Multiply matrices by scalars to produce new
matrices, e.g., as when all of the payoffs in a game
are doubled.
Vector and Matrix Quantities
Reasoning with Equations and
Inequalities
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Perform operations on matrices and use matrices in
applications
Find the components of a vector by subtracting the
coordinates of an initial point from the coordinates
of a terminal point.
• Adding vectors
Algebra 2
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
• Exploring standard deviation 1
Exeter MAT40S: Introduction to
Statistics
• Quadratic formula
Exeter MAT 11T / 120 / 130 :
Algebra
• Fun Trig Problem
•
•
•
•
Exeter MAT 11T / 120 / 130 :
Algebra
Inverse Trig Functions: Arccos
Inverse Trig Functions: Arcsin
Inverse Trig Functions: Arctan
Polar Coordinates 1
Exeter MAT 210/220/230:
Integrated Mathematics
• Inverses of functions
• Inverse Trig Functions: Arcsin
• Inverse Trig Functions: Arctan
• Inverses of functions
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Page 95
Trigonometry
9-12.F-BF.4.c
Building Functions
Trigonometry
9-12.F-IF.7.e
Interpreting Functions
Trigonometry
9-12.F-TF.1
Trigonometric Functions
Read values of an inverse function from a graph or
a table, given that the function has an inverse.
Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period, midline,
and amplitude.
•
•
•
•
•
Understand radian measure of an angle as the length
•
of the arc on the unit circle subtended by the angle.
Explain how the unit circle in the coordinate plane
enables the extension of trigonometric functions to
all real numbers, interpreted as radian measures of
angles traversed counterclockwise around the unit
circle.
Trigonometry
9-12.F-TF.2
Trigonometric Functions
Trigonometry
9-12.F-TF.3
Trigonometric Functions
Trigonometry
9-12.F-TF.4
Trigonometric Functions
Use the unit circle to explain symmetry (odd and
even) and periodicity of trigonometric functions.
Trigonometry
9-12.F-TF.5
Trigonometric Functions
Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency,
and midline._
Trigonometry
9-12.F-TF.6
Trigonometric Functions
Trigonometry
9-12.F-TF.7
Trigonometric Functions
Trigonometry
Trigonometry
9-12.F-TF.8
Trigonometric Functions
9-12.F-TF.9
Trigonometric Functions
Trigonometry
9-12.G-SRT.10
Similarity, Right Triangles, and
Trigonometry
Trigonometry
9-12.G-SRT.11
Similarity, Right Triangles, and
Trigonometry
Trigonometry
9-12.G-SRT.6
Similarity, Right Triangles, and
Trigonometry
• Inverse Trig Functions: Arctan
•
•
•
•
•
Extend the domain of trigonometric functions using •
the unit circle
•
•
•
•
•
•
•
•
Understand that restricting a trigonometric function •
to a domain on which it is always increasing or
always decreasing allows its inverse to be
constructed.
Use inverse functions to solve trigonometric
•
equations that arise in modeling contexts; evaluate •
the solutions using technology, and interpret them
•
Prove the Pythagorean identity sin2(_) + cos^2(_) =
1 and use it to find sin(_), cos(_), or tan(_) given
sin(_), cos(_), or tan(_) and the quadrant of the
angle.
•
Prove the addition and subtraction formulas for
sine, cosine, and tangent and use them to solve
problems.
•
•
•
•
•
•
•
• Inverses of functions
Determining the equation of a trigonometric function
Graphing trig functions
Graphs of trig functions
More trig graphs
Radians and degrees
The unit circle definition of trigonometric function
• Unit circle
Graph of the sine function
Radians and degrees
The unit circle definition of trigonometric function
Unit Circle Definition of Trig Functions
• Unit circle
Inverse Trig Functions: Arcsin
The unit circle definition of trigonometric function
Using Trig Functions
• Special right triangles
Graphing trig functions
Graphs of trig functions
More trig graphs
• Graphs of sine and cosine
Determining the equation of a trigonometric function
Graphing trig functions
Graphs of trig functions
More trig graphs
Graphs of trig functions
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Inverse Trig Functions: Arcsin
Polar Coordinates 1
• Inverse trig functions
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Fun Trig Problem
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Trigonometric Identities
• Trig identities 1
IIT JEE Trigonometric Constraints
IIT JEE Trigonometric Maximum
IIT JEE Trigonometry Problem 1
Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)
Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)
Trigonometric System Example
Trigonometry Identity Review/Fun
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
• Trig identities 1
Trigonometry
9-12.G-SRT.7
Similarity, Right Triangles, and
Trigonometry
Similarity Right Triangles an
•
Prove the Laws of Sines and Cosines and use them
•
to solve problems.
•
•
Understand and apply the Law of Sines and the
•
Law of Cosines to find unknown measurements in
•
right and non-right triangles (e.g., surveying
•
problems, resultant forces).
•
•
Understand that by similarity, side ratios in right
triangles are properties of the angles in the triangle, •
leading to definitions of trigonometric ratios for
•
acute angles.
Explain and use the relationship between the sine
and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean
•
•
•
•
•
•
•
•
•
Law of cosines
Navigation Word Problem
Proof: Law of Sines
Ferris Wheel Trig Problem
Ferris Wheel Trig Problem (part 2)
Law of cosines
Navigation Word Problem
Proof: Law of Sines
IIT JEE Trigonometric Constraints
Unit Circle Definition of Trig Functions
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
Exeter MAT 210/220/230:
Integrated Mathematics
Using Trig Functions Part II
Fun Trig Problem
• Trigonometry 0.5
Graphs of trig functions
• Trigonometry 1
Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)
Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)
The unit circle definition of trigonometric function
Basic Trigonometry
Basic Trigonometry II
Ferris Wheel Trig Problem
Ferris Wheel Trig Problem (part 2)
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT 210/220/230:
Page 96
Trigonometry
9-12.G-SRT.8
, Right
Trigonometry
, and
Theorem to solve right triangles in applied
problems._
MAT
Integrated Mathematics
• Graph of the sine function
• IIT JEE Trigonometric Constraints
• ...and 15 more ...
• Trigonometry 1.5
• Trigonometry 2
Trigonometry
9-12.G-SRT.9
Calculus
9-12.A-APR.5
Similarity, Right Triangles, and
Trigonometry
Derive the formula A = 1/2 ab sin(C) for the area of • 2003 AIME II Problem 11.avi
a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
Arithmetic with Polynomials and Rational
Use polynomial identities to solve problems
Expressions
Calculus
9-12.A-CED.2
Creating Equations*
Calculus
9-12.A-CED.3
Creating Equations*
Calculus
9-12.A-CED.4
Creating Equations*
• Proof: d/dx(x^n)
• Calculus: Derivatives 1 (new HD version)
• Epsilon Delta Limit Definition 2
Create equations in two or more variables to
represent relationships between quantities; graph
• Introduction to Limits
equations on coordinate axes with labels and scales. • Introduction to Limits (HD)
• Limit Examples (part 1)
Represent constraints by equations or inequalities, • Epsilon Delta Limit Definition 2
and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in
a modeling context. For example, represent
• Limit Examples (part 1)
inequalities describing nutritional and cost
constraints on combinations of different foods.
Create equations that describe numbers or
relationship
• Epsilon Delta Limit Definition 2
9-12.A-REI.10
Reasoning with Equations and
Inequalities
Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the • Calculus: Derivatives 1 (new HD version)
coordinate plane, often forming a curve (which
could be a line).
• Limit Examples (part 1)
Calculus
9-12.A-REI.4
Reasoning with Equations and
Inequalities
Solve quadratic equations in one variable.
Calculus
9-12.A-SSE.1.b
Seeing Structure in Expressions
Calculus
9-12.A-SSE.2
Seeing Structure in Expressions
Calculus
9-12.A-SSE.3.a
Seeing Structure in Expressions
Calculus
9-12.A-SSE.3.a
Seeing Structure in Expressions
Calculus
9-12.F-BF.1
Building Functions
Calculus
9-12.F-BF.1.c
Building Functions
9-12.F-IF.1
Interpreting Functions
Calculus
9-12.F-IF.2
Interpreting Functions
Calculus
9-12 F-IF 4
Interpreting Function
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
• Calculus BC 2008 2 a
Calculus
Calculus
Exeter MAT 310/320/330/340:
Advanced Integrated Mathematics
• Extreme Derivative Word Problem (advanced)
Interpret complicated expressions by viewing one or • Chain Rule Examples
more of their parts as a single entity. For example,
interpret P(1+r)^n as the product of P and a factor
not depending on P.
• Chain Rule Examples
Interpret the structure of expressions
Factor a quadratic expression to reveal the zeros of •
the function it defines.
Factor a quadratic expression to reveal the zeros of •
the function it defines.
•
Write a function that describes a relationship
•
between two quantities._
•
Compose functions. For example, if T(y) is the
temperature in the atmosphere as a function of
height, and h(t) is the height of a weather balloon as
a function of time, then T(h(t)) is the temperature at
the location of the weather balloon as a function of
time.
Understand that a function from one set (called the •
domain) to another set (called the range) assigns to
each element of the domain exactly one element of
the range. If f is a function and x is an element of its
domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the
graph of the equation y = f(x).
Use function notation, evaluate functions for inputs •
in their domains, and interpret statements that use
function notation in terms of a context.
•
For a function that models a relationship between
two quantities, interpret key features of graphs and
tables in terms of the quantities, and sketch graphs
showing key features given a verbal description of
the relationship Key features include: intercepts;
Limit Examples (part3)
Limit Examples w/ brain malfunction on first prob (part 4)
Introduction to Limits
Limit Examples (part 1)
Introduction to Limits
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Squeeze Theorem
Exeter MAT 420/430/440/450:
Calculus
Introduction to Limits
Exeter MAT 420/430/440/450:
Calculus
Calculus: Maximum and minimum values on an interval
Exeter MAT 420/430/440/450:
Page 97
.F-IF.
Interpreting
Calculus
9-12.F-IF.5
Interpreting Functions
Calculus
9-12.F-IF.6
Interpreting Functions
Calculus
9-12.F-IF.7
Interpreting Functions
Calculus
9-12.F-IF.7.a
Interpreting Functions
Calculus
9-12.F-IF.7.c
Interpreting Functions
Calculus
9-12.F-IF.7.d
Interpreting Functions
Calculus
9-12.F-IF.7.e
Interpreting Functions
Calculus
9-12.F-IF.8
Interpreting Functions
Calculus
9-12.F-IF.8.a
Interpreting Functions
Calculus
9-12.G-GMD.1
Geometric Measurement and Dimension
Statistics
9-12.S-CP.1
Statistics
9-12.S-CP.2
Statistics
9-12.S-CP.3
the
. Key
include:
• Limit Examples (part 2)
intervals where the function is increasing,
decreasing, positive, or negative; relative maximums
and minimums; symmetries; end behavior; and
periodicity._
• Squeeze Theorem
Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives
the number of person-hours it takes to assemble n
engines in a factory, then the positive integers
would be an appropriate domain for the function._
Calculate and interpret the average rate of change • Mean Value Theorem
of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of
change from a graph._
• Calculus Graphing with Derivatives Example
• Calculus: Graphing Using Derivatives
Graph functions expressed symbolically and show • Graphing with Calculus
key features of the graph, by hand in simple cases • Introduction to definite integrals
and using technology for more complicated cases._ • Introduction to Limits
• More Limits
• ...and 2 more ...
• Calculus: Maximum and minimum values on an interval
Graph linear and quadratic functions and show
intercepts, maxima, and minima.
Graph polynomial functions, identifying zeros when • Calculus: Graphing Using Derivatives
suitable factorizations are available, and showing
end behavior.
• Limit Examples (part 1)
Graph rational functions, identifying zeros and
asymptotes when suitable factorizations are
• Limit Examples (part 2)
available, and showing end behavior.
Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period, midline,
and amplitude.
Write a function defined by an expression in
different but equivalent forms to reveal and explain
different properties of the function.
Use the process of factoring and completing the
square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and
interpret these in terms of a context.
• Visualizing Taylor Series Approximations
Explain volume formulas and use them to solve
problems
• Introduction to rate-of-change problems
• Visualizing Taylor Series for e^x
• Limit Examples (part3)
i d
d t
dt
i
t
diti
l
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
Exeter MAT 420/430/440/450:
Calculus
• Limit Examples (part3)
Exeter MAT 420/430/440/450:
Calculus
•
•
•
•
•
•
Understand that two events A and B are
•
independent if the probability of A and B occurring
Conditional Probability & the Rules of
•
together is the product of their probabilities, and
Probability
•
use this characterization to determine if they are
•
independent.
•
Understand the conditional probability of A given B •
as P(A and B)/P(B), and interpret independence of •
Conditional Probability & the Rules of A and B as saying that the conditional probability of •
Probability
A given B is the same as the probability of A, and •
the conditional probability of B given A is the same •
as the probability of B.
•
Construct and interpret two-way frequency tables
•
of data when two categories are associated with
each object being classified. Use the two-way table
•
as a sample space to decide if events are
Conditional Probability & the Rules of Understand independence and conditional
Probability
probability and use them to interpret data
Calculus
Birthday Probability Problem
Conditional Probability and Combinations
Probability (part 5)
Probability and Combinations (part 2)
Probability using Combinations
Independent Events 1
Independent Events 2
Independent Events 3
Probability (part 4)
Probability of Dependent Events
Probability of Dependent Events 2
Conditional Probability and Combinations
Dependent Probability Example 1
Dependent Probability Example 2
Probability (part 6)
Probability (part 7)
Exeter MAT 210/220/230:
Integrated Mathematics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
• Dependent probability
ANOVA 1 - Calculating SST (Total Sum of Squares)
ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi
ANOVA 3 -Hypothesis Test with F-Statistic
Page 98
Statistics
Statistics
9-12.S-CP.4
9-12.S-CP.5
Statistics
9-12.S-CP.6
Statistics
9-12.S-CP.7
Statistics
9-12.S-CP.8
independent and to approximate conditional
Conditional Probability & the Rules of probabilities. For example, collect data from a
Probability
random sample of students in your school on their
favorite subject among math, science, and English.
Estimate the probability that a randomly selected
student from your school will favor science given
that the student is in tenth grade. Do the same for
other subjects and compare the results.
• Conditional Probability and Combinations
Recognize and explain the concepts of conditional
probability and independence in everyday language
Conditional Probability & the Rules of and everyday situations. For example, compare the
Probability
chance of having lung cancer if you are a smoker
with the chance of being a smoker if you have lung
cancer.
•
•
•
•
•
Conditional Probability and Combinations
Dependent Probability Example 1
Dependent Probability Example 2
Probability (part 6)
Probability (part 7)
•
•
Conditional Probability & the Rules of Use the rules of probability to compute probabilities •
of
compound
events
in
a
uniform
probability
model
Probability
•
•
•
•
Conditional Probability & the Rules of Use the rules of probability to compute probabilities
Probability
of compound events in a uniform probability model
Conditional Probability and Combinations
Dependent Probability Example 1
Dependent Probability Example 2
Probability (part 6)
Probability (part 7)
Probability (part 8)
Probability (part 5)
• Probability using Combinations
• Independent probability
•
•
•
•
Use permutations and combinations to compute
Conditional Probability & the Rules of
•
probabilities of compound events and solve
Probability
problems.
•
•
•
•
•
•
•
•
Understand statistics as a process for making
Making Inferences and Justifying
inferences about population parameters based on a •
Conclusions
random sample from that population.
•
•
•
•
Decide if a specified model is consistent with results •
9-12.S-CP.9
Statistics
9-12.S-IC.1
Statistics
9-12.S-IC.2
Making Inferences and Justifying
Conclusions
Statistics
9-12.S-IC.3
Making Inferences and Justifying
Conclusions
9-12.S-IC.4
• Pearson's Chi Square Test (Goodness of Fit)
Exeter MAT40S: Introduction to
Statistics
• Independent probability
Apply the general Multiplication Rule in a uniform • Probability (part 6)
Conditional Probability & the Rules of probability model, P(A and B) = P(A)P(B|A) =
• Probability (part 7)
Probability
P(B)P(A|B), and interpret the answer in terms of
• Probability (part 8)
the model.
Statistics
Statistics
Exeter MAT40S: Introduction to
Statistics
• Independent Events 2
Making Inferences and Justifying
Conclusions
Birthday Probability Problem
Combinations
Conditional Probability and Combinations
Permutations
Permutations and Combinations 1
Permutations and Combinations 2
Permutations and Combinations 3
Permutations and Combinations 4
...and 2 more ...
Central Limit Theorem
Confidence Interval Example
Law of Large Numbers
Margin of Error 1
Margin of Error 2
Sampling Distribution of the Sample Mean
Sampling Distribution of the Sample Mean 2
Standard Error of the Mean
...and 4 more ...
Chi-Square Distribution Introduction
from a given data-generating process, e.g., using
simulation. For example, a model says a spinning • Pearson's Chi Square Test (Goodness of Fit)
coin falls heads up with probability 0.5. Would a
result of 5 tails in a row cause you to question the • Type 1 Errors
model?
Recognize the purposes of and differences among •
sample surveys, experiments, and observational
studies; explain how randomization relates to each.
•
•
•
Use data from a sample survey to estimate a
•
population mean or proportion; develop a margin of
•
error through the use of simulation models for
•
random sampling.
•
•
•
•
•
•
Surveys and Samples
Confidence Interval 1
Confidence Interval Example
Law of Large Numbers
Margin of Error 1
Margin of Error 2
Sampling Distribution of the Sample Mean
Statistics: Sample vs. Population Mean
Statistics: The Average
...and 1 more ...
ANOVA 1 - Calculating SST (Total Sum of Squares)
ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi
ANOVA 3 -Hypothesis Test with F-Statistic
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Page 99
Statistics
9-12.S-IC.5
Making Inferences and Justifying
Conclusions
Statistics
9-12.S-IC.6
Making Inferences and Justifying
Conclusions
Statistics
9-12.S-ID.1
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.2
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.2
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.3
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.4
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.5
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.6
Interpreting Categorical and Quantitative
Data
Use data from a randomized experiment to compare • Chi-Square Distribution Introduction
two treatments; use simulations to decide if
• Comparing Population Proportions 1
differences between parameters are significant.
• Comparing Population Proportions 2
• Confidence Interval of Difference of Means
• Contingency Table Chi-Square Test
• ...and 4 more ...
• Hypothesis Testing and P-values
Evaluate reports based on data.
• One-Tailed and Two-Tailed Tests
• T-Statistic Confidence Interval
• Box-and-whisker Plot
• Central Limit Theorem
• Histograms
• Law of Large Numbers
Represent data with plots on the real number line
• Sampling Distribution Example Problem
(dot plots, histograms, and box plots).
• Sampling Distribution of the Sample Mean
• Sampling Distribution of the Sample Mean 2
• Standard Error of the Mean
• ...and 1 more ...
• Average or Central Tendency: Arithmetic Mean, Median, and Mode
Use statistics appropriate to the shape of the data
distribution to compare center (median, mean) and
spread (interquartile range, standard deviation) of
two or more different data sets.
• Central Limit Theorem
• Confidence Interval of Difference of Means
• Difference of Sample Means Distribution
• Hypothesis Testing and P-values
• Range, Variance and Standard Deviation as Measures of Dispersion
Use statistics appropriate to the shape of the data
• Sampling Distribution of the Sample Mean
distribution to compare center (median, mean) and
• Standard deviation
spread (interquartile range, standard deviation) of
• Sampling Distribution of the Sample Mean 2
two or more different data sets.
• Variance
• ...and 1 more ...
• Z scores 1
• Z scores 2
• Z scores 3
Interpret differences in shape, center, and spread in • ck12.org Normal Distribution Problems: Qualitative sense of normal distributions
the context of the data sets, accounting for possible • Sampling Distribution of the Sample Mean
effects of extreme data points (outliers).
• Creating box and whisker plots
• Central Limit Theorem
• ck12.org Exercise: Standard Normal Distribution and the Empirical Rule
• ck12.org Normal Distribution Problems: Empirical Rule
• ck12.org Normal Distribution Problems: Qualitative sense of normal distributions
Use the mean and standard deviation of a data set • ck12.org Normal Distribution Problems: z-score
• ck12.org: More Empirical Rule and Z-score practice
to fit it to a normal distribution and to estimate
• Confidence Interval Example
population percentages. Recognize that there are
data sets for which such a procedure is not
• Introduction to the Normal Distribution
appropriate. Use calculators, spreadsheets, and
• ...and 7 more ...
tables to estimate areas under the normal curve.
• Empirical rule
• Exploring standard deviation 1
• Z scores 1
• Z scores 2
• Z scores 3
• Contingency Table Chi-Square Test
Summarize categorical data for two categories in
two-way frequency tables. Interpret relative
frequencies in the context of the data (including
joint, marginal, and conditional relative
frequencies). Recognize possible associations and
trends in the data.
• Calculating R-Squared
• Covariance and the Regression Line
• Fitting a Line to Data
Represent data on two quantitative variables on a • Law of Large Numbers
scatter plot, and describe how the variables are
• Proof (Part 1) Minimizing Squared Error to Regression Line
related.
• Proof (Part 3) Minimizing Squared Error to Regression Line
• Proof (Part 4) Minimizing Squared Error to Regression Line
• R-Squared or Coefficient of Determination
• ...and 2 more ...
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Page 100
•
•
•
•
•
•
•
•
•
•
Informally assess the fit of a function by plotting
•
and analyzing residuals.
•
•
•
•
•
•
•
Fit a linear function for a scatter plot that suggests a
•
linear association.
•
•
•
•
•
•
Interpret the slope (rate of change) and the
•
intercept (constant term) of a linear model in the
context of the data.
•
•
•
Compute (using technology) and interpret the
correlation coefficient of a linear fit.
Linear, Quadratic, and Exponential Models
Predicting with Linear Models
Proof (Part 1) Minimizing Squared Error to Regression Line
Proof (Part 3) Minimizing Squared Error to Regression Line
Proof (Part 4) Minimizing Squared Error to Regression Line
Second Regression Example
Squared Error of Regression Line
Calculating R-Squared
Proof (Part 1) Minimizing Squared Error to Regression Line
Proof (Part 3) Minimizing Squared Error to Regression Line
Proof (Part 4) Minimizing Squared Error to Regression Line
R-Squared or Coefficient of Determination
Second Regression Example
Squared Error of Regression Line
Calculating R-Squared
Fitting a Line to Data
Predicting with Linear Models
Proof (Part 1) Minimizing Squared Error to Regression Line
Proof (Part 3) Minimizing Squared Error to Regression Line
Proof (Part 4) Minimizing Squared Error to Regression Line
R-Squared or Coefficient of Determination
Second Regression Example
...and 2 more ...
Calculating R-Squared
Fitting a Line to Data
Second Regression Example
X and Y intercepts
X and Y intercepts 2
Calculating R-Squared
•
Define a random variable for a quantity of interest •
by assigning a numerical value to each event in a
•
sample space; graph the corresponding probability •
distribution using the same graphical displays as for •
data distributions.
•
•
•
•
•
Calculate the expected value of a random variable; •
interpret it as the mean of the probability
•
distribution.
•
•
•
•
•
Develop a probability distribution for a random
•
variable defined for a sample space in which
theoretical probabilities can be calculated; find the •
•
expected value. For example, find the theoretical
probability distribution for the number of correct
•
answers obtained by guessing on all five questions •
of a multiple-choice test where each question has •
four choices, and find the expected grade under
•
various grading schemes.
•
•
Develop a probability distribution for a random
•
variable defined for a sample space in which
•
probabilities are assigned empirically; find the
•
expected value. For example, find a current data
•
distribution on the number of TV sets per
household in the United States, and calculate the
•
expected number of sets per household. How many •
TV sets would you expect to find in 100 randomly •
selected households?
•
•
Weigh the possible outcomes of a decision by
•
Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Introduction to Random Variables
Law of Large Numbers
Probability Density Functions
Bernoulli Distribution Mean and Variance Formulas
Chi-Square Distribution Introduction
Expected Value: E(X)
Introduction to Random Variables
Law of Large Numbers
Mean and Variance of Bernoulli Distribution Example
Pearson's Chi Square Test (Goodness of Fit)
Probability Density Functions
...and 1 more ...
Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Birthday Probability Problem
Expected Value of Binomial Distribution
Expected Value: E(X)
Independent Events 2
...and 4 more ...
ANOVA 1 - Calculating SST (Total Sum of Squares)
Bernoulli Distribution Mean and Variance Formulas
Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Chi-Square Distribution Introduction
Expected Value of Binomial Distribution
...and 8 more ...
Bernoulli Distribution Mean and Variance Formulas
Confidence Interval of Difference of Means
Statistics
9-12.S-ID.6.a
Fit a function to the data; use functions fitted to
data to solve problems in the context of the data.
Interpreting Categorical and Quantitative
Use given functions or choose a function suggested
Data
by the context. Emphasize linear, quadratic, and
exponential models.
Statistics
9-12.S-ID.6.b
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.6.c
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.7
Interpreting Categorical and Quantitative
Data
Statistics
9-12.S-ID.8
Statistics
9-12.S-ID.9
Interpreting Categorical and Quantitative
Data
Interpreting Categorical and Quantitative
Distinguish between correlation and causation.
Data
Statistics
9-12.S-MD.1
Using Probability to Make Decisions
Statistics
9-12.S-MD.2
Using Probability to Make Decisions
Statistics
9-12.S-MD.3
Using Probability to Make Decisions
Statistics
9-12.S-MD.4
Using Probability to Make Decisions
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Page 101
Statistics
9-12.S-MD.5
Using Probability to Make Decisions
Statistics
9-12.S-MD.5.a
Using Probability to Make Decisions
Statistics
9-12.S-MD.5.b
Using Probability to Make Decisions
Statistics
9-12.S-MD.6
Using Probability to Make Decisions
Statistics
9-12.S-MD.7
Using Probability to Make Decisions
assigning probabilities to payoff values and finding • Expected Value of Binomial Distribution
expected values.
• Expected Value: E(X)
• Mean and Variance of Bernoulli Distribution Example
• Birthday Probability Problem
• Conditional Probability and Combinations
Find the expected payoff for a game of chance. For
• Dependent Probability Example 1
example, find the expected winnings from a state
• Dependent Probability Example 2
lottery ticket or a game at a fastfood restaurant.
• Probability (part 6)
• Probability using Combinations
• Poisson Process 1
Evaluate and compare strategies on the basis of
expected values. For example, compare a highdeductible versus a low-deductible automobile
insurance policy using various, but reasonable,
chances of having a minor or a major accident.
• Poisson Process 2
MAT40S:
Statistics
to
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
• Term Life Insurance and Death Probability
•
•
Use probabilities to make fair decisions (e.g.,
drawing by lots, using a random number generator). •
•
•
•
•
Analyze decisions and strategies using probability •
•
concepts (e.g., product testing, medical testing,
pulling a hockey goalie at the end of a game).
•
•
•
•
Poisson Process 1
Poisson Process 2
Small Sample Hypothesis Test
Type 1 Errors
Conditional Probability and Combinations
Confidence Interval of Difference of Means
Hypothesis Testing and P-values
Introduction to Random Variables
One-Tailed and Two-Tailed Tests
Poisson Process 1
Poisson Process 2
Probability (part 6)
...and 7 more ...
Exeter MAT40S: Introduction to
Statistics
Exeter MAT40S: Introduction to
Statistics
Page 102
Denver Public Montessori Secondary School
Performance School Application 2012
Respectfully Submitted
on behalf of the DPMSS Formation Committee by:
Katy Myers
1900 East St. Golden,
CO 80401 (303) 4312385
[email protected]
DPMSS Application
for performance school
Page 103
Denver Public Montessori Secondary School
EXECUTIVE SUMMARY
This section in its entirety will be provided to the Board of Education of Denver Public
Schools and will be posted online for the public to review, immediately upon
submission of this application.
Essential Information Form
Name of Proposed School Denver Public Montessori Secondary School
School Type (Select One) Performance School
Grade Configuration 7th - 12th (6th in first and second year only)
Model or Focus (e.g., Arts, CollegeMontessori
Prep, etc)
Proposed Region for School Attached to an existing DPS Montessori
elementary or centrally located to the four DPS
Montessori elementary schools.
Primary Contact Person Katy Myers; 303-431-2385;
[email protected]
Enrollment Projections: Delete unnecessary rows and/or provide additional columns if
you will not reach full enrollment by year five. Project your student headcount (not your
funded FTEs).
GRADE
6
7
8
9
10
11
12
Total #
students
2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20
25
25
40
40
40
40
40
40
25
40
40
40
40
40
25
40
40
40
40
20
35
35
35
20
35
35
20
35
50
Proposed Demographics
65
105
140
175
220
225
FRL %
Denison: 57
SPED %
Denison: 11
ELL %
Denison: 19
Lincoln 37
Lincoln: 6
Lincoln: 11
Academia Ana
Academia Ana
Academia Ana
Maria Sandoval:39 Maria Sandoval: 5 Maria Sandoval: 41
Gilpin: 89
Performance School Application Guide
Gilpin:: 12
Gilpin: 23
for schools to open 2013-14
Page 104
I. Culture: Denver Public Montessori Secondary School (DPMSS) will combine
Montessori best practices with current research on adolescent brain
development to provide a learning environment that promotes high
achievement for each student while also supporting them socially and
emotionally. Graduates, regardless of ethnicity or income status, will be
prepared for college or a career as well as demonstrate ingenuity, adaptability,
creativity, initiative and excellent communication and problem solving skills.
DPS currently has four Montessori magnet schools that end in either 5th
grade or 6th grade. There are approximately 133 4th grade and 128 5th grade
students. These students do not have an opportunity to continue Montessori
education within DPS. The purpose of this application is to give DPS Montessori
students the ability to continue Montessori education through high school
graduation. DPMSS will work with DPS and the Montessori elementary principals
to either centrally locate the secondary school to the Montessori elementary
schools, or join an existing Montessori school at their campus. DPS Montessori
school leaders recognize the need to continue Montessori education. Without a
secondary option, many students leave Montessori after 5th grade in order to
secure placement at a DPS middle school. Sixth grade students are crucial to
maintaining a high quality Montessori upper elementary classroom. However,
Montessori schools will only be able to retain these students if there is a high
quality Montessori option available to students when they move to 7th grade.
Montessori secondary education focuses on the whole child, self
construction, valorization and preparation for adult life. By creating a high
quality 7th through 12 grade program on these principles, students will
graduate with the academic skills necessary to thrive in both post secondary
education or career options, while at the same time have well developed
communication and problem solving abilities along with strong interpersonal
relationship skills. Finally, they will have developed creativity, ingenuity,
adaptability and initiative through the many problem solving, community
building and real world experiences they will encounter at DPMSS.
This application has the support of all four DPS Montessori elementary
principals. Surveys, both in English and Spanish, have recently been sent to
families in those schools, and, in just three weeks, 52 families indicated strong
interest. DPMSS has reached out to Montessori and community leaders both in
Denver and nationally. DPMSS has included the following people during the
development of this application: Dr. Martha Urioste, Principal Janice Spearman,
Principal Frank Vincent, Katy Mattis (incoming Denison Principal) , Principal
JoAnn Trujillo Hays, John Fowler, Judi Orion (AMI Trainer), David Kahn
(Executive Director of NAMTA), Virginia McHugh, (Director of AMI/USA), along
with Montessori administrators, teachers and parents. DPMSS recognizes that it
takes a strong community to build an excellent school and intends to build that
community during every stage of development.
DPMSS Application
for performance school
Page 105
Denver Public Montessori Secondary School
II. Leadership: Katy Myers is an established Montessori leader. She was a
founding parent of Compass Montessori School which is a pre-k through 12th
grade charter school in Jefferson County, Colorado. Katy was the business
manager and assistant head of school for four years, and head of school for six
years. Katy has experience in all aspects of school leadership, including
budgeting, safety, accountability, staff evaluation, creating positive culture and
climate, and facilities. Katy has also been involved in the national Montessori
secondary movement for the last ten years. She is trained in Montessori
elementary (AMI) and Montessori adolescent education (NAMTA) and earned a
MEd in education leadership and administration at Arizona State University.
At Compass, Katy worked with staff to create an outcomes based
Montessori education system that includes graduation outcomes and written
outcomes for every level. During her tenure as head of school, Compass High
School moved from a non-performing school to a high performing school. In
2011, Compass won the Governor’s award for schools with the highest
2009-2010 academic growth rates in Colorado.
III. Education Plan: Montessori education is a constructivist model based on
creating an optimal prepared environment for students. For preschool through
6th grade, this means creating beautiful, spacious classrooms filled with
scientifically designed Montessori materials that allow students to acquire deep
mathematical, language, science and cultural knowledge. Each classroom
includes a Montessori guide that has obtained rigorous training in child
development, classroom content, and Montessori methodology. In the
September 28, 2006 issue of Science Magazine, Angeline Stoll Lillard published
findings of Montessori education study with the following conclusion:
Comparing outcomes of children at a public inner-city Montessori school with
children who attended traditional schools indicates that Montessori education
leads to children with better social and academic skills.
Montessori secondary education has been in development for 30 years.
During the last fifteen years, there has been signifiant increase in the number of
Montessori schools throughout the United States providing excellent education
from 7th through 12th grade. Leaders in the Montessori secondary education
movement have documented best practices, established training centers, and
provided a network of support to insure new schools can open successfully.
Montessori secondary education is designed for students who have attended
Montessori elementary schools. Montessori observed that this stage of a child’s
development provided excellent opportunity for a student to develop and hone
social and problem solving skills. Montessori wrote about what we now call the
value of 21st Century Learning Skills back in the early 1900s. She predicted that
if adolescent students were allowed to learn in an environment specially
designed for their specific stage of brain development, the result would be
adaptable, independent, ingenious and creative adults with excellent
Performance School Application Guide
for schools to open 2013-14
Page 106
communication and problem solving skills. She laid out a design for this type of
education in “From Childhood to Adolescence”.
Montessori secondary schools are divided into two “sub-planes”. The 7th
- 9th grade program is a land based program with real life problems solving
scenarios. Students combine didactic, academic lessons with real world
scenarios. They are daily working with both their head and their hands to
deeply internalize academic concepts. The 10th - 12th grade program is a
highly academic program preparing students for university. Having come
through the Montessori program to this point, students are well able and ready
to handle the most rigorous content. The high school remains centered on core
Montessori values. This includes Montessori trained teachers, long periods of
uninterrupted work time, key lessons, and a variety of methods whereby a
student can demonstrate mastery of knowledge. Assessments will include
rubrics, portfolios, presentations, quizzes on vocabulary and skills, end of unit
knowledge assessments plus all Federal and Colorado State mandated testing.
IV. Teaching: Along with being highly qualified, teachers and school leaders
employed at DPMSS must be Montessori trained through an accredited AMI or
AMS program, and have an orientation on adolescent Montessori education.
DPMSS will create a culture of shared learning among staff based on the
principals of recursive learning. For this application, recursive learning is
defined as the process of examining the principals of Montessori theory in
order to improve Montessori practice. Staff meetings will include seminars on
Montessori theory and experiential learning. There will be weekly level meeting
where staff can meet with their teams or across teams to problem solve.
Observation of staff will occur daily and, more formally, monthly using
established rubrics and feedback mechanisms designed to improve
performance.
V. Finance
2013-14 2014-15 2015-16 2016-17 2017-18
Number of Students
50
Per Pupil Revenue
221,850 288,453 465,933 621,180 776,523
Grant Funds *See V. for evidence
111,339
65
105
140
175
Private Funds
Other Sources
Total Revenue
333,189 288,453 465,933 621,180 776,523
Employee Salaries (inc. benefits)
Building Expenses
285,933 285,933 451,957 595,380 753,250
Services/Supplies
1,750
1,750
1,750
1,750
1,750
Other Expenditures
8,464
8,464
10,291
17,168
17,168
Total Expenses
296,147 296,147 463,998 614,298 772,169
NET INCOME
37,042
DPMSS Application
-7,694
1,935
6,882
4,354
for performance school
Page 107
Denver Public Montessori Secondary School
Section I. CULTURE
A. Rationale
The current DPS Montessori schools are magnet schools managed by
Denver Public Schools. In order to maintain cohesiveness and continuity, it
makes sense for Denver Public Montessori Secondary School to also be
managed by Denver Public Schools. The performance school model combined
with innovative school status will give DPMSS the freedom necessary to create
an authentic Montessori secondary school while at the same time providing the
support and structure necessary to succeed within the DPS framework.
B. Mission Statement
Denver Public Montessori Secondary School will combine Montessori best
practices with current research on adolescent brain development to provide a
learning environment that promotes high achievement for each student while
also supporting them socially and emotionally. Graduates, regardless of
ethnicity or income status, will be prepared for college or a career as well as
demonstrate ingenuity, adaptability, creativity, initiative and excellent
communication and problem solving skills.
All students, regardless of ethnicity or income status, deserve a high
quality education and school choice. DPS recognized this fact when creating
Montessori elementary schools in four of its five regions. However, these
students do not currently have the ability to continue Montessori education
after 6th grade. DPMSS will create this option for students graduating from DPS
Montessori elementary programs. The school can either be located at an
existing DPS Montessori school or centrally located to all four schools.
Of the four DPS Montessori schools, one is rated as “Distinguished”, two
are rated at “Meets Expectations” and the fourth school was recently converted
via priority turn-around status to a Montessori school in order to improve
academic achievement. Data from the four schools indicate that students are
meeting or exceeding growth percentile benchmarks in reading, writing and
math. Areas of improvement include CELA growth and achievement gaps in
reading, writing, math and science. By creating a high quality Montessori
secondary school, DPMSS intends to continue the excellent Montessori
education students are receiving, while at the same time focus on narrowing
achievement gaps in reading, writing, math and science. DPMSS intends to
achieve the following goals within the first three years of opening:
• DPMSS will achieve and maintain a median growth percentile of at least 55 in
reading, mathematics and writing as reported on state assessments
(Transitional Colorado Assessment Program).
• DPMSS will increase the achievement in subcategories, including minority,
F&RL, student with disabilities and ELL and thereby decrease the achievement
Performance School Application Guide
for schools to open 2013-14
Page 108
gap by 5% per year while keeping Median Growth Percentiles above 55 for
each of the subgroup categories. Median Growth Percentiles will be measured
after the first year. Decreases in gaps will be measured after year two.
• Knowing that one of the four priorities in DPS is to better support ELLs, DPMSS
will also focus on improving academic achievement growth for ELL students.
We will increase the achievement of ELLs learners and decrease the
achievement gap between ELLs and Non-ELLs. Our goal will be to have an
achievement gap less than that of the district which is currently at 13%
difference for Math, 24% difference for Reading and 22% for Writing. DPMSS
will work to diminish achievement gap between ELLs and Non-ELLs so that the
difference will be less than 10% in Math and less than 20% in Reading and
Writing.
• DPMSS will achieve a rating of “exceeds” regarding parent satisfaction as
reported on the DPS School Performance Framework Stoplight Detailed Report
Card.
• DMPMSS will achieve a rating of “exceeds” regarding student engagement as
reported on the DPS School Performance Framework Stoplight Detailed Report
Card.
Montessori secondary education focuses on the whole child, self
construction, valorization and preparation for adult life. By creating a high
quality 7th through 12 grade program on these principles, students will
graduate with the academic skills necessary to thrive in both post secondary
education and career options, while at the same time have well developed
communication and problem solving abilities along with strong interpersonal
relationship skills. By graduation, they will have developed creativity, ingenuity,
adaptability and initiative through the many problem solving, community
building and real world experiences they will encounter at DPMSS.
C. Targeted Student Population
DPS currently has four Montessori magnet schools located in four of the
five DPS regions that end in either 5th grade or 6th grade.There are
approximately 133 4th grade and 128 5th grade students.Two of the four
Montessori elementary schools, Gilpin and Lincoln, end in 5th grade. The
optimal Montessori elementary design is for elementary to end in 6th grade. In
year one and possibly year two, DPMSS will provide an option for the graduating
5th graders. When the leadership at Gilpin and Lincoln believe the timing is
right, the intention is to work with these two Montessori schools towards
adding back 6th grade to their upper elementary classrooms. Year two or three,
depending on the success of bringing 6th grade back to Gilpin and Lincoln,
DPMSS would serve 7th and 8th and grow one grade at a time through grade
12. In its first year, DPMSS will serve 25 6th grade and 25 7th grade students.
DPMSS Application
for performance school
Page 109
Denver Public Montessori Secondary School
The demographics for the existing four elementary schools are as follows:
Proposed Demographics
FRL %
Denison: 57
SPED %
Denison: 11
ELL %
Denison: 19
Lincoln 37
Lincoln: 6
Lincoln: 11
Academia Ana
Academia Ana
Academia Ana
Maria Sandoval:39 Maria Sandoval: 5 Maria Sandoval: 41
Gilpin: 89
Gilpin:: 12
Gilpin: 23
The demographics indicate that DPMSS will have over 50% of students who
qualify for the Federal Free and Reduced Lunch Program, about 10% of students
who qualify for special education services, and, depending on which schools
matriculates the majority of students to DPMSS, approximately 30% who qualify
for ELL services. Based on these percentages, the DPMSS principal and the
school psychologist / social worker will need to determine professional
development regarding best practices supporting students who qualify for FRL.
DPMSS will also have one of its full time staff qualified ELA-E and the Principal
and all other teachers will be at a minimum ELA - T qualified.
From these demographics, DPMSS may have only five to ten students who
qualify for special education services in its first year. DPMSS will hire a parttime special education teacher to support these students while also work
closely with DPS to insure students are receiving the support they need.
Montessori education is individualized and designed to engage each
student at their level and then advance them through interesting, meaningful
work. In direct alignment with goals as set for in the Call for Quality Schools,
DPMSS will increase the achievement in subcategories, including minority, F&RL,
student with disabilities and ELL and thereby decrease the achievement gap as
outlined in our SMART goals set forth in Section I B.
D. School Culture
Montessori schools are designed on a culture of respect. All members of
the community are asked to respect themselves, each other and the
environment. Creating healthy, positive culture is a core component of
Montessori education. This goal is accomplished in several ways.
The first method for creating positive healthy culture is to create a
welcoming environment for staff, students, families and community members.
This began at the first stages of this application process. Members from all
sectors of the DPS Montessori community were invited to participate in the
application and submit ideas, thoughts and concerns. The applicants are
partnering fully with the DPS Montessori schools. Throughout the planning
year, the applicants will host multiple parent education nights to discuss the
benefits of Montessori education while also including perspective parents in the
design of the school. These parent nights will be held in both English and
Performance School Application Guide
for schools to open 2013-14
Page 110
Spanish. If there are families requiring additional languages, every effort will be
made to find interpreters. The goal is to create a deep sense of community and
inclusivity for all stakeholders.
Once school is open, students will be active members of the school
community. The Junior High (7th, 8th, 9th) and high school (10th, 11th, 12th)
will be set up into advisements. Students check in daily with their advisors to
review progress and set goals. Junior high and senior high School staff and
students will also hold weekly community meetings. There will be monthly all
school (7th - 12th) community meetings for celebrations and discussion.
A second core component of Montessori is peace education. Peace
education starts at the youngest grades and continues through high school. In
the junior high program, peace education manifests through positive behavior
support, conflict resolution, community service and lessons and discussion on
what it means to create a peaceful environment. High school continues this
practice but also adds a social justice class that allows students to explore
peace at a more national and global level.
A third component of Montessori education is the belief that all work is
noble and that work normalizes the child. What this means at the secondary
level is that students gain self confidence and self respect through challenging
work. DPMSS’ academic studies will be based on a culture of high challenge
combined with high skills and high support in order to create maximal
engagement or “flow”. This design is based on Dr. Mihaly Csikszentmihalyi’s
research as explained in Flow, The Psychology of Optimal Experience and flow
research in Montessori middle schools conducted by Dr. Kevin Rathunde.
Finally, Montessori schools provide individualized education that meets
each student at his or her level. All lessons and instruction are differentiated
and follow up work is initiated by the student based on his or her interests.
DPMSS will meet the needs of special education students through this
differentiated learning while still holding high expectations that appropriately
challenges each student as determined by their IEP and through teacher
observation. ELL learners will demonstrate learning both in their native
language and, with appropriate assistance as needed, in English. DPMSS will
employ at least one teacher who qualified ELA-E along with a full time highly
qualified Spanish teacher. At risk students will benefit from the inclusive
culture, the advisement model, and the academic program that is specifically
designed to help students find their voice and self-confidence through work.
D. Parent and Community Involvement: Prior to submitting the letter of intent,
the founding members of DPMSS contacted DPS Montessori principals, teachers
and community members to gauge interest in providing Montessori secondary
education for DPS Montessori students. Response was enthusiastic with the
caveat that the secondary program must be high quality, rigorous and
DPMSS Application
for performance school
Page 111
Denver Public Montessori Secondary School
based on Montessori core principles. DPS Montessori community members
were invited to participate at every stage of this application, and their input has
been invaluable. The next step was creating an interest survey for existing
Montessori families. Surveys were sent out in English and Spanish in midMarch. In just three weeks, 52 families indicated strong interest with surveys
responses still coming in.
Attached in Appendix F are emails of community support from the
following stakeholders: Katy Mattis, incoming Denison Montessori principal,
Principal Frank Vincent, Gilpin Montessori, Principal JoAnn Trujillo Hays,
Academia Ana Maria Sandoval, Principal Janice Spearman, Lincoln Montessori,
Dr. Martha Urioste, founding principal of Mitchell (now Denison) and Montessori
consultant, Judith Orion, Director of Training, The Montessori Institute Denver,
and Yamile Reina-Ayadi, Denison parent and DPS School Improvement Partner.
DPMSS is partnering with the North American Montessori Teaching
Association (NAMTA) for school design and teacher development. NAMTA,
presented to DPMSS a cash grant of $3000.00 in start-up funds along with an
additional $5000 for services in-kind donated from David Kahn and Laurie
Ewert-Krocker. David Kahn is the executive director of NAMTA and the
established global expert on Montessori adolescent education. Laurie EwertKrocker is the founding director of The Hershey Montessori School, which is a
private, adolescent Montessori program that has been successfully operating
for fifteen years and has established curriculum and best practices that can be
replicated at DPMSS. Finally, DPMSS is partnering with Compass Montessori
School, a Jefferson County pre-k through 12th grade charter school located in
Wheat Ridge and Golden Colorado. Compass Montessori has an established,
high quality junior and senior high Montessori program. Compass Montessori
designed Montessori graduation outcomes, uses CSAP data to improve
Montessori instruction, and created record keeping systems that align
Montessori methods with education state standards. In 2010, Compass received
the Governor’s award for for schools with the highest 2009-2010 academic
growth rates in Colorado.
DPMSS has contacted the following organizations regarding partnering on
the urban farm program: the GrowHaus (in the Elyria-Swansea neighborhood),
GreenLeaf (a youth-internship urban farming program), and Sprout City Farms,
the non-profit that runs the farm at the Denver Green School. They are all
willing to sit down and talk about DPMSS and its inclusion of an urban farm. A
representative from DPMSS has meetings scheduled in April with these
organizations to determine how these partnerships might work and level of
commitment. Once the high school program is underway, DPMSS will partner
with local business and cultural institutions to establish student internships,
community service opportunities and expanded learning options.
Performance School Application Guide
for schools to open 2013-14
Page 112
DPMSS will embrace its families and community members in a variety of
ways. First, families will be included in the initial design. Although the core
Montessori mission and values must remain intact, families will provide
invaluable ideas regarding how to accomplish the school’s mission. Families
will be invited to participate in key decision making processes such as helping
to select the location of the school (as long as there are choices available), after
school activities, school committees and ideas on initiating school traditions,
fundraising and creating excellent communication structures. One of the best
ways for families to feel part of the school community is through community
volunteer events such as school work days. DPMSS will identify early on a
volunteer parent coordinator and then support that person to create school
work days along with numerous school volunteer opportunities.
DPMSS will also create a vibrant School Accountability Committee (SAC)
that will include no less then one staff member along with the head of school,
three parents and two community members. The SAC will assess school
performance based on agreed upon outcomes that include academic goals,
student well-being and community involvement. The SAC will meet once per
month to discuss school progress and make recommendations to the principal.
D. Parent Satisfaction
DPMSS intends to achieve a rating of “exceeds” in the DPS parent
satisfaction survey along with a high response rate. Parent satisfaction is a key
component for school success. The first step in insuring parent satisfaction is
clear communication regarding the school’s mission and vision along with
parent education regarding Montessori adolescent education. This
communication must happen prior to parents choosing DPMSS for their student.
Once students are enrolled, DPMSS will manifest multiple ways to connect with
parents and gauge satisfaction. Some methods will be as simple as the principal
being outside during drop off and pick-up so parents can engage in quick
conversation if necessary. The principal will also maintain an open door policy
along with a school policy that all parent phone or email messages must be
replied to within 24 hours (except during week-ends or holidays).
Each year, the chairperson of the school accountability committee will
insure that the DPS parent satisfaction survey measuring parent satisfaction
regarding the school achieving established outcomes is delivered to all parents
and guardians. All surveys will be delivered in English and the parent’s native
language. Surveys will be anonymous but the SAC chairperson will assess
percentage of surveys returned based on school population. If that percentage
is less than 75%, the SAC committee will assess the current population and find
solutions on how to bring that percentage up to 75%. Should parent satisfaction
not meet the standard on the SPF rubric, DPMSS will take the following steps: 1)
Hold community meetings to determine the root of parent dissatisfaction, 2)
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increase parent education to insure that parents are comfortable with the
Montessori Method and how it is being implemented at DPMSS, 3) create a
strategic plan that includes tactical and strategic steps to resolve concerns.
E. Student Engagement
The goal for student attendance is 95% or better every school year.
Montessori schools are designed as a place where students feel safe, welcome
and love school. Because Montessori education is designed on student selfconstruction and student choice, students have the ability to deeply study
subjects that are of interest to them. These studies combined with meaningful
work result in students demonstrating competency and therefore gaining in self
respect and self worth. If a student starts to demonstrate a lack of engagement,
the advisor will connect with the student to determine the cause. If needed, the
student and their family will meet with the advisor to determine how to reengage the student towards meaningful work.
Attendance will be conducted at the beginning of the school day, prior to
lunch and mid-afternoon. If a students receives more than three excused
absences in a month, the advisor will contact the family to make sure all is well.
If the student receives any unexcused absences, again, the advisor will contact
the family to determine why the student is not in school and ask how can we
support the student and the family. If the student has three or more unexcused
absences in a month, or is approaching more than ten unexcused absences in a
semester, the principal will actively work with the family while at the same time,
initiate a truancy plan as outlined by DPS. At all times, DPMSS will adhere to the
DPS attendance policies.
Student satisfaction will also be measured in multiple ways. The school
will track on-time, daily attendance and work with students who are
demonstrating a lack of engagement through tardiness or poor attendance.
Advisors will address student concerns at the daily and weekly community
meetings. Both the advisors and the principal will maintain an open door policy
to address student concerns and complaints. Finally, the principal will insure
that the DPS student satisfaction survey is delivered to every student. Students
will be given access to the survey during school hours in a manner that allows
them to maintain confidentiality.
DPMSS intends to achieve a rating of “exceeds” on the SPF for student
attendance and on the DPS student satisfaction survey. Should the results of the
survey not meet the standard on the SPF rubric, the school will invite students
to more clearly articulate concerns through both an anonymous forum and a
community forum. Staff will then work with students to create a strategic plan
that includes both tactical and strategic steps to address student concerns.
Follow-up meetings will be held twice per month until concerns are
satisfactorally addressed.
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Section II. LEADERSHIP
A. Leadership Team Personnel
DPMSS has identified the following characteristics for successful
leadership of a public Montessori school. The leader must be trained both in
Montessori elementary education and in Montessori adolescent education. The
leader must hold a Master’s degree in Education and Administration or similar
school leadership program. The leader must have experience leading a public
school, preferably a public Montessori school. He or she must have experience
working with adolescents and preferably teaching adolescents. Finally, the
leader must demonstrate a leadership style that is reflective of Montessori core
values including respect, inclusivity, shared decision making, recursive learning,
and empowering staff to work at their highest level.
DPMSS will be led by Katy Myers. Katy Myers is an established Montessori
leader. She was a founding parent of Compass Montessori School which is a
pre-k through 12th grade charter Montessori school in Jefferson County,
Colorado. Katy led the Compass steering committee composed of nine parents
through the process of writing the charter application, working with Jefferson
County School District to achieve approval of the charter, hiring the founding
principal and staff, locating, financing and purchasing the Wheat Ridge facility,
designing and remodeling the facility, purchasing furniture, fixtures and
Montessori materials, and enrolling 150 students. Two years later, Katy was
hired as the Compass business manager and assistant head of school. Her
primary role was to start the Compass Montessori Secondary School. During
that time, Katy worked with the head of school and a parent committee to
locate, purchase, finance and build the Compass Montessori Golden campus.
This included obtaining $5.5 million in CECFA bond financing, hiring both an
architect and contractor, and working closely with staff and parents to create
the beautiful 35,000 square foot campus that has two buildings, a working
farm, commercial kitchen and an art studio with kiln. The project was
completed on time and under budget.
Compass opened the Golden campus in 2002 with 180 students grades
7th - 10th and twelve full time staff. During the next few years, there were
successes but also many challenges. In analyzing the situation, Katy realized
that she was missing key education components to be a successful leader in
this public, secondary Montessori environment. After the first year, Katy
attended Montessori adolescent training through the North American
Montessori Teachers Association. The following year, Katy applied and was
accepted to the Federally funded Leadership for Education Entrepreneurs
program at Arizona State University. There she obtained her Master’s in
Education and Administration. She then enrolled in the elementary education
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diploma program through Association Montessori Internationale, which will be
completed this June.
Through observation and data analysis, Katy and the Compass leadership
team began determining best practices that had to be implemented for
Compass to succeed. In 2005, Katy became Head of School of the Golden
Campus and instituted the following reforms at the school. First, the secondary
program was downsized so that a super-majority of students entering 7th
grade came from Compass 6th grade. This insured that the junior high program
had a majority of students and families that were familiar with Montessori and
specifically choosing Montessori to continue their education. Katy then worked
with staff to create Montessori high school graduation outcomes. Staff took
these outcomes and backward mapped them all the way to Compass
kindergarten, so that staff had a clear roadmap towards educating students to a
successful graduation and beyond. Finally, Katy, working with staff, analyzed
CSAP benchmark data provided by Jefferson County to determine what areas of
instruction needed improvement. She then worked with staff to determine what
Montessori materials, key lessons and Montessori based curriculum matched
those instructional areas and created professional development to improve
instruction using Montessori methods. During this process, Compass High
School moved from “non-performing” to “performing” to “high-performing”. In
2011, Compass won the Governor’s award for schools with the highest
2009-2010 academic growth rates in Colorado.
During this time, Compass became an early adopter of the Response to
Intervention (RtI) model for identifying students requiring special education
services and insuring that all student received strategic, targeted interventions
when demonstrating need for such intervention. The RtI model matched well
with the Montessori method, and staff embraced this innovative approach to
improving student achievement for all students.
In 2008, Katy became head of school over Compass Wheat Ridge campus
as well. Compass Wheat Ridge is a pre-k through 6th grade Montessori charter
school that then matriculates to the Golden campus. At that time, Compass
Wheat Ridge was experiencing decreasing CSAP scores, high teacher turnover
and was in a budget crisis that was bringing the school to the edge of
bankruptcy. During the three years that Katy was head of school over both
Compass Wheat Ridge and Compass Golden, Katy was able to bring the Wheat
Ridge budget from a projected deficit of ($180,000) to a positive cash flow of
$40,000. She improved the culture and community of the school by creating a
shared leadership model resulting in very high staff and student retention. Katy
added Montessori professional development and created a culture of high
student behavior and academic expectations. By 2010, CSAP scores had risen
dramatically and the school was thriving as indicated by staff, parent and
student surveys.
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While working locally within Compass to document best practices, Katy
also worked with the national Montessori secondary school movement through
NAMTA. Katy collaborated with other Montessori administrators throughout the
U.S. and Mexico to determine what exactly high quality secondary Montessori
education looks like and how it could be measured. Because of her experience
in public charter Montessori education, Katy has been a frequent presenter at
NAMTA conferences and most recently teamed with three other experienced
administrators to lead a four day Montessori leadership training for current and
prospective Montessori administrators who came from as far away as the
Philippines and Monaco to attend.
DPMSS will work with the “Self-Governance” leadership model that is
successfully being implemented at Compass Montessori School. An outline of
this model is included in Exhibit G. During year one and two, the school will
have up to 65 students. In order to be economically sustainable, the school
leader will also work half time in the classroom. During that time, she will work
with the other advisors to create a culture of shared leadership. Key leadership
roles and responsibilities will be reviewed with staff to insure reasonable
redundancies can be created. In year two, a junior high program director will be
identified and that person will start attending professional leadership and
administration development as offered through DPS. In year three, the school
principal will decrease teaching hours in order to focus on the well being of the
105 students, data analysis, and professional development for staff. She will
also conduct curriculum and programmatic review to insure that 9th grade is
successfully meeting DPS high school standards and that DMPSS is ready to
move forward with adding the high school program. Also In year three, a high
school program director will be identified and will start attending professional
leadership and administration development as offered through DPS. In year
four, the leadership team will consist of the principal, the junior high and the
senior high program directors. At that point, the principal will insure that both
program directors have the knowledge base needed to assume the principal
role of the school should that event be necessary.
The principal’s roles and responsibilities include creating and maintaining
the school’s mission and vision, hiring and evaluating staff, maintaining a
culture of high expectation regarding behavior and academic achievement,
creating and reviewing measurable data systems to insure the students are
obtaining a rich and rigorous education, creating and linking staff to
professional development, visiting classrooms every day and conducting
monthly, longer staff observations, creating and maintaining a welcoming
environment for all community members, high level student discipline and
attendance.
The program director’s roles and responsibilities include maintaining a
culture of high expectations regarding student behavior and academic
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achievement, daily check in with fellow staff, weekly staff meetings to insure
that the school is holding to its mission and vision, ground level parent
communication, and resolving low level student conflict and discipline. Program
Directors will also be advisors / teachers.
Program directors must be highly qualified teachers who are Montessori
trained in both elementary and adolescent education. They need to have
completed or be willing to complete a Master’s level leadership program. They
must demonstrate either in their DPMSS position or in past positions they they
can create a culture of respect, inclusivity, shared decision making, recursive
learning, and empowering staff to work at their highest level.
B. Leadership Team Coaching and Evaluation
DPMSS will use a variety of data points and observation to determine the
school leader’s need for coaching and professional development. First, the SAC
team will review monthly achievement data and the annual SPF to see if the
school has met set targets. Second, the SAC will review annual parent, staff and
student surveys to determine the overall health of the school and community
opinions of the school. Third, the SAC will meet with a Montessori consultant
who will be hired in year 1, 2, 3 and year 5 to observe the school and provide
feedback to the SAC, school leadership and staff.
The SAC will use the DPS Framework for Effective School Leadership as
their evaluative tool. The principal will also welcome designated DPS leadership
to observe the school and provide feedback using the DPS Framework. Every
month, the principal will meet with the SAC to discuss the school’s successes
and challenges based on data and observation. During those meetings, the
principal will seek out feedback regarding current leadership effectiveness. The
principal will also solicit feedback from staff and community members during
informal meetings. At all times, the DPMSS principal will model the value of
recursive learning, seeking and accepting feedback, and inclusive problem
solving in order to continue to evolve towards distinguished leadership.
Should the SAC and/or DPS leadership determine that the principal
require additional coaching and professional development, the principal, SAC
and DPS Leadership will create a professional development plan along with
benchmarks to measure progress. Progress will be reviewed monthly. If, after
six months, the principal has not made satisfactory improvement, DPS will
replace the him or her with a program director and begin the search for a new
principal.
B. School Personnel Structure
DPMSS will have 50 students for the first year of operation and 65
students in the second year. During that time, DPMSS will enroll one full time
licensed teacher who is ELA-T qualified, one full time teacher who is highly
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qualified in Spanish and is also ELA - E qualified along with part-time staff for
special education, psychologist/social worker, nurse, office support, and
principal.2 The principal will work half time as head of school and half time as a
teacher / advisor which brings the total number of teachers to 2.5. (including
the Spanish / ELA-E teacher). After that time, the school will grow by 40
students per year. Staff will be added to maintain a teaching ration of 25
students to 1 teacher. Hours for the part time staff will increase based on the
number of special education students being served. The principal will relinquish
all teaching duties and become a full time position in year six.
An organization chart is included as Appendix I and a Staff Roster is
included as Appendix J.
C. Student Enrollment
DPMSS is designed to be the secondary school for DPS Montessori
elementary schools. The entire curriculum is designed as a continuation of the
Montessori elementary curriculum, the Montessori methodology and the
education design structures students have experienced throughout their
elementary Montessori experience. Priority enrollment will be given to all
students graduating from Dension, Academia Ana Maria Sandoval, Lincoln and
Gilpin Montessori schools along with any DPS Montessori elementary schools.
Each of these schools currently have a diverse population representative of
Denver. DPMSS will not deny admissions to any student based on income
status, academic achievement, disabilities or at risk of academic failure. DPMSS
staff will meet with designated staff of the sending schools to discuss transition
of students and to review any IEP, ALP, ILP, and ELL plans along with discussing
learning styles, RTI and productive strategies for all students matriculating to
DPMSS.
Should there still be available spots at DPMSS, DPMSS will accept students
via the following DPS approved choice enrollment process:
Beginning with the 2012-13 school year, DPS will offer the SchoolChoice
enrollment process. Enrollment will follow five steps for any student who wants
or needs to attend a new school as of 2012-13, especially “transitioning”
students.
1.
2.
3.
2
Research DPS schools by reviewing the SchoolChoice Enrollment Guide and
online resources, and by visiting schools of interest.
Prioritize your student’s top five preferences and list them in order on the
SchoolChoice form.
Complete any extra enrollment steps and submit them to your schools of
interest if they are required. Submit your SchoolChoice form by January 31.
Clarification to CDE: ELA qualified teachers will also meet state highly qualified requirements.
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4.
5.
SchoolChoice will combine your student’s top five preferences with each
school’s admissions priorities and available space. For schools with more
interested students than available space, students will be randomly
assigned a lottery number that will determine the order in which they are
enrolled with a school.
Students will be awarded a seat at their highest-preference school with an
available seat in March 2013.
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Section III: EDUCATION PROGRAM.
A. Curriculum
The 6th grade through 12th grade Montessori curriculum that DPMSS will
implement is rigorous, innovative, interesting and is designed to engage
students to produce optimal academic achievement as well as social and
emotional maturity and well-being. Montessori adolescent curriculum has been
designed and tested over the last fifteen years at both private and public
Montessori schools. This curriculum, referenced throughout this application as
the National Montessori Curriculum, has been collected, refined and reported
through The NAMTA Journal, A National Montessori Curriculum Report, The
NAMTA Journal, Volume 37, No. 1, Winter 2012. DPMSS will design its program
using this curriculum. Recently, the National Montessori Curriclum for the
Adolescent Program from Twelve to Fifteen/Sixteen Years was reviewed by the
Australian Curriculum Assessment and Reporting Authority. Their findings, as
reported in A National Montessori Curriculum Report, are as follows: ACARA
(Australian Curriculum Assessment and Reporting Authority) established an
extremly rigorous recognition process to determine the extent to which a wellestablished alternative national curriculum can deliver comparable educational
outcomes for students to those based on the Australian National Curriculum.
ACARA have advised that (the National Montessori Curriculum) aligns with the
Melbourne Declaration on Educational Goals for Young Australians, meets the
particular principles and guidelines in relation to the Shape of the Australian
Curriclum v3 paper, and allows for broadly comparable educational outcomes in
English, mathematics, science and history by the end of year 10.
Although DPMSS will use the National Montessori Curriculum, DPMSS will
also use the Colorado Academic Standards (CAS), the Common Core Standards
(CCS)and the Higher Education Admission Requirements (HEAR) as its education
standards. DPMSS will compare the Montessori National Curriculum to the CAS
and the CCS to insure that there are no gaps and that the students are
achieving the benchmarks as stated in these standards.
The priorities for the secondary program are first to provide the optimal
environment for student achievement. This will include a beautiful physical
environment that includes an urban farm, an art and micro-economy studio
with kiln, a commercial kitchen and science laboratories. The school will need
to be located in an area that allows for public transportation to the local cultural
institutions. For high school, the prepared environment will include
professional work environments, a laboratory fitted out for advanced chemistry,
biology and physics instruction, an art studio fitted out for advanced work in a
variety of artistic media, and computers with refined publishing and
demonstration software.
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The next priority is to extend and deepen the Montessori education
students have received through their elementary program. By sixth grade, the
Montessori students will have completed most of the elementary Montessori
materials. DPMSS will build upon the skills and knowledge acquired through the
materials via a carefully constructed curriculum that recognizes the specific
stage of brain development students are entering upon adolescence.
Here is one example of this extension as related to math. Upon entering
DPMSS, students should have completed Montessori math materials up through
the trinomial cube, measurement, volume, mathematical laws, introduction to
algebra, Pythagoras theorem, and geometry. At this point, students need to
practice their skills while using these skills to solve challenging problems. They
also need to advance their skills through algebra, advanced geometry and into
trigonometry and calculus. In the 7th, 8th and 9th grades, students will practice
math skills solving real problems that involve the urban farm, culinary arts and
micro-economies. They will also receive direct instruction in math along with
working a self-paced on-line math program to continue to practice, develop
and build math knowledge.
By 10th grade, students will be ready for direct instruction in advanced
algebra, geometry, trigonometry and calculus. The curriculum in high school
will be a combination of small group lesson and on-line math curriculum to
allow the students to advance at his or her own rate while, at the same time,
insuring they have the support they need to continue making, at a minimum,
one year of academic progress in one year’s time.
DPMSS is also committed to providing a strong Spanish language
program and support dual language acquisition. It will have one teacher in both
the junior and senior high who is highly qualified in Spanish and Montessori
trained and who is also qualified ELA - E. At least one Occupation per year will
be delivered in Spanish to offer an immersion experience and to extend the
dual education students have received at Academia Ana Maria Sandoval.
DPMSS will be using the National Montessori Curriculum for grades 7-9
for science, history and language arts. DPMSS will use an on-line math
curriculum that is individualized for each student combined with small group
lessons. The small group lessons will be designed to meet each student at the
particular benchmark the student is currently working, and the teacher will use
a variety of instructional methods, including Montessori math materials, to
assist the student in mastering that benchmark and preparing to work on the
next on-line unit. Students will also apply math towards a variety of hands-on
projects utilizing the farm, the culinary arts program and micro-economy. The
7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS matches the
meaningful, relative approach that defines Montessori education.
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The high school, grades 10, 11 and 12, will use an integrated college
prepatory curriculum such as the curriculum currently in place at Compass
Montessori High School in Jefferson County. The Compass three year SPF results
for this curriculum are a median growth percentile of 58 for reading, 54 for
mathematics and 66 for writing and an academic achievement score for science
of 59%. The academic growth gaps achieved a level of “exceeds” for reading
and “writing” and meets for math. The three year ACT composite is 21.7.
Although the curriculum for high school will be similar to advance
placement curriculum in DPS for English, history, math, science and Spanish,
there will still be innovative differences. First, the curriculum will be integrated
so that literature studied in language arts will support the history curriculum for
an overall integrated humanities curriculum. The math and science teacher will
work together to insure students are obtaining the mathematical skills needed
to work out currently studied complex scientific equations. Linkages between
science, math and history will be explored. Throughout all areas of study, there
will be indepth reading and writing instruction.
The junior high program will include 6th grade in its first and possibly
second year. Currently, 6th grade is offered at Denison and Academia Ana
Maria Sandoval, but not at Lincoln or Gilpin. When the leadership at Gilpin and
Lincoln believe the timing is right, the intention is to work with these two
Montessori schools towards adding back 6th grade to their upper elementary
classrooms. Year two or three, depending on the success of bringing 6th grade
back to Gilpin and Lincoln, DPMSS would serve 7th and 8th and grow one grade
at a time through grade 12. The long range design is for the junior high to be
composed of 7th, 8th and 9th grade. There will be 120 students divided into
five advisements of 24 students each. All five teacher / advisors will be
Montessori trained. There will be a highly qualified math teacher, language arts
teacher, social studies teacher, science teacher and Spanish teacher.
The high school will be composed of 105 students. There will be four
teacher/advisors including a highly qualified math teacher, language arts
teacher, social studies teacher and science teacher. There will be a fifth teacher
who will be highly qualified in Spanish and ELA-E. These same teachers will
offer afternoon electives in subject areas that they are qualified to teach.
The junior high program has, as a key component, a curriculum called
Occupations. In the NAMTA National Montessori Curriculum Report,
Occupations is defined as follows: “Through work, the students in the
Montessori adolescent community engage with the natural environment and the
wider society. The work undertaken within the community which has purposeful
problem solving and economic contributions but which draws on necessary
academic expertise is called Occupations. Occupations in the adolescent
community have the following characteristics: The work is meaningful to the
students, the work is both physically and intellectually challenging, the work is
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valued in the wider community, society and culture, and the work has economic
validity. Occupations with these characteristics inspire students to engage in
the work with integrity and passion, to develop their own interests and
expertise, to gain recognition for their contribution and to experience a sense
of ownership and accomplishment.” The NAMTA Journal, Volume 37, Number 1,
Winter 2012. The scope and sequence and an example of a science Occupation
are included in Appendix K.
Staff at DPMSS will create Occupations and humanities units that are
meaningful to the target population and inclusive of diverse cultures and
academic learning styles. Occupations integrate all of the core subject areas,
with a focus on Science. Humanities is taught using a similar scope and
sequence as Occupations but with a focus on history. An example of the
Humanities curriculum is in Exhibit C. Throughout the school day, students will
be engaged in the various Occupations and Humanities. During this time,
additional small group lessons will occur providing direct instruction in math,
ELA, and Spanish. Here is the curriculum summary as outlined in A National
Montessori Curriculum Report and adapted to DPMSS:
Pedagogy: The themes that govern the approach to pedagogy implemented in
the Montessori adolescent community are synthesis and integration. Montessori
adolescent pedagogy integrates concrete and active learning experiences with
opportunities for reflective and contemplative study of increasingly abstract
concepts and ideas. Second, the pedagogy integrates intellectual and ethical
development, creative expression and the academic disciplines, giving students
the opportunity to apply discipline knowledge, judgement and creative skills to
problem solving in projects that require physical activity, ethical choices, selfexpression and abstract application of interdisciplinary knowledge. The focus of
the pedagogy is the adolescent’s civic, ethical and social development as well
as the adolescent’s adaptation to the demands of the changing natural and
human world.
The expansive nature of the curriculum, and the pedagogy used to
implement the curriculum, ensures that the curriculum can be adjusted to
accommodate knowledge, skills and understandings required by the CAS, the
CCS, and the State assessments. Students become active participants with
teachers in the task of identifying individual learning needs and, where needed,
to design individualised learning programs to meet these requirements and
demands. The goal is to hand over to students increasing responsibility for
planning and managing their own learning as one aspect of the overall aim of
the Montessori learning environment prepared for adolescents: to prepare
students for social and economic independence.
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The National Montessori Curriculum Summary
Intellectual Development (cross-curricular)
· civility, citizenship, civics and community life (civil society and moral
development)
· mathematics, including arithmetic, geometry, algebra and measurement
· language, English language, as well as at least one language other than
English
Self-Expression (cross-curricular)
· language for creative expression
· music
· visual arts
Preparation for adult life and contemporary culture
· Science curriculum embedded in the Occupations
· the study of the Earth and living things, incorporating studies in:
• Earth and space sciences: cosmology, including astronomy;
geology and physical geography, including the geology and
geography of prehistoric periods
• Biological sciences: biology, including studies in botany,
zoology, ecology, physiology, comparative anatomy health
sciences, and ecology(sustainability)
· the study of human progress and civilisation, incorporating studies in:
• Physical sciences: physics and chemistry
• Contemporary sciences: mechanics and engineering, history of
science and technology, including genetics
Occupations
· practical daily life tasks, including maintenance of the community
environment
· working on and being stewards of the land, including care of the natural
environment, horticulture, agriculture and animal husbandry
· participating in the micro-enterprises of the adolescent community
History and the humanities curriculum
· the study of humanity
· the study of the building of human civilisation
These studies incorporate studies in geography, anthropology, politics and
economics.
By high school, (10th - 12th), Montessori students are well adept at
taking charge of their education, and are eager for further intellectual
challenge. At this point, the curriculum looks similar to more traditional college
preparatory curricula. However, the delivery of curriculum maintains the core
values of Montessori and are designed specifically for students who have
progressed through Montessori education. Instruction is delivered via key
lessons that convey to the students fundamental concepts and serve as
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“jumping off” points for further exploration. Studies are self-directed in an
environment of high expectations and high support. Teacher/advisors work
with students to insure that students have the advanced skills necessary to
explore advanced concepts.
In combination with the challenging academic setting, high school
students are also encouraged to go out to local cultural institutions to further
study. DPMSS intends to create partnerships with the Museum of Nature and
Science, the Denver Zoo, the Denver Botanic Gardens, the Denver Art Museum
and other local cultural centers so that our students can easily access experts
within those settings. DPMSS will also create partnership with CU Denver and
Metropolitan State College of Denver so that students who wish to dually enroll
in some classes during their senior year have the ability to do so. Another key
experience for high school will be international travel. DPMSS will determine
appropriate fund raising venues so that all students will be able to attend at
least one international trip during high school.
In 2003, Dr. Kevin Rathunde published a study titled “A Comparison of
Montessori and Traditional Middle Schools: Motivation, Quality of Experience,
and Social Context.” With the help of co-investigator Mihaly Csikszentmihalyi,
Dr. Rathunde compared the experiences and perceptions of 150 middle school
students in Montessori and 150 middle school students in traditional schools
using the Experience Sampling Method (ESM). The ESM statistical procedure
allowed Dr. Rathunde to determine, in an objective manner, whether there were
significant differences between the two groups of students (Montessori and
Traditional) and to adjust or “control” for any differences that were due to other
factors such as background variables.
The statistical analysis revealed that there were strong differences
between the Montessori and Traditional students. The differences included:
1) Montessori students reported a significantly better quality of experience in
academic work than the traditional students,
2) Montessori students appeared to feel more active, strong, excited, happy,
relaxed, sociable, and proud while engaged in academic work,
3) Montessori students enjoyed themselves more, they were more interested in
what they were doing, and they wanted to be doing academic work more than
the traditional students,
4) Montessori students reported significantly higher percentages of
undivided interest, higher motivation and higher levels of importance with
regard to schoolwork,
5) Montessori students reported more conditions where the challenges and
skills used while doing academic work were above average.
B. School Schedule & Calendar: The school calendar and School Day Schedule
are outlined in Appendix L. The junior high portion of DPMSS will be
centered around an urban farm. In order to take advantage of the short
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growing season in Colorado, DPMSS will start one week earlier than Denver
Public Schools. DPMSS will also end one week later. During the year, DPMSS will
have a one week fall break in late October and extend spring break to two
weeks. Prior to school opening year one, there will be 10 non-contact days
before the first day of school. The schedule for this professional development is
described in Section IV C.
The DPMSS junior and senior high curriculum is outcomes based, with the
outcomes measured via benchmarks achieved as noted in the farm school and
high school portfolios, and data gathered through the on-line math
assessments, mastery level quizzes, end of unit assessments and completed
follow-up work. The schedule is therefore individualized to meet the needs of
every learner, including students needing intervention or acceleration.
The junior high school day will start at 8:00 and run until 3:30. There will
be one half hour for lunch and one half hour for outdoor recreation time and
6.5 hours for academic work time. On Wednesdays, the school day will end at
1:30 so that teachers can meet to review student progress and for integrated
planning. A supervised study hall will be offered from 1:30 to 3:30 for those
students who are not able to go home at 1:30 on Wednesdays. The day will
start at 8:00 in advisement. Students will then proceed to their Academic Work
Time, which includes lessons in all curriculum subjects, for the remainder of
the day. During this time, students will meet in small group lessons for math,
Spanish and ELA instruction. All other instruction, including enrichment, will be
integrated into Occupations and/or humanities with lessons and work time
scheduled throughout the Academic Work Time. A sample of a student’s
schedule is included in Appendix L. After lunch, there will be a 45 minute quiet
work time dedicated to reading and journal writing. During this time, advisors
will also do individual portfolio review with students. Students will then proceed
back into Academic Work Time. Students will meet back in advisements at 3:10
to restore the environment and have a closing meeting.
Teachers, including the special education teacher and ELA-E teacher, will
plan lessons for the entire week. All teachers will list their lessons for the
following week on Thursday. Students will then sign up for their lessons on
Friday for the following week. Advisors will review what lessons their students
have signed up to insure that there are no gaps. Staff will note what students
need additional intervention through data gleaned at the Wednesday afternoon
staff integration time, portfolio checks, review of data from the on-line math
program, assignments and assessments. Teachers will include these lessons in
their weekly lesson plan and advisors will insure that students are signed up to
attend those lessons. The ELA-E teacher will also have lesson sign up times for
every day and review the lists to insure that every ELL student is receiving direct
instruction for 45 minutes per day.
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A teacher will start their school day with their advisement, working with
students to insure they are ready for the day and the week. Teachers then
spend the morning teaching lessons. When they are not teaching lessons, they
are available to students to answer questions, assess work, and observe
students. Teachers will eat lunch with the students and attend recess,
alternating the schedule so that each teacher will have a 30 minute break. After
lunch, teachers will conduct a portfolio check and individual advising with
students. Teachers will then teach additional lessons and continue to work with
students until 3:10. At 3:10, teachers will work with students to restore the
environment and talk with students about their successes and challenges for
the day. On Wednesday afternoons, teachers will have two hours of staff
integration time to review data, discuss students and determine what additional
lessons, interventions, and challenges students need to maintain an optimal
learning environment.
A student might spend his day as follows: Monday he will start in
advisement. There, advisors will talk to the students about their weekly
schedule, inform students of any gaps and require students to adjust their
schedules to fill the gaps, and insure students are organized and ready for the
week. After the advisor has signed off on the student’s weekly lesson plan,
students will start their Academic Work Time. During Academic Work Time, a
student might then choose to spend time on the on-line math program or other
follow up work. He would then attend the various lessons he signed up for that
day. In-between lessons, he is working on chosen follow up work that could
include project based work, writing a research paper, reading documents in
preparation for seminar, and the on-line math program. The students will be
allowed to choose their work, but they will not be allowed to choose not to
work. Although social interaction is a part of every Montessori classroom, the
culture at DPMSS will require that social interaction is not interfering with
student work. This is a balance that has been worked on in Montessori
adolescent programs throughout the country, and best practices have been
ascertained. One best practice that keeps students on task is to insure they
have choice. A second best practice is to insure that the work is meaningful and
engaging. A third best practice is to hold a culture of high challenge, high skills
and high support. And finally, the most important best practice, is to insure
that a supermajority of the students have come up through Montessori
education and therefore have worked in classrooms that have schedules very
similar to the adolescent program. If an adolescent program implements these
best practices, this schedule is the optimal schedule for students to succeed.
During lessons, students will note in their portfolios the lesson received,
the benchmarks related to the lesson, and ideas for follow up work. When
follow-up work is turned in, the advisor and the student will assess the follow
up work to see if it demonstrates that the student is proficient in those
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benchmarks. After lunch, students will have 45 minutes of quiet time for
journaling, reflection and reading. During this time, advisors will individually
meet with students for portfolio check and individual advisement. After this
time, students will again begin Academic Work Time. At the end of the day,
students will meet back in advisement to restore their environment and discuss
their successes and challenges for the day.
For high school, the schedule will be also 8:00 - 3:30. There will be 45
minutes for lunch. The mornings will be blocks of small group lessons and
independent work time. The afternoon will be comprised of two one-hour
electives. From 2:30 - 3:30, students can study, practice school team sports
such as Ultimate Frisbee or rehearse dramatic or other student productions,
and staff will be available to students for advisement and tutoring. On
Wednesday afternoons, students will leave school at after lunch to attend
internships, mentorships or volunteer work. Advisors will work with student to
obtain appropriate placements. Advisors will work closely with the supervisors
for the off-campus learning opportunities to insure students are arriving on
time, and appropriately contributing and demonstrating the core values of our
Montessori program. This schedule has been modeled after the Compass
Montessori High School schedule, where it is extremely successful as measured
by observation, student and staff satisfaction and student academic growth.
C. Progress Monitoring and Assessment
This description of Montessori assessment is from the NAMTA National
Montessori Curriculum Report and has been adapted to specifically address the
Montessori adolescent program and the assessment design for DPMSS.
The Montessori curriculum is organized in a developmental sequence
from one phase of learning to the next. Individual students, however, are able
to work successfully through elements of the curriculum in a sequence unique
to themselves. Assessment in Montessori classrooms, therefore, is based on
each student’s mastery of skills and knowledge at any point in the sequence.
Students display their progress and achievement through a variety of modes,
including spoken and written language, interaction with others, creative arts
such as drama, visual arts, model-making and importantly, through applying
what they have learned in practical ways.
Formative Assessment: Montessori teachers, working closely with the
adolescents, keep careful records to ensure the students are provided with
appropriate lessons when they are ready. Daily observation of students and
detailed record-keeping help teachers plan the lessons individuals will need
next. Working together, the adolescent students and the Montessori teachers
keep records of lessons given,the follow-up work completed by each students,
student progress and achievement, difficulties encountered by individual
students and how those difficulties were resolved. Montessori teaching and
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learning practices provide enhanced opportunities for formative assessment.
Here are some examples:
Because Montessori Junior high and Senior High teachers have students in
their class for three years, they come to know each student in a way that is not
possible when students move to new classes with new teachers every school
year. Through close observation over three years, Montessori teachers become
very aware of their students’s learning styles, strengths and areas requiring
further development.
Because most lessons are presented to individuals or small groups, the
teacher can easily observe and record levels of understanding and mastery in
individuals. Before a lesson draws to a close, all students in the lesson are given
the opportunity to show they understand the newly acquired skills or content.
Any student who needs further teaching can review the lesson when it is
presented to the next group of students ready for the lesson.
When students choose their own work extensions, they reveal a great
deal about their interest and ability at any point in time, which teachers are
then able to observe and record. During regular individual conferences with the
teacher, students become co-assessors of their work with the teacher. Junior
and senior high students are given rubrics prior to any assignment which they
can then use to assess their work. Students will also be provided with a detailed
Junior High or Senior High portfolio that identifies all standards and
benchmarks for their grade levels. They will then record the date they received
lessons addressing these benchmarks and also provide evidence of
understanding and academic achievement related to the benchmark.
Summative Assessment: Learning achievement in Montessori classrooms is
recorded through observation, the compilation of portfolios and detailed
records of progress. Progress will also be measured against achievement
benchmarks that are based on the Colorado Academic Standards and the
Common Core Standards. In these ways each student’s progress can be
expressed in terms meaningful to the student, as well as to teachers, parents
and the wider community.
The DPMSS SMART Goals are listed in Section I B. These SMART Goals will
be achieved in the following manner:
At the beginning of the school year, students’ math skills will be assessed
via the on-line math program’s assessment tools. One example of an on-line
math program is Renaissance math and their STAR assessment. DPMSS will
review the current on-line math offerings during its planning year to determine
which program is the most successful and most compatible with the Montessori
program. Students will take weekly and end of unit on-line assessments which
are summarized within the on-line program. Teachers will check student
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progress weekly to determine what math lessons students need in order to
continue making appropriate progress for that particular student. Teachers will
incorporate Montessori math materials along with more traditional math
instruction techniques during math lessons. If students are not making adequate
progress in math, despite additional support from teachers, then staff will begin
the RTI process.
Also at the beginning of the year, students will receive the DRA -2 to
determine reading levels. The principal, working with staff, will review this data
to determine what areas each individual students requires assistance in order to
continue to make adequate progress with reading. Students will be allowed to
choose their own literature books from a list provided by the school. Staff will
then work with students to make adequate progress in all aspects of reading,
including vocabulary, literary technique and structure, reading elements, and
the ability to analyze text. Reading instruction will occur via literature circle,
seminar and book clubs. During the first year, staff will administer the DRA-2
again half-way through the year and at the end of the year in order to obtain
data on effective reading instruction. Staff will continue to use the DRA-2 for
new students and students who are demonstrating difficulty with reading as
observed in seminar and literature circles, previous DRA-2 assessments and
State assessments. If a students continues to demonstrate a lack of progress
with reading after receiving additional lessons, staff will begin the RTI process.
The third assessment students will complete at the beginning of the year
is a writing assessment. Teachers will review the student’s written work using a
rubric based on Colorado Academic Standards for that grade level. Teachers will
identify what small group instruction each student requires, and place that into
the schedule. Students will be required to complete writing assignments
throughout each Occupations. Teachers will review progress, again based on
the CAS rubric, and continue to develop lessons plans for each individual
student. Should students continue to demonstrate a lack of progress after
additional teacher support, staff will begin the RTI process. DPMSS will use the
6 +1 Trait Writing Curriculum as a guide for lesson development.
At all times, the expectation is that students will be working at or beyond
grade level as determined by the on-line math assessments, the DRA-2, and
the writing rubric. If students are not working at grade level, staff will create a
lesson plan to bring students to grade level. That lesson plan will be a part of
that individual students junior or senior high portfolio.
Every month, the principal will review student portfolios to determine
percentage gained regarding achieved benchmarks. The principal will also
review data compiled from the on-line math program, the DRA-2, writing
samples, quizzes and end of unit assessments. Because the school will only
have 50 and 65 students in its first two years, the principal will be able to take
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a hands on approach to data review. As the school grows, some of these duties
regarding individual student data management will transfer back to the
program directors, and the principal will focus on overall school data trends.
This data will be reviewed monthly with the SAC Committee. Individual student
performance will be presented to parents during two parent/teacher/student
conferences per year. At these conferences, students will walk their families
through their portfolios. Teachers, students and families will discuss student
achievements, student challenges, and create goals for further progress.
The principal will use data management systems as recommended by
DPS. During the planning year, DPMSS will design electronic junior and senior
high portfolios that can be filled in by both teachers and students. Once State
assessment data and SPF are released after year one, the principal will review
data based on prioritized benchmarks. The principal will identify gaps in DPMSS
achievement as compared to other DPS schools and state averages. The
principal will work with staff to determine causes for these gaps and identify
small group Montessori lessons to improve student achievement.
The SAC committee will review student data monthly through reports
compiled by the principal. When the SPF is released, the SAC will work with the
principal to analyze successes and challenges, and create a formal report for all
stakeholders. This report will include SMART goals on those areas where the
school did not achieve satisfactorily. The SAC and the principal will also work
together with staff to create the Unified Improvement Plan that will include the
SMART goals along with other areas identified as needing improvement.
DPMSS high school graduation requirements will reflect the HEAR
requirements including four years of English, four years of Mathematics, three
years of Natural/Physical Science including two lab-based units, three years of
Social Sciences (with at least one unit of U.S. and one unit of World History), one
year of Foreign Language and two years of Academic Electives. Starting in
eighth grade, every DPMSS will develop a personal education plan which will
become part of their junior and then their senior high portfolios. These plans
will be completely integrated with their portfolios to insure students are
receiving 100% of the credits needed to graduate. Occupation curriculum will be
compared to course objectives for traditional classwork to determine
appropriate credit for ninth grade. Tenth through 12th grade classes will have
the same course objectives as traditional schools for the academic areas.
Students will receive grades and transcripts starting in 9th grade.
DPMSS is designed to respect stages of adolescent development, and
promotion and retention criteria will reflect this value. Students will be
expected to be promoted within their established class. A key time for
evaluation will occur towards the end of the ninth grade year. If a student is
demonstrating significant gaps in academic achievement, social and/or
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emotional growth to the level that they may not yet thrive in the high school, a
conference will be called between the student, their family, the principal and
the student’s advisor to determine if the student should spend an additional
year in the junior high. In high school, if a student is not on track to meet all
DPMSS graduation requirements, the student, their family, the principal and the
student’s advisor will meet to create a plan in order for the student to graduate.
One possible outcome of that plan may be for the student to spend an
additional semester or year at DPMSS until all graduation requirements are met.
If a student has exceeded graduation requirements before the end of
their 12th grade year, that student will have the option to graduate early or
dually enroll in UCD, Metropolitan State, or another college that offers dual
enrollment. Again, a meeting will be called between the student, their family,
the principal and the student’s advisor to determine the best course of action.
At all times, if a student is demonstrating academically, socially or
emotionally that he or she is struggling to make academic progress in the
school in order to achieve or maintain grade level, the advisor will meet with
the student and their family to analyze the cause. If improvement does not
occur, the advisor will work with staff to initiate RTI.
Compass Montessori High School created graduation outcomes for its
students. DPMSS will adopt the outcomes as a starting point for creating its own
outcomes reflective of is target population. The outcomes are as follows:
Outcome One : Is an experienced thoughtful writer and reader, adjusts
use of spoken, written, and visual language, to respond to the needs of society,
to acquire new information and for personal fulfillment.
Outcome Two: Has developed a mathematical mind: experienced use of
the power of mathematical thinking in problem solving and paradigm
formation.
Outcome Three: Is competent and knowledgeable in life sciences,
physical sciences and advancing technology.
Outcome Four: Is economics literate and an ethical entrepreneur
Outcome Five: Is effective and capable of expressing ideas, contributing
to a community of inquiry, actively listening and collaborating
Outcome Six: Is locally and globally aware, well worldly traveled in fact or
through reading of human encounters; historical minded and historically
literate about human history and the human condition.
Outcome Seven: Is physically active, a participant in activities that create
mental / physical challenges that foster whole person development.
Outcome Eight: Is a developing artist, song writer, poet, musician, actor,
etc.through practice, experience in, appreciation for and understanding of the
arts.
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Outcome Nine: Is aware and knowledgeable of self-construction and
actualization; has an immense sense of humor and an ingenious love of
learning.
When our high school students have achieved these outcomes, the result
will be graduates, regardless of ethnicity or income status, who will be prepared
for college or a career as well as demonstrate ingenuity, adaptability, creativity,
initiative and excellent communication and problem solving skills.
D. English Language Learner Students
Montessori education is an individualized inclusive approach for all
students in all cultures. It is a world recognized curriculum with Montessori
schools in nearly every country. Providing excellent ELA education is
completely in line with the DPMSS mission and vision. With their educational
focus of connecting the hand and the mind in all learning activities, DPMSS
teachers will be well prepared to assist ELL learners to acquire English in a fun,
engaging and meaningful manner. Prior to opening DPMSS, the principal will
attend DPS professional development regarding meeting the needs of ELL
learners. The Spanish teacher will attend all required DPS professional
development and classes to obtain ELA-E certification. The principal and all
other DPMSS teachers will obtain a minimum level of training to obtain ELA-T
certification. The principal and teachers will be expected to continue to attend
DPS ELA professional development in order to insure that best practices for ELA
are being implemented at DPMSS.
When a student enrolls at DPMSS, the administrative assistant will insure
that the newly enrolled family receives and completes a DPS Home Language
Questionnaire translated to the family’s native language. The administrative
assistant will compile the information and give to the principal a list of all
students who qualify for ELL services because their families speak a language
other than English at home. The administrative assistant will also give to the
principal a list of all incoming students who are already receiving ELA services
at their elementary schools.
Within the first two weeks of school, the principal will insure that the
ELA-E certified teacher gives the CELA Placement Test to the list of students
who qualify for ELL services and who are not currently receiving ELA services.
The ELA-E teacher will use the data gleaned from the CELA Placement Test to
determine the level of ELL services each student requires and give that
information to the principal. The ELA-E teacher will also review the ELL plans
for all incoming designated ELL students.
Within 30 days of school opening, the principal will send to all ELL
eligible students’ families a letter written in English and in their native language
stating that their student is eligible for a language instruction education
program and ELL services. The school will describe how ELL services will be
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provided at DPMSS. The school will request permission from the families to
begin ELL services for their students. The principal and the ELA-E teacher will
talk to any families with questions using interpreter assistance as needed.
During the planning year, DPMSS will research ELA curriculum to
determine what scientifically proven curriculum matches best with Montessori
curriculum and instruction. The chosen curriculum will provide lessons and
plans to support full implementation of State ELD standards. The ELA-T teacher
will use DPS established best practices to implement the curriculum. Examples
of these best practices include:
The teacher will provide a minimum of 45 minute block instruction for all
ELL students. The teacher will implement the ELD block in target language daily,
implementing the instructional components of the curriculum to design lessons
that provide explicit instruction of English language development in the four
domains: listening, speaking, reading and writing daily. There will be clearly
defined content and language objectives posted and articulated in student
friendly language at the beginning of lesson and revisited at the end of the
lesson. Lessons will address identified standards and meet students’ language
proficiency levels and academic needs as determined by ongoing observation
and assessment. There will be focused, appropriate lessons that introduce and/
or support social and academic language development in the four domains.
The teacher will create a positive classroom culture to support student
learning. The teacher will use a variety of techniques to make content concepts
clear and accessible including modeling, visuals, hands-on activities,
demonstrations, gestures, body language, and sufficient wait time for student
responses. The teacher will consistently use effective strategies to promote
academic language and learning (ex. chants, songs, graphic organizers,
cooperative groupings, Total Physical Response, visuals). The teacher will
provide frequent opportunities for interaction and discussion between and
amongst teacher and students. The teacher will encourage elaborated
responses to clarify lessons and and key concepts. The teacher will incorporate
and model sentence stems and patterns differentiated for student’s language
proficiency levels.
Daily lessons will be a combination of the selected curriculum and
Montessori curriculum. The teacher will rely on the selected curriculum to
insure that lessons are sequential, purposeful and address oral, reading, and
written language development, building background, language functions and
structures, grammar skills, vocabulary, comprehension strategies, reading
strategies and reading components (word work, fluency, vocabulary, writing
strategies and genres). With teacher modeling, there will be active student
involvement, with significant opportunities for accountable talk and extended
discourse to practice different functions of language, vocabulary, and, reflecting
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a balance of student and teacher talk, extended student language and modeled
correct language use. There will be a deliberate balance between teacher/
student talk striving for 80% student talk and 20% teacher talk. The Montessori
curriculum will include sheltered instruction within the different Montessori
environments including the farm, art studio and the commercial kitchen.
The ELA-E teacher will conduct, review and use end of unit and ongoing
progress monitoring (both individual and group) to assess progress in oral
language, reading and writing. Assessments will include progress tests, writing
samples, and oral interaction that assess stages of language acquisition. The
teacher will keep a body of evidence to monitor student progress and
encourage self-assessment. The ELA-E teacher will provide this data to the
principal and the student’s advisor. The principal will compile the data and
include ELA progress monitoring in the monthly reports that the principal
shares with the SAC. Advisors will include student data in student conferences
and parent/student/advisor conferences to set learning goals and communicate
with parents. The ELA-E teacher will link goals to students independent
reading, speaking and writing levels and will consistently provide effective
feedback to students that focuses on what the students can do.
When a student has demonstrated proficiency in all four domains as
measured by CELA testing and is at a minimum partially proficient in all State
mandated tested areas, the student, the student’s family, the ELA -E teacher
and the student’s advisor will meet to determine if the student is ready to exit
the ELL program and be redesignated as no longer requiring ELL services. This
team will determine appropriate ways to monitor student progress over the
next two years to insure that the student continues success. If the student
demonstrates, through student work or State mandated testing, a need for
continue ELL services, the student, with parent permission, will be incorporated
back into the ELL program, or receive supplemental targeted instruction
E. Special Education Students
DPMSS will use the Response to Intervention (RtI) model to identify
students requiring special education.3 The RtI model requires that achievement
data and a body of evidence is maintained for all students. DPMSS will insure
that universal screening is happening through the DRA-2, weekly on-line math
assessments, observation, mastery level quizzes and end of unit assessments
for both the junior and senior high. If a student is demonstrating a lack of
appropriate progress, the student’s advisor will contact and discuss concerns
with parents and work with teachers to begin implementation of strategic
3
Clarification to CDE: The RtI process will not be used in a way that will delay identification of a student who is suspected of
having a disability. Further, RtI is a general education process and framework for providing a multi-tiered system of support to
all students.
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interventions with fidelity. Staff will document these interventions and whether
or not the interventions are successful during a predetermined length of time
such as 8 - 12 weeks. The documentation will occur on a secure, shared
document format so that all teachers can review what interventions are being
tried for each student, and share their own observations of successful
interventions. Progress will be monitored via observation, weekly written
samples, weekly on-line math assessments, participation in seminar, mastery
quizzes and end of unit assessments, and DRA-2 assessment.
If the student responds to the interventions, they will remain in place as
long as necessary. If the student does not respond to the interventions as
documented by insufficient progress towards specific benchmarks in the given
area of concern, the advisor will bring the student to the monthly convened
student intervention team. The student intervention team will consist of the
principal, the special education provider, and at least two additional teachers.
The student’s parents will also be invited to participate in this meeting only
during the time that their particular student is being discussed. At student
intervention team, the team will review the student performance data collected
before and during interventions. The team will then discuss further
interventions for the teachers to use for that student within a determined
number of weeks. Teachers will implement the interventions with fidelity and
record the student’s response to the interventions. Progress will again be
monitored via observation, weekly written samples, weekly on-line math
assessments, participation in seminar, mastery quizzes and end of unit
assessments, and DRA-2 assessment.
If, after trying a variety of interventions, the student is still not making
sufficient progress as compared to his/her peers, the special education
provider will begin the process to determine if the student qualifies for special
education services. This process will follow all Federal and Colorado special
education guidelines including parent notification, a complete record review,
additional testing if needed and appropriate written permission. Once the
assessment process is completed, the special education provider will convene
an initialization meeting that consists of the student, the student’s family, the
student’s advisor, the general education teacher, the principal, the special
education provider, the psychologist/social worker, the school nurse, and any
other experts necessary to create a holistic picture of what the student requires
in order to achieve a free, appropriate, public education and to thrive at DPMSS.
If this team determines that the student requires special education services, the
team will then determine how much and what type of services the student
requires and set initial goals for the student. The special education provider,
the student’s advisor, and the family will continue to work together to set
appropriate goals for the student. Progress on these goals will be monitored by
the student advisor and the special education provider.
DPMSS will accept students coming from DPS Montessori schools without
discrimination towards students with disabilities. Prior to the start of every
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school year, the DPMSS special education provider will review the list of
incoming students to determine who is currently on an individualized education
plan (I.E.P). The provider will review the I.E.P. and conduct transition meetings
with the student, the student’s families and the special education team from
the sending school. Goals will be reviewed to insure they align with the DPMSS
junior high program.4 Progress will be monitored by both the special education
provider and the student’s advisor via observation, weekly written samples,
weekly on-line math assessments, participation in seminar, mastery quizzes
and end of unit assessments, and DRA-2 assessment.
The student’s I.E.P. will be formally reviewed no less than once per year
with documentation of progress written quarterly. During the annual review,
student goals will be discussed to determine if goals have been met and if new
goals need to be set based on a collected body of evidence of both formal and
informal assessment. Every three years, the special education provider will
convene a triennial meeting to determine if the student still requires special
education services.5 At that meeting, all student progress, including scores on
State standardized assessments, DPMSS internal assessment, the student’s
portfolio and a body of evidence gleaned from observation and student work
will be discussed, along with any required testing. The meeting will consist of
the special education provider, the principal, the student, the student’s family,
the student’s advisor, the psychologist / social worker, the school nurse, and
any additional staff or experts deemed necessary for this meeting based on the
student’s needs. If the team determines that the student no longer requires
special education services, the I.E.P. will be terminated. The team will then
determine appropriate progress monitoring for the next year to determine if the
I.E.P. needs to be re-opened as well as make appropriate recommendations to
the general educator in supporting the student. If the team determines that the
I.E.P. needs to stay in place, the team will evaluate services provided, adjust as
deemed necessary, and create new short term and long term goals.
The DPMSS special education teacher and the psychologist / social
worker will be highly qualified and duly licensed as such by C.D.E. to serve
students from 6th grade to 12th grade. The school nurse will be a licensed
nurse by the State of Colorado. All other experts used in the I.E.P. process will
hold appropriate C.D.E. or State licensing in their respective area of expertise.
During the first few years, DPMSS will require only part time staff. DPMSS
intends to partner with other schools within DPS to share employees for special
education provider, psychologist / social worker and school nurse.
Montessori education is an ideal match for serving students with
disabilities. All students are educated in an individualized manner, with
personal goals and personalized progress monitoring. Lessons are presented in
small group format with multiple opportunities to check for understanding, ask
4
Clarification to CDE: All goals in the IEP will be developed to meet the individual needs of the students, resulting from the
disability.
5
Clarification to CDE: The triennial meeting will be a triennial evaluation and meeting and a regular education teacher will be
a required member of the IEP team.
Page
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questions, and demonstrate knowledge. All lessons are differentiated to meet
the needs of attending students. Students are then allowed to demonstrate
learning in a wide variety of ways. In Montessori, the special education provider
is integrated into the classroom, working side by side with all students, with
and without I.E.Ps. At the same time, the special education provider insures that
students with I.E.Ps are receiving the required minutes of service. If the special
education teacher needs to meet with I.E.P. students one on one or in small
groups, the schedule easily allows for these types of pull-out lessons.
Secondary Montessori Special Education involves awareness of the student
to understand his/her disability and learning style. Much like regular education,
DPMSS will encourage students to become self directed learners and find
strategies that work for them. As they ready themselves for the next level,
students learn to become increasingly more independent in their learning. They
learn to ask for help from a variety of resources and ask for accommodations
based upon their need. Students learn to be their own best advocates and are
then able to carry this skill to college and post secondary careers.
A student’s disability is treated as a learning difference. In Montessori,
students recognize that all students learn differently, and staff work with all
students to determine optimal learning styles. Because of this culture, students
with disabilities leave behind much of the stigma around being a different type
of learner. Instead, they embrace their differences, understand strategies they
need to succeed, and work with the special education provider and their
teachers to receive accommodations necessary for academic achievement.
The strategies used by the special education provider will vary depending
on student disability. The provider will use the existing Montessori materials,
key lessons and curriculum as the basis for instruction. If a student requires
additional, outside curriculum such as Wilson Reading Systems, the special
education provider will consult with DPS to determine the most current highly
effective curriculum for the specific targeted intervention. Any outside
curriculum used will be scientifically proven to help students with that
particular targeted intervention. For our high school students with I.E.P.s, the
special education provider will work with the student, the student’s family, and
the student’s advisor to create transition plans to assist the student in
identifying and determining post secondary options.
The principal and teaching staff will attend DPS sponsored professional
development regarding RtI. If DPS does not have such professional development
available, DPMSS will work with the special education provider to create this
professional development including bringing in consultants if needed. The
special education provider and the psychologist/social worker will seek out
professional development as provided by DPS to insure they have the latest
understand of adolescent brain development and how that applies to students
with disabilities, application of RtI, and current high quality and scientifically
proven interventions that will blend well within the Montessori environment.
The special education provider and the psychologist/ social worker will then
share this information with the general education staff.
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E. Academic Intervention and Acceleration
The DPMSS schedule is designed so that teachers are easily able to
schedule and conduct small group lessons. These lessons will be created to
meet the needs of the variety of learners at DPMSS, including special education,
ELL, gifted and talented and intervention students. There will be key lessons to
advance the curriculum, targeted intervention lessons for students
demonstrating a need for additional support, and challenge lessons for
students demonstrating a need and ability to work beyond the established
curriculum. Montessori education uniquely supports all types of learners
because of its focus on individualized education.
During the Wednesday afternoon staff integration time, the principal and
the teachers will review data gleaned from on-line math assessments, the
writing samples and the DRA-2, along with observations, and body of evidence
including student portfolios. Through these meetings, staff will determine what
students are succeeding with tier I intervention and therefore only needing key
lessons. Staff will also identify tier II students who are lagging behind their piers
and demonstrating weak progress. Staff will collaborate and determine what
targeted lessons these students require and plan for those lessons. Staff will
work together to determine specific interventions and document the use and
success or lack of success of these interventions in a secured, shared document
format. If students continue to demonstrate a lack of success after different
interventions are attempted, the student will need tier III intervention and will
be referred to the student intervention team as described in the Section D.
Targeted interventions in math will include revisiting the elementary
Montessori math materials. These materials provide concrete representations of
advanced math concepts in a manner that allows students to understand the
concepts with their hands as well as their heads. Additional targeted
intervention includes small group lessons that meet students at the level they
need to make progress. The on-line math program will support these
interventions as math programs such as Renaissance Math are designed to
meet the individual skills and challenges required by the individual student.
Targeted interventions in reading will include small group lessons or one
on one assistance depending on the individual student’s needs. At this level,
deficiencies are often in fluency and/or comprehension. Comprehension can be
improved by working with students to practice pulling out important
information or highlighting. Fluency typically improves with practice, practice,
practice as most struggling readers avoid reading. Teachers will create safe,
small group lessons that allow students to practice reading. Students will also
be allowed to choose their literature books, from a list generated by the school,
so that they have more ownership of the books that they are reading. Targeted
interventions in writing will incorporate the 6+1 Trait Writing program.
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Teachers will determine what traits students need reinforcement on and create
small group lessons using this scientifically proven curriculum.
Montessori education meets the needs of students requiring additional
challenge. Montessori students determine what follow up work they want to
investigate within the curriculum. Because of the open ended nature of this type
of approach, students are able to take their follow up work as wide and as deep
as they choose. Presentations of learning can be accomplished using a variety
of modalities including PowerPoint, dramatis personae, extended essay, song
writing, poetry and creating physical models. The goal of the teachers and
student advisors is to insure that students are working a majority of the time to
the top level of their ability. Should a student demonstrate a lack of
engagement, the student’s advisor will meet with the student to determine what
additional skills a student requires to reach the next level of learning. These
challenge lessons will then be designed and delivered.
Dr. Mihaly Csikszentmihalyi through his research created a chart that
demonstrates optional flow or engagement. (Flow, the Psychology of Optimal
Experience, p. 74) The chart demonstrates that optimal flow, or engagement,
occurs at the intersection of challenge and skills. If a person in experiencing
high challenge and low skills, the result is anxiety. If the person is experiencing
high skills but low challenge, the result is boredom. The goal at DPMSS is to
insure that students are fully supported so that they are working at the exact
intersection of high challenge and high skills in order to make optimal
academic along with social and emotional progress.
At DPMSS, a high school student who is at risk of dropping out or not
graduating will be identified long before the situation becomes a crisis.
Through the integrated planning time and review of data, staff will be aware of
students who are not making adequate academic progress and work with the
student and the student’s family to create a plan for the student to get back on
track. Student advisors will create professional, trusting relationships with
students so that they will be aware if a student is experiencing challenges
beyond school that affect their ability to succeed at school. In this event,
advisors will link the student and the school psychologist / social worker to
insure the student is getting support needed outside of school to succeed at
school. Students needing additional academic support will receive this support
through the RtI process. If a high school student is still struggling with
obtaining credits necessary for graduation, the student, the student’s advisor,
the student’s family and the high school program director will meet to create a
graduation plan that may include summer studies, on-line education,
partnership with other DPS schools, an additional year at DPMSS, and any other
support necessary to insure that the student graduates ready and able to attend
college or succeed in a career.
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G. Gifted and Talented Students
Montessori education is an ideal match for students who are identified as
gifted and talented. Because the majority if not all of the students will be
coming from DPS Montessori schools, gifted and talented students should
already be identified and have ALPs. For the first two years of the school, the
principal will also be the GT coordinator. That task will eventually be delegated
to a selected and trained teacher. Both the principal and, when selected, the
staff GT coordinator will attend DPS sponsored professional development for
identifying and serving GT students. The principal will also conduct
professional development for the staff to insure the needs of GT students are
being addressed at DPMSS.
When a GT student is enrolled at DPMSS, the principal will review ALPs of
all incoming GT students and discuss the ALPs with sending teachers and GT
coordinators. At the start of the school year, the principal, the student, the
student’s advisor and the student’s family will meet to review the ALP and
discuss how best DPMSS can support the student towards reaching ALP goals.
Montessori students determine what follow up work they want to
investigate within the curriculum. Because of the open ended nature of this type
of approach, students are able to take their follow up work as wide and as deep
as they choose. For GT students, further connection to challenging curriculum
may be required. Depending on the situation, this could occur via connecting
the students to outside experts related to the Occupation, having the student
research and co-teach with staff key lessons, having the student design and
implement management roles, and having students create polished,
professional presentations that can be shared with the greater community. For
High School, students can take on-line coursework that better meets their
academic level and can dually enroll in college coursework. Students can also
create and co-teach with staff elective coursework and test preparation classes.
All of these options will be available to all students, regardless of if they
have a GT designation or not. This will allow students who perhaps qualify for
GT designation but have chosen not to purse the designation to also work at
their highest levels. If a DPMSS student who does not have a GT designation
and who demonstrates the potential to qualify for GT designation and also they
(or their family) desires to pursue the GT designation, the principal will follow
the GT designation criteria as outlined on the DPS Gifted and Talented website
to determine if the student qualifies for GT services.
H. Supplemental Programming
Montessori adolescent programs are designed to address the social,
emotional and mental well being for students. The advisor model and three
year cycle are designed so that teachers create professional, positive
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relationships with students and are able to understand students’ abilities at a far
deeper level than if they only had students for one class or one year. During this
time, the student’s advisor is also able to create positive partnership with the
student’s family so that there is an entire network of communication and
support for students. Throughout Montessori education, students are strongly
encouraged to develop and use their voice, to advocate for themselves and to
figure out solutions to their challenges with adult support. If a student requires
further intervention than the advisement model can support, the advisor will
connect the student to the school psychologist / social worker so that he or she
can determine appropriate resources for the student.
Nurturing physical health is also a core value of Montessori. One of the
purposes of the urban farm is to connect students to a wide variety of
organically grown food. The food grown will be added to the school lunch
program so that students have fresh vegetables that they have grown
themselves. The outdoor work is physical and requires students to challenge
themselves in order to complete the required tasks. Because the students are
working side by side with their friends and with an adult, the students
partcipate generally with a positive attitude. One of the Occupations will be
focused on adolescent development, nutrition and health. Students will learn
the science of adolescent development and nutrition, and have the opportunity
to ask questions and discuss the negative affects of alcohol and drug use on
the developing brain.
Another core value of Montessori education is the creation of positive
communities. There is extensive conversation regarding creating community,
supporting positive behavior and being inclusive. Students are invited to bring
up community concerns at daily advisement meetings and weekly community
meetings. Behavior that resembles bullying, exclusivity, discrimination,
prejudice and any other non-inclusive behavior is immediately addressed and
processed with involved parties. Montessori students take pride in their healthy
communities, and they advocate in a variety of ways to maintain them.
The junior high will have a supervised study hall on Wednesday
afternoons to give students an opportunity for a quiet environment to catch up
on work. DPMSS will also work to find background checked parent or
community volunteers to create afterschool clubs and team sports. One sport
that Montessori students gravitate towards is Ultimate Frisbee. DPMSS intends
to create a high school ultimate frisbee team, but will need to do so with
volunteer support.
DPMSS will partner with existing summer school programs if the
student’s advisor, the principal, the student and the student’s parents
determine a student would benefit by attending summer school.
Volunteer programs have been addressed in the schedule portion of this
application.
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Section IV: TEACHING
The primary goal for teacher coaching is to create a recursive learning
environment where teachers can evaluate and improve their practice through
reflective conversation with other teachers, the principal, peer observers and
Montessori consultants. Our definition of a recursive learning environment is
the process of improving Montessori practice by examining the principles of
Montessori theory and how it applies to adolescent education. Colleagues then
share their acquired knowledge and skills with one another resulting in the
knowledge being reinforced for the “teacher” and spread exponentially among
the other staff members. At DPMSS, we will focus on implementing Montessori
theory and understanding adolescent brain development. The school will be
constructed around how these two factors can be maximized to insure an
optimal learning environment.
The tools we will use for teacher observation include the Framework for
Effective Teaching used by principals and peer evaluators to evaluate
Montessori teachers in DPS. Another tool we will use will be an observation
rubric specifically created for DPMSS. That rubric will include prepared
environment, engagement of students, quality of key lessons, portfolio quality
and completion, ability of teacher to link students to high quality follow up
work, overall quality of the Occupation including involvement of outside
experts, initial engaging experiences (first period lessons), challenging and
interesting follow up work (second period) and high quality presentations of
learning (third period). The third tool we will use is data review. This includes
student portfolio review, review of the on-line math assessments, review of
mastery and end of unit assessments, review of writing samples throughout the
year and standardized test results. At least 50% of a teacher’s overall evaluation
will be based on review of student data.
DPMSS is an integrated learning environment that allows teachers to work
together or separately depending on the need for that day. Additionally, DPMSS
will require that teachers formally observe each other using the DPMSS
Observation Rubric at least twice per year. Staff will then use the results of this
observation as an opportunity for recursive learning during integrated staff
time. The school leader will observe teachers once per month alternating
between the Framework for Effecting Teaching Evidence Guide and the DPMSS
Observation Rubric. This information will again be brought to staff in a nonthreatening way during teacher integration time. DPMSS will also welcome
observations by LEAP peer observers.
During the weekly staff integration time, there will be dedicated time on
the agenda to discuss teacher observation and student data. The goal always is
to create a recursive and reflective learning environment to insure that we are
improving the Montessori program and student outcomes. If personnel issues
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arise from the observations, that will be handled privately through the teacher
evaluation process.
B.Teacher Evaluation
Prior to the new school year, DPMSS will create a teacher self-evaluation
tool based on the desired outcomes of the school, the DPMSS observation
rubric, SMART goals as set forth in this application and thereafter in the Unified
Improvement plan, and the Framework for Effective Teaching. This evaluation
tool will be discussed during professional development. Teachers will then be
given time during professional development days to thoughtfully identify areas
of strength and to create goals for areas of improvement. The principal will
review the self-evaluation tool individually with each teacher and work with the
teacher to add strengths and areas of improvement.
No less than two times per year, the principal will meet with the teacher
to review the self-evaluation tool and determine progress based on
observations and data. The second meeting will be the formal teacher
evaluation and it will be between the principal and the teacher, using
information gathered from peer observations, peer observer observations,
principal observations and data on student performance as demonstrated
through student portfolios, weekly on-line math assessments, DRA-2
assessments, writing samples evaluated against a grade leveled rubric, mastery
quizzes and end of unit assessments. At least 50% of the evaluation outcome
will be based on student improvement as demonstrated through data. Prior to
the formal evaluation, the teacher will fill out their self-evaluation based on
goals set at the beginning of the school year.The teacher will share that
document with the principal in advance, so that the principal can better prepare
for the formal evaluation.
At the formal evaluation, the teacher and the principal will discuss
strengths and successes. They will also discuss goals and what goals were met,
where progress was made, and where progress did not occur. Together, the
principal and the teacher will create a plan to assist the teacher towards
meeting goals necessary to improve student outcomes.
If a teacher is not making progress as determined through observation
and data, the principal will inform the teacher privately after each monthly
observation. The principal will encourage the teacher to bring forward their
challenges at the weekly staff integration meeting for advice and support. The
principal will also find professional development to assist the teacher, and work
personally to coach the teacher. If, after additional professional development
and coaching, the teacher continues to not make reasonable progress as
determined through observation and data, the principal will create a formal
performance improvement plan based on the goals set forth in the Teacher
Self-Evaluation rubric. This plan will require improvement as determined
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through observation and data within 60 days or by the end of the school-year
depending on the timing of the performance improvement plan. If improvement
is not made, DPMSS will have the option to terminate or not renew the teacher’s
contract. Prior to school opening, DPMSS will create a staff policy handbook that
will include a grievance procedure that will allow staff sufficient opportunity to
appeal in the event they feel their contract has been wrongfully terminated.
C. Professional Development
The principal at DPMSS will ultimately be responsible for managing and
evaluating professional development. There will be several areas of professional
development. The first area will be DPS sponsored. This will include RtI, ELA-T
and ELA-E, Positive behavior support, and any other DPS professional
development that will insure our staff is well educated in providing an optimal
education to a diverse student body.
The second area of professional development will be on Montessori
education and adolescent brain development. All teaching staff will be required
to attend training on Montessori adolescent education such as the AMI
Montessori Orientation to Adolescent Education. This five week intensive course
of study includes all aspects of adolescent Montessori education. During the
school year, each member of the teaching staff and leadership team will lead a
seminar based on Montessori literature. The North American Montessori
Teachers Association has given DPMSS a $3,000 grant and an additional $5,000
in-kind for professional development. The principal will create a professional
development plan to utilize this grant throughout the first three years.
The third area of professional development will be led by the principal
and will be on data collection and evaluation. The principal, working with DPS,
will work with staff to create appropriate data collection tools and methods
whereby the data is frequently reviewed.
The fourth area of professional development will be led by the special
education provider and/or the psychologist social worker. This area will cover
adolescent brain development, differentiated learning, implementing effective
teaching strategies with students who have special needs, and ongoing
professional development on RtI. The Special Education teacher and/or school
psychologist/social worker will attend professional development on these
topics at DPS and review materials and/or attend workshops by professionals
such as Dr. Steve Hughes and the Gurian Institute.
Prior to the first day of the first school year, DPMSS will have ten
professional development (PD) days in order to insure that we are fully prepared
for the very first day of school. During this time staff will attend DPS
professional development for ELA and RtI. Because staff will already be trained
in Montessori at both the elementary and adolescent levels, a majority of the
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planning time will allow for staff to prepare their environments and review
curriculum for the first series of Occupations. The Occupations curriculum
requires a deep understanding of the land, the local area, public transportation,
and local community resources. Staff will work with the principal to make sure
that all necessary materials to run successful Occupations are readily available
so that the school year can start as smoothy as possible. There will also be
professional development around positive behavior support and Discipline
through Love and Logic offered by the Love and Logic Institute. The principal
will review with staff the DPMSS farm school portfolio, rubrics, record keeping,
assessment and all other tools necessary to frequently and accurately obtain
data regarding student achievement.
After the first year, DPMSS will have five PD days prior to the first day of
school. During the school year, DPMSS will have an additional five professional
development days. The topics for the professional development days during the
first school year will be as follows: Record keeping and assessment, RtI and
meeting the individual learning needs for all of students, review of and creating
best practices for writing and implementing Occupations curriculum, further
work regarding RtI and meeting the individual learning needs for all students,
and understanding the Urban Farm and how it applies to Montessori adolescent
education. In addition, on Wednesday afternoons from 1:30 - 3:30, staff will
attend staff integration meetings. These meetings will include data review,
discussion on recent observations, curriculum review and student discussion.
DPMSS will have monthly ninety minute staff meetings on where the
primary focus is Montessori theory and understanding adolescent brain
development.These staff meetings will support the recursive learning
environment. The meetings will allow for reflective conversation to evaluate
and improve practice. Staff will improving Montessori practice by examining the
principles of Montessori theory and how it applies to adolescent education.
Colleagues will share their acquired knowledge and skills with one another
resulting in the knowledge being reinforced for the “teacher” and spread
exponentially among the other staff members.
D. Teacher Recruitment, Hiring, and Retention
DPMSS teachers will be Montessori trained at the elementary level. If a
teacher is identified who has not yet obtained this Montessori training, they will
be required to do so during summer sessions. DPMS teachers will also have
attended Montessori adolescent training. Again, if a teacher is identified who
has not obtained Adolescent Orientation, they will be required to do so during
summer session. Every effort will be made to find high quality teachers who
already have one if not both of these trainings.6
DPMSS will recruit teachers through the NAMTA, AMI, AMS and Public
Montessorian websites. In the first year, DPMSS intends to hire a licensed
teacher who is highly qualified in science and math and is Montessori trained.
6
Clarification to CDE: All teachers who teach core content classes will meet the Highly Qualified requirements by holding a
Colorado teaching license and demonstrating subject matter competency.
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There are teachers who have all of these designations. However, it is highly
likely that DPMSS will hire someone who has most but not all of these
designations.7 Upon selecting the right teacher, DPMSS will work with that
individual to obtain summer training or enroll in coursework so that they have a
clear, achievable path to obtaining all of these designations. The second
teacher hired will be a licensed teacher highly qualified in Spanish, ELA-E
certified and Montessori trained. Again, it is highly likely that DPMSS will hire
someone who has most but not all of these designations.8 Upon selecting the
right teacher, DPMSS will work with that individual to obtain summer training or
enroll in coursework so that they have a clear, achievable path to obtaining all
of these designations.
The junior high and senior high program directors will be selected from
the existing staff as long as there are candidates ready, willing and qualified to
take on these leadership positions.
During the first two years, DPMSS will be serving 6th, 7th and 8th grades
in an integrated learning environment. Teachers are highly qualified to teach
these levels if they have k-8 elementary licensure. Prior to adding the 9th
grade, DPMSS will need to have teachers in place who are highly qualified to
teach secondary math, science, language arts, social studies and Spanish.
DPMSS will begin recruitment, identification and training of these teachers
during the first two years so that all teachers are highly qualified in their
subject area and Montessori trained. DPMSS will continue to aggressively reach
out locally and nationally to find teachers who are excited about teaching in a
public Montessori secondary environment and willing to complete the rigorous
training in order to do so.
DPMSS will request a waiver regarding licensed staff in order to insure the
best possible Montessori teachers are hired. All teachers will still be required to
be highly qualified (as determined by a bachelors degree, 24 hours of
completed coursework in their subject area, and/or passing the PRAXIS or
PLACE testing for their subject area) prior to hiring. All unlicensed teachers will
be required to pursue alternative teaching licensure through programs
approved by DPS.
Teacher retention will be the highest priority at DPMSS. Montessori
adolescent programs work best when there is a consistent, well trained, highly
effective staff. DPMSS will operate under the principals of shared leadership.
The culture at DPMSS will be respectful, inclusive and consistent. As
demonstrated at Compass Montessori School in Jefferson County, CO, a positive
inclusive school culture results in high staff retention, even during difficult
times such as the recent decline in school funding.
7
Clarification to CDE: All teachers who teach core content classes will meet the Highly Qualified requirements by holding a
Colorado teaching license and demonstrating subject matter competency.
8
Clarification to CDE: All teachers who teach core content classes will meet the Highly Qualified requirements by holding a
Colorado teaching license and demonstrating subject matter competency.
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Section V: FINANCE
A. Budget and Policy Narrative
The DPMSS school leader will be in charge of managing and overseeing
the school budget. Katy Myers has ten years of experience managing the
Compass Montessori School budget. Compass is a Jefferson County Public
School located in Wheat Ridge and Golden. The two campuses were treated as
separate business units, and Katy managed the budgeting, variance reports,
audit process and all aspects of the school’s finances. When Katy departed
Compass in 2011, both schools had positive fund balances. The Golden fund
balance was over $200,000. The Wheat Ridge fund balance was at a prospective
($180,000) when Katy took over that site in 2008. By 2011, the Wheat Ridge
fund balance was at $40,000. By the end of this year, based on the budget Katy
created last year, that Wheat Ridge fund balance will be closer to $100,000.
Based on the budget template provided, DPMSS will be cash positive by
year 3. In year 0, year 1 and year 2, DPMSS will rely on a $300,000 grant for
performance schools to cover salaries until the school reaches enrollment of
105. DPMSS will maintain a cash positive budget throughout the next four
years, including when it reaches steady state enrollment of 225 students and
10 teachers and related administration and support staff.
A minimum of 95% of allocated SBB revenue will be spent on salaries to
support a student - teacher ratio of 25 to 1. In year one and two, the school will
have 50 and then 65 students. Because of this small size, the principal will be
paid 50% at the principal’s salary level and 50% at the teacher’s salary level. The
principal will spend 50% of her time teaching. In years three, four and five, the
principal will spend 75% of her work time on principal duties and the remaining
25% teaching. Her salary will reflect this distribution. In year six, the school will
require and be able to afford a full time principal.
For years one and two, DPMSS projects a population of students requiring
special education services of about 10% of the total population. At 50 and 65
students, that equates to 5 and then 7 students. Therefore, the school is
planning on special education staffing of 25% FTE or 10 hours per week. DPMSS
hopes to partner with other small DPS schools to share resources. As the school
grows, the percentage of this position grows as well until year six when it is a
full time position. DPMSS also intends to hire a school pschologist / social
worker for the equivalent of one day per week during year one and two. As the
school grows, this position will also grow until year seven when it will remain at
28 hours per week.
For school nurse, DPMSS intends to use the clinic aid model often used in
charter schools. The office support will also be the clinic aid and will be
delegated to dispense medications in the manner authorized by law. The school
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nurse will supervise the clinic aid in these duties. For years one and two, the
school nurse will come to the school twice a week for two hours to review
records and insure the school is in compliance. As the school grows, the hours
for school nurse will grow as well until year seven, when this postion will
remain at twelve hours per week.
During year 0 and year 1, DPMSS will use a performance school grant to
retrofit a DPS facility to insure that the school has a commercial kitchen, science
laboratories, an art studio with a kiln, and the ability to create an urban farm.
The ideal environment will have a gym and a performance space. DPMSS intends
to create a 2 to 1 ratio of students to computers. DPMSS will work with DPS to
create an efficient technology plan that could incorporate the use of thin client
or other inexpensive but effective computer hardware set ups. All staff will have
a laptop or tablet in order to efficiently record what students are attending
which lessons and related follow up work.
DPMSS will require classroom materials including a well stocked
laboratory to handle high school chemistry, biology and physics, reference,
non-fiction research books and fiction books for the library, literacy books, and
classroom materials to allow for the instruction of a wide variety of
Occupations , US history, Civics, Economics, A.P. World History, A.P.
Environmental Science, A.P. Biology, Advanced Algebra, Geometry,
Trigonometry and Calculus, A.P. Spanish and A.P. Language Arts. DPMSS will
also require access to an on-line math program for every enrolled student plus
a wide variety of math resources.
Non-typical expenses will include materials to build and maintain an
urban farm, including a water system. One very successful Occupation in other
Montessori adolescent programs is a culinary arts program that provides lunch.
Compass Montessori is its own School Food Authority and provides lunch for
the entire 330 student Golden campus. If DPMSS is able to work with the DPS
lunch program to create a similar opportunity, that would be ideal. DPMSS will
also require a complete set of Montessori materials equal to one large
classroom in an elementary setting.
DPMSS will use proceeds from the performance school start up grants to
buy the typical and non-typical classroom materials and technology. Once all
purchases are made via grant funding, DPMSS will set up a replacement
schedule to make sure that classroom materials are replaced in a methodical
manner and that school technology is updated every three years.
An ongoing need will be travel money for extended overnight trips. The
junior high program will travel within Colorado and adjacent states to visit
farms, ranches and historic sites related to the Occupations and humanities
curriculum. The high school will have one international trip per year. DPMSS will
create an ongoing fundraising effort to assist in funding these trips. No student
will be excluded from going on a trip due to inability to pay for the trip.
The next two pages is evidence supporting grant estimates.
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Start Up Grant
Lauren Masters <[email protected]>
Wed, Mar 21, 2012 at 7:36 PM
To: "Murray, Alison" <[email protected]> Cc: "Neal, Mathew"
<[email protected]>, "Proctor, Grant"
<[email protected]>, Katy Myers <[email protected]>
Hi all,
Alison - thank you so much for your quick response and for being so
willing to help (as always)! I think a quick phone call or a look at Katy's budget
template thus far would be really helpful. Katy - your other budget questions
re: nursing and social worker requirements are something that Alison can help
answer.
I also wanted to provide some further clarity (on top of Mathew's email)
about the start up grants for new performance schools. Performance schools
get 2 sources of grants from DPS - 1) FFE and 2) start up funds to cover non
FFE.
1) FFE: All new approved performance schools will receive a separate grant
fund for FF&E, which is why there are not line items for curriculum materials,
furniture, computers, etc. on the budget form. Those expenses are covered
separately. This also includes maintenance facility upgrades for DPS sites that
are required to fit the school into a DPS building. Please note these facility
upgrades cover the bare minimum to retrofit a school into a space and some
schools want to use funds to do additional facility upgrades as Mathew
mentioned (again very site specific).
2) Start up funds:Tends to be @ $300-400,000 for non-FF&E (largely to
fund operating deficits as enrollment ramps up)over year 0, year 1, and year 2.
Schools should be sustainable on PPR by year 2 or 3. Mathew did a great job
describing the typical year 0 expenses, but year 1 and year 2 also normally have
operating gaps that need to get filled as the school's enrollment grows, so it is
not unusual to see start-up funds go towards salaries and PD (and not
facilities). Alison and Grant have a great perspective on this as well from past
experience. While 300-400K has been the available amount in the past, the pot
of money that funded past new performance schools continues to dwindle so I
just want to also add a disclaimer to be as conservative as you can with start up
funding (i.e. as close to $300K over year 0 - year 2 that you can get your
budget at, the better).
I hope this helps. Let me know if you have any outstanding budget
questions once you talk to Alison.
Thanks!
Lauren
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Denver Public Montessori Secondaty School
March 19, 2012
N· A· M · T·A
13693 Butternut Road
Burton, Ohio 44021
tel 440.834.4011
fax 440.834.4016
Katy Myers
10923 Magnolia Dr.
Apt. B,
Cleveland, OH 44106.
Dear Katy,
[email protected]
www.montessori-namta.org
Montessori Development Partnerships and the North American Montessori
Teachers' Association have authorized a cash grant of $3000.00 in start-up
funds to be used primarily for Montessori consultancy and services from
Project 2012. Services in kind constitute an additional $5000 in honoraria
donated from David Kahn and Laurie Ewert-Kroeker (and others) in providing
on-site programming and materials for the project. The $3000.00 will be
disbursed in June.
We have elected your program for sponsorship because of our faith in your
history of making Montessori secondary programs work, especially
demonstrated in the viability and authenticity of Compass Montessori School
located in Golden, Colorado. Having had contact with Montessori High
School at University Circle and Hershey Montessori School Farm Program,
we are hoping you adopt some of our successful curriculum design and
orientation creating a unique blend of school cultures that will inevitably lead
the country in Adolescent work.
With best wishes for Denver Public Montessori Secondary School.
k:t..._
0
David Kahn
Si
Executive Director, NAMTA
Executive Director, MDP
e
in affiliation with the Association Montessori In temationale-Amsterdam, Netherlands
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Optional Section VI: Innovation School Status
DPMSS will be requesting Innovation Status through the DPS Innovation
School Application. The 6th grade through 12th grade Montessori curriculum
that DPMSS will implement is rigorous, innovative, interesting and is designed
to engage students to produce optimal academic achievement as well as social
and emotional maturity and well-being. Montessori adolescent curriculum has
been designed and tested over the last fifteen years at both private and public
Montessori schools. This curriculum, referenced throughout this application as
Montessori National Curriculum, has been collected, refined and reported
through The NAMTA Journal, A Montessori National Curriculum Report, The
NAMTA Journal, Volume 37, No. 1, Winter 2012. DPMSS will design its program
using this curriculum. Recently, the Montessori National Curriclum for the
Adolescent Program from Twelve to Fifteen/Sixteen Years was reviewed by the
Australian Curriculum Assessment and Reporting Authority. Their findings, as
reported in A National Montessori Curriculum Report, are as follows: ACARA
(Australian Curriculum Assessment and Reporting Authority) established an
extremly rigorous recognition process to determine the extent to which a wellestablished alternative national curriclum can deliver comparable educational
outcomes for students to those based on the Australian National Curriculum.
ACARA have advised that (the National Montessori Curriculum) aligns with the
Melbourne Declaration on Educational Goals for Young Australians, meets the
particular principles and guidelines in relation to the Shape of the Australian
Curriclum v3 paper, and allows for broadly comparable educational outcomes in
English, mathematics, science and history by the end of year 10.
In order to effectively implement the curriculum, DPMSS will need to
adopt its own schedule, its own standards for hiring teachers, its own school
calendar and professional development plan, its own assessments, and, of
course the National Montessori Curriculum. If DPMSS is not able to achieve
innovation school status, it is highly unlikely that the school will open. For a
school to achieve excellence, it must hold on to its vision and implement the
vision as clearly and effectively as possible. DPMSS will require the innovative
school status to maintain fidelity to its mission and vision.
Examples of the DPMSS curriculum are included in Exhibits C and K.
DPMSS will be using the National Montessori Curriculum for grades 7-9 for
science, history and language arts. DPMSS will use an on-line math curriculum
that is individualized for each student combined with small group lessons. The
small group lessons will be designed to meet each student at the particular
benchmark the student is currently working, and the teacher will use a variety
of instructional methods, including Montessori math materials, to assist the
student in mastering that benchmark and preparing to work on the next online unit. Students will also be expected to apply math towards a variety of
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hands-on projects utilizing the farm, the culinary arts program and microeconomy. The 7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS
matches the meaningful, relative approach that defines Montessori education.
The high school, grades 10, 11 and 12, will use an integrated college
prepatory curriculum such as the curriculum currently in place at Compass
Montessori High School in Jefferson County. The Compass three year SPF results
for this curriculum are a median growth percentile of 58 for reading, 54 for
mathematics and 66 for writing and an academic achievement score for science
of 59%. The academic growth gaps achieved a level of exceeds for reading and
writing and meets for math. The three year ACT composite is 21.7.
Although the curriculum for high school will be similar to advance
placement curriculum in DPS for English, history, math, science and spanish,
there will still be innovative differences. First, the curriculum will be integrated
so that literature studied in language arts will, at the same time, support the
history curriculum for an overall integrated humanities curriculum. The math
and science teacher will work together to insure students are obtaining the
mathematical skills needed to work out currently studied complex scientific
equations. Linkages between science, math and history will be explored.
Throughout all areas of study, there will be in-depth reading and writing
instruction. This integrated approach will be supported by the innovative
schedule.
The schedules for both the junior high and the senior high will support
the Montessori approach. There will be minimal required transition times.
Instead, students will be called to small group lesson as those lessons are
needed to support the next level of study. This schedule is currently in place at
Compass Montessori high school. During the morning, students are
independently working on a variety of assignments and further exploration of
their current units of study. At the same time, teachers are giving small group
lessons to students in math, science, language arts and history. The culture of
respect and hard work is resolutely held by both the staff and the students. One
hundred percent of the students are on task and engaged because they are
enjoying their academic studies. This on task and engaged behavior is the
hallmark of Montessori education, and this is what we intend to create at
DPMSS.
DPMSS has outlined in Exhibit D the State, District and collective
bargaining wavers that it is requesting.
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Appendix A: Letter of Intent
This letter of intent (LOI) will provide formal notice to the Office of School Reform and
Innovation in Denver Public Schools regarding an applicant’s intention to submit a new
school proposal for the 2013-2014 school year cycle.
The information presented in the LOI is non-binding.
Name of ProposedDenver Public Montessori Secondary School
School:
Type of School: Performance
Grade Configuration: 7th - 12th (6th grade in first year only)
Model or Focus: Montessori secondary education
Primary Contact Person:Katy Myers
Phone:303-431-2385
Email:[email protected]
Region:Preferably attached to an existing DPS Montessori
elementary school or centrally located to serve the four
existing Montessori elementary schools
Proposed Leader (ifKaty Myers
known):
Replication: No
Contract with ESP/EMO: No
Enrollment Projections: Provide additional rows and columns if necessary.
GRADE
6
7
8
9
10
11
Total # of Students
2013-14
25
25
2014-15
0
40
25
2015-16
0
40
40
25
2016-17
0
40
40
40
20
50
65
105
140
Proposed Demographics
2017-18
0
40
40
40
35
20
175
FRL %
Denison: 57
SPED %
Denison: 11
ELL %
Denison: 19
Lincoln 37
Lincoln: 6
Lincoln: 11
Academia Ana
Academia Ana
Academia Ana
Maria Sandoval:39 Maria Sandoval: 5 Maria Sandoval: 41
Gilpin: 89
DPMSS Application
Gilpin:: 12
Gilpin: 23
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Denver Public Montessori Secondary School
Mission of School:
Denver Public Montessori Secondary School will combine
Montessori best practices with current research on adolescent
brain development to provide a learning environment that
promotes high achievement for each student while also
supporting them socially and emotionally. Graduates,
regardless of ethnicity or income status, will be prepared for
college or a career as well as demonstrate ingenuity,
adaptability, creativity, initiative and excellent communication
and problem solving skills.
Denver Public Montessori Secondary School will provide a
Provide a brief
overview of the
continuation of Montessori education to students primarily
education program of coming from the DPS Montessori elementary programs. The
the proposed school: school will combine Montessori best practices with current
research on adolescent brain development to provide a
learning environment that promotes high achievement for each
student while also supporting them socially and emotionally.
The junior high (7th, 8th and 9th) will be centered around an
urban farm containing real life, hands on experiences that
extend and deepen rigorous academic learning. The high
school (10th, 11th and 12th), will partner with local Denver
cultural institutions along with community colleges in order to
prepare each graduate for college or a career. .
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Appendix B: School Facility Questionnaire
Core Classroom Requirements Years 1-3:
Baseline assumption for number of students per classroom: _25_
Year 1
50
Year 2
65
Year 3
105
School Name:
Year 4
Year 5
140
175
Year 6
210
Year 7
225
Denver Public Montessori Secondary School
Primary Contact for Facility Planning: Katy Myers
Telephone:
School Type:
303-431-2385
Performance School
Email:
[email protected]
Charter School
Grade levels and student enrollment estimates for the first five years:
2013-2014
2014-2015
2015-2016
2016-2017
2017-2018
Grades
6th - 7th
6th - 8th
7th - 9th
7th - 10th
7th - 11th
Enrollment
50
65
105
140
175
Region: Centrally located to serve the current four DPS Montessori elementary schools
or attached to an existing DPS Montessori elementary school
Description of the facility/ies under consideration including available square footage
and quotes (for years 1-5) from property owners:
1.
2.
3.
Are you interested in investigating the possibility of occupying a district-owned
facility?
Yes
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Denver Public Montessori Secondary School
Administrative/Support Spaces
Main Office
Yes
If yes, list number of private offices needed (e.g., principal, AP, etc.): 3
Satellite Office
Yes
Work Room/Copy Room
Yes
Supplies Storage
Yes
Teacher Work Room(s)
If yes, list number of teacher work/planning rooms needed:
Yes
2
Specialty Classroom Needs
Number of Science Labs:
2
Number of art rooms ( one with kiln):
2
Number of computer labs:
0
Library Media Center (LMC)
Yes
Performance/Dance Room
Yes
Auditorium
Other (list room type and number): Commercial Kitchen
Yes
1
Physical Education/Athletic Requirements
Gymnasium
Yes
Locker Rooms
No
Weight Room
No
Field(s) – soccer, football, multipurpose
Yes
Baseball Field
No
Softball Field
No
Other (please list): Land suitable to start an urban farm
Other Needs
Playground(s)
No
Large space for class/school assemblies (e.g., morning meeting,
Yes
cafeteria)
Spaces not addressed and/or special considerations: DPMSS would like to eventually
run its own school lunch program using a commercial kitchen on site.
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Appendix C: Questions for Schools Requesting Waivers
Schools requesting waivers from district curriculum, DPS’s benchmark assessment
program, and/or promotion and graduation policies are required to complete the
below questions in this appendix.
A. Instructional Design & Curricular Materials
Denver Public Montessori Secondary School (DPMSS) will combine
Montessori best practices with current research on adolescent brain
development to provide a learning environment that promotes high
achievement for each student while also supporting them socially and
emotionally. Graduates, regardless of ethnicity or income status, will be
prepared for college or a career as well as demonstrate ingenuity, adaptability,
creativity, initiative and excellent communication and problem solving skills.
In order to accomplish this mission, DPMSS will be requesting Innovation Status
through the DPS Innovation School Application.
Dr. Montessori designed an education program with 21st Century
outcomes long before there was a definition of 21st Century outcomes.
Through her extensive observation, research and innovative practice, she
developed a curriculum for children from age 0 - 12. She also created a
curriculum framework for students ages 12 - 18. That framework is outlined in
her book, From Childhood to Adolescence, published in 1948.
In 1996, a concentrated effort began to bring Montessori’s adolescent
framework to life through carefully run school programs. This effort was led by
the Northern American Montessori Teacher’s Association (NAMTA). NAMTA
gathered curriculum and best practices from existing schools throughout the
United States. NAMTA also partnered with the Hershey Montessori Foundation
to create an exemplary school that contained every element of Montessori’s
vision as presented in From Childhood to Adolescence. At this school, the
Occupations curriculum and the Montessori adolescent humanities curriculum
has been developed, implemented and modified through practical application
research. In 2001, NAMTA started the AMI Montessori Orientation to Adolescent
Studies for adolescent teachers. This intensive five week summer course trained
teachers on pedogy, curriculum and curriculum implementation. Every year,
there are conferences on various aspects of program implementation. The
Montessori adolescent program has arrived at a point where it is replacatable
and can work in both private and pubic school environments.
In 2011, The Montessori Australian Foundation partnered with NAMTA to
create a full 0 to 16 Montessori curriculum alignment to the Australian
Educational Goals for Young Australians. This curriculum alignment project
was published through The NAMTA Journal, A National Montessori Curriculum
Report, The NAMTA Journal, Volume 37, No. 1, Winter 2012. The National
Montessori Curriclum for the Adolescent Program from Twelve to Fifteen/
Sixteen Years was reviewed by the Australian Curriculum Assessment and
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Reporting Authority. Their findings, as reported in A National Montessori
Curriculum Report, are as follows: ACARA (Australian Curriculum Assessment
and Reporting Authority) established an extremly rigorous recognition process
to determine the extent to which a well-established alternative national
curriclum can deliver comparable educational outcomes for students to those
based on the Australian National Curriculum. ACARA have advised that (the
National Montessori Curriculum) aligns with the Melbourne Declaration on
Educational Goals for Young Australians, meets the particular principles and
guidelines in relation to the Shape of the Australian Curriclum v3 paper, and
allows for broadly comparable educational outcomes in English, mathematics,
science and history by the end of year 10.
DPMSS will use the National Montessori Curriculum, as presented in the
NAMTA journal and modified to meet the cultural orientation of our target
students and all CAS and CCS standards. The 6th grade through 12th grade
Montessori curriculum is rigorous, innovative, interesting and is designed to
engage students to produce optimal academic achievement as well as social
and emotional maturity and well-being.
Montessori is inquiry based. Self-direction, collaboration,information
literacy, critical thinking and reasoning and invention are all core components
of the Montesssori curriculum. Montessori education teaches students how to
learn, how to acquire information, and how to make connections. Montessori
wrote, “Here is an essential principle of education: to teach details is to bring
confusion; to establish the relationship between things is to bring knowledge.”
The curriculum, the schedule, the pedagogy and even the assessments are all
created to foster an environment that allow students to explore, to work
together, to work independently, and most importantly, to become confident,
competent adults who know how to problem solve because they have been
practicing this skill for years.
Students who leave Montessori programs to go to traditional schools are
easily able to make this transition. They have learned to create healthy, trusting
relationships with teachers because of the advisor model. Students are able
and willing to seek out adults at school for help. They are confident speakers
and able to use their voice. They understand that they are in charge of their
education. Even though they may not have been using traditional curriculum,
Montessori students are easily adaptable and are used to challenges.
Montessori said, “For success in life depends in every case on self-confidence
and the knowledge of one’s own capacity and many-sided powers of
adaptation.”
Montessori education is individualized education. The schedule, small
group lessons, individualized assessment and follow up work that is based on
the students’ interests and explorations allow for every type of learner to excel.
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This includes students with special needs, ELL learners, accelerated learners
and students from every culture.
One example of the DPMSS junior high curriculum is included in Exhibit
K. DPMSS will be using the National Montessori Curriculum for grades 7-9 for
science, history and language arts. DPMSS will use an on-line math curriculum
that is individualized for each student combined with small group lessons. The
small group lessons will be designed to meet each student at the particular
benchmark the student is currently working, and the teacher will use a variety
of instructional methods, including Montessori math materials, to assist the
student in mastering that benchmark and preparing to work on the next online unit. Students will also be expected to apply math towards a variety of
hands-on projects utilizing the farm, the culinary arts program and microeconomy. The 7,8,9 Spanish curriculum will be the TPRS curriculum. TPRS
matches the meaningful, relative approach that defines Montessori education.
The high school, grades 10, 11 and 12, will use an integrated college
prepatory curriculum such as the curriculum currently in place at Compass
Montessori High School in Jefferson County. The Compass three year School
Performance Framework results for this curriculum are a median growth
percentile of 58 for reading, 54 for mathematics and 66 for writing and an
academic achievement score for science of 59%. The three year academic
growth gaps achieved a level of exceeds for reading and writing and meets for
math. The three year ACT composite is 21.7. Grove High School, located in
Redlands, CA, is another public Montessori charter school that has a farm
school program for its junior high and college preparatory program for its high
school, very similar to the design we are proposing. Their California State
School Accountability Report Card shows Grove at a 2011 API growth level of
857, well above the 800 median and an overall 2010 proficient and advanced
rate in English Language Arts of 77 % and Science at 66%.
By high school, (10th - 12th), Montessori students are well adept at
taking charge of their education, and are eager for further intellectual
challenge. Although the curriculum for high school will be similar to advance
placement curriculum in DPS for English, history, math, science and spanish,
there will still be innovative differences. The delivery of curriculum maintains
the core values of Montessori and are designed specifically for students who
have progressed through Montessori education. Instruction is delivered via key
lessons that convey to the students fundamental concepts and serve as
“jumping off” points for further exploration. Studies are self-directed in an
environment of high expectations and high support. Teacher/advisors work
with students to insure that students have the advanced skills necessary to
explore advanced concepts.
In combination with the challenging academic setting, high school
students are also encouraged to go out to local cultural institutions to further
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study. DPMSS intends to create partnerships with the Museum of Nature and
Science, the Denver Zoo, the Denver Botanic Gardens, the Denver Art Museum
and other local cultural centers so that our students can easily access experts
within those settings. DPMSS will also create partnership with CU Denver and
Metropolitan State College of Denver so that students who wish to dually enroll
in some classes during their senior year have the ability to do so. Another key
experience for high school will be international travel. DPMSS will determine
appropriate fund raising venues so that all students will be able to attend at
least one international trip during high school.
Here is an example of a high school Humanities Unit from Compass
Montessori High school:
Modern American Studies
Reconstruction to Modern Times
Curriculum Summary
English & American History credit - ½ each per semester
Required Textbooks
American History: Taking Sides: Clashing Views on Controversial Issues in
American History. Vol. II: Reconstruction to the Present.
Larry Madaras & James M. SoRelle, eds. Guilford, CT:
Dushkin/McGraw Hill, 2000. Eighth edition.
Modified:
Reasoning with Democratic Values: Ethical Problems in
United States History, Volume 2. Alan L. Lockwood and
David E. Harris, eds. Teacher College Press, 2002
Geography:
Geography Coloring Book, by Wynn Kapit. Third Edition
English:
Short Takes: Model Essays for Composition. Elizabeth
Penfield. New York:
Longman, 2002. Seventh Edition.
Literature, American Authors as assigned.
AP English:
The Norton Reader. Peterson, Linda H., and John C.
Brereton, eds. New York: W. W. Norton & Co.
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Overview:
American Studies surveys significant social, cultural, and political developments
in United States society from the late nineteenth century to the present. This
course explores the political and social meanings of cultural conflict and
national identity through close analysis and classroom discussion of historical
documents, literature, and scholarly writings. How ideas about race, gender,
sexuality, class, and religion have shaped legal and political contests in past
and modern society are examined. Students will engage these issues through
seminars, lectures, and course readings. Students will not only be expected to
know the "facts" but also to understand and interpret those facts and their
interrelationships in both historical and modern context.
Literature and writing work focuses upon the themes of each quarter’s studies.
Essay writing in description, exposition, argumentation, classifying, comparing,
contrasting and narrative are covered within this course. Required literature
includes classic, modern, short stories and poetry from American authors.
1st Quarter: “How do you get to Carnegie Hall? Lessons from the Gilded
Age”
In this quarter we will examine America after the Civil War until 1910. Themes
of study will include urbanization, imperialism, industrialization and
immigration.
Literature - Examples: The Jungle, Devil in the White City, 42nd Parallel,
Fountainhead
2nd Quarter:
“War, Roar, Bust & Dust”
Topics in this quarter will include WWI, the Roaring Twenties, including the
Harlem Renaissance, The Great Depression and the Dust Bowl. Themes will
include progressivism, economics, labor unrest and isolationism.
Literature – Examples: Johnny Got his Gun, The Grapes of Wrath, The Heart is a
Lonely Hunter, The Great Gatsby, To Kill a Mockingbird, Poetry selections Langston Hughes
3rd Quarter:
“WW-II to MCMXC-II”
Overview of the U.S. involvement in the Second World War and the cold war until
the fall of the Berlin Wall is presented. Topics of study will include WWII, the
Korean and Vietnam conflicts, Civil Rights Movement, The Counterculture, the
70’s and 80’s. Themes of study will include propaganda, conflict among
conformity, popular culture & consumerism.
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Literature – Examples: The Things they Carried, Slaughterhouse Five, Catch 22,
One Flew over the Cuckoo’s Nest
4th Quarter: “The State of the Union”
An examination of our current political and social climate both domestically and
internationally. This term will investigate cultural aspects of Latin America,
partly in preparation for a May 2008 trip to Costa Rica. A brief survey of cultural
aspects of Latin America’s cultural, social economic, racial, and environmental
concerns. In addition, a weekly survey of current issues of concern to the U.S.Latin American relations.
Literature - Examples: 1984, Clockwork Orange, Anthem, 100 Years of
Solitude, Like Water for Chocolate, Love in the time of Cholera
The National Montessori Curriculum aligns with nearly every benchmark
of the Colorado Academic Standards and Common Core Standards. Below are a
few examples. During the planning year, DPMSS will completely adapt the
National Montessori Curriculum to the Colorado Academic Standards and
Common Core Standards. Assessments will then be created using the CAS
aligned curriculum. Because the junior high will integrate grades 7, 8 and 9, all
alignment will be based on the 9th grade standards. For high school, alignment
will be based on the 12th grade standards.
English Instruction - Grades 7 - 9 (partial example)
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Content
Strand
Knowledge, Skills and Understandings
Typically students will:
Reading
Understand the role reading plays in social life, and its
Activities include:
applications in the life of the adolescent community and in - evaluating the expression of
the wider community
comparable ideas across a
variety of sources for a variety
Understand the purpose for reading, and how to read
of audiences
different formats, including literar y, factual and persuasive - analysing how individual,
texts of different types in paper-based, digital or multimedia groups, events and places are
forms
represented in literar y, factual
and persuasive texts in order
Read, respond to and interpret a range of literar y texts,
to influence audience
including shor t stories, novels, plays, and poetr y
perception or opinion
- designing a checklist for
evaluating the quality of
Recognise and label the elements of a literar y text,
information found in sources
including:
such as websites, magazines,
- the setting, plot, characterization, dialogue, climax and
adver tisements, television and
denouement of a narrative
newspaper current affairs e.g.
- the form, metre and rhyme scheme of a poem
credibility, accuracy, reliability,
fact distinguished from opinion
Recognise literar y technique and structures, including
using evidence from literar y,
figures of speech such as:
factual and persuasive texts to
- metaphor and simile
reveal how authors create
- personification
emotional responses, influence
- hyperbole and irony
and/or position an audience
- pun
e.g. through comparison,
- alliteration
contrast, exaggeration,
Par ticipate in a book group to share and discuss ideas and juxtaposition, the changing of
interpretive questions collaboratively
chronological order, or the
expansion and compression of
Respond personally, analytically and critically to a variety of time
literar y works by:
- analytical, interpretive and
- interpreting, analysing and evaluating different
evaluative comprehension tasks
perspectives on issues, events, situations, individuals or
related to intellectual
groups
development and creative
- identifying and analysing implicit and explicit values, beliefs expression
and assumptions
Read for enjoyment beyond assigned reading tasks
Appreciate the diversity of the literary tradition through
reading works by authors from many racial, ethnic, and
cultural groups
DPMSS Application
Activities and Resources
Resources include:
- classical and contemporar y
literature
- texts from popular culture
- inter views with authors
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- literar y criticism
- study guides
- librar y
Read closely, analytically and critically a range of non-fiction/ - reference and research
factual texts, including information texts, biography, newspaper materials (paper-based, digital,
and journal articles by interpreting, analysing and evaluating
web-based, multimedia)
different perspectives on issues, events, situations, individuals
or groups
Read to build understanding of subject matter across the
curriculum
Read a range of persuasive texts, including speeches, media
commentary, essays, journal articles and opinion pieces
Recognise and describe an author’s intention and point of
view
Use annotation and citation effectively when interpreting a
text
Reading
for life
Build and expand, through reading, an increasingly mature and
sophisticated vocabulary relevant to range of contexts and
language varieties
Read for information across the curriculum and beyond
Activities include:
(e.g. mass media and popular culture in community and
- preparation for seminars,
meetings, presentations and
Occupations contexts)
debates
Read to ‘do’ i.e. reading to learn how to complete practical - research, analytical, interpretive
tasks and how to use equipment and technology
and evaluative comprehension
tasks related to the under taking
Read for enjoyment and enter tainment
of practical and community
projects
Read as a study skill:
lunchtime book club
- applying reading strategies such as skimming, scanning,
- reading out loud for an
vocabular y building, text analysis and synthesis,
audience as performance e.g.
summarising, paraphrasing, acknowledging sources and
stor y-telling, choral reading, and
note-taking to achieve study goals
information sharing
- establishing reading goals and priorities as par t of larger
research or other projects
Resources include:
- developing analytical, interpretive, evaluative and critical
- literar y texts, reference and
reading skills
research materials (paperbased, digital, web-based,
multimedia)
- DIY instructions and operating
manuals (paper-based, digital,
web-based, multimedia)
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Colorado Students Can:
Academic
Standard for a.
Determine a theme or central idea of a text
Grade 9
and analyze in detail its development over
b.
c.
d.
e.
f.
DPMSS Application
Concepts and skills students
master:
Increasingly complex literary
elements in traditional and
the course of the text, including how it
contemporary works of
emerges and is shaped and refined by specific literature require scrutiny and
details; provide an objective summary of the comparison
text. (CCSS: RL.9-10.2)
Analyze how complex characters (e.g., those
with multiple or conflicting motivations)
develop over the course of a text, interact
with other characters, and advance the plot or
develop the theme. (CCSS: RL.9-10.3)
Analyze how an author's choices concerning
how to structure a text, order events within it
(e.g., parallel plots), and manipulate time
(e.g., pacing, flashbacks) create such effects
as mystery, tension, or surprise. (CCSS: RL.
9-10.5)
Analyze a particular point of view or cultural
experience reflected in a work of literature
from outside the United States, drawing on a
wide reading of world literature. (CCSS: RL.
9-10.6)
Identify the characteristics that distinguish
literary forms and genres
◦
Analyze how an author draws on and
transforms source material in a
specific work (e.g., how Shakespeare
treats a theme or topic from Ovid or
the Bible or how a later author draws
on a play by Shakespeare). (CCSS:
RL.9-10.9)
◦
Use literary terms to describe and
analyze selections
By the end of grade 9, read and comprehend
literature, including stories, dramas, and
poems, in the grades 9-10 text complexity
band proficiently, with scaffolding as needed
at the high end of the range. (CCSS: RL.
9-10.10)
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Denver Public Montessori Secondary School
Colorado Students Can:
Concepts and skills students
Academic
master:
Standard for a.
Determine a central idea of a text and analyze Increasingly complex
Grade 9
its development over the course of the text, informational texts require
b.
c.
d.
e.
f.
g.
h.
including how it emerges and is shaped and mature interpretation and
refined by specific details; provide an
study
objective summary of the text. (CCSS. RI.
9-10.2)
Analyze in detail how an author's ideas or
claims are developed and refined by
particular sentences, paragraphs, or larger
portions of a text (e.g., a section or chapter).
(CCSS: RI.9-10.5)
Evaluate clarity and accuracy of information
through close text study and investigation via
other sources
Analyze how the author unfolds an analysis
or series of ideas or events, including the
order in which the points are made, how they
are introduced and developed, and the
connections that are drawn between them.
(CCSS: RI.9-10.3)
Use flexible reading and note-taking
strategies (outlining, mapping systems,
skimming, scanning, key word search) to
organize information and make connections
within and across informational texts
Critique author's choice of expository,
narrative, persuasive, or descriptive modes to
convey a message
Delineate and evaluate the argument and
specific claims in a text, assessing whether
the reasoning is valid and the evidence is
relevant and sufficient; identify false
statements and fallacious reasoning. (CCSS:
RI.9-10-8)
By the end of grade 9, read and comprehend
literary nonfiction in the grades 9-10 text
complexity band proficiently, with
scaffolding as needed at the high end of the
range. (CCSS: RI.9-10.10)
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Content
Strand
Knowledge, Skills and Understandings
Activities
Resources
and
Typically students will:
Writing
Introduce, consolidate and/or review knowledge about:
- written texts, their purposes and structure
- the structure of paragraphs
- the study of grammar : the function of words, groups
and phrases, the analysis and composition of clauses
and sentences
- the study of style
- word study, spelling and etymology
- punctuation
- handwriting and keyboarding
Activities include:
- modelled and guided writing
activities in which students
develop written composition
skills
- composition of a range of
written texts to achieve
purposes across all curriculum
domains
- writer’s conferences
- engaging in real life tasks that
demand written texts to achieve
a range of purposes
Writing Uses the steps of the writing process as a means to
as experi- composing texts:
ence
- planning: generating ideas, selecting a topic/focus,
gathering and collating details, building vocabular y,
organising information
- seeking and responding to feedback
- editing to improve clarity and effectiveness
- proofreading for spelling and punctuation
- publishing (handwriting/word processing, illustrating,
presenting)
Resources include:
- model texts
- purposeful writing contexts
across the curriculum
- a range of writing media (paperbased, digital, web-based,
multimedia)
Build a reper toire of text structures to achieve a range of
purposes, including:
- describe, recount, narrate
- respond, interpret, critique
- instruct, explain, repor t
- persuade
Write for a range of audiences:
- from informal to formal
- from peers to an audience of higher or lower status in
the context e.g. more or less exper t, older or younger
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Write for a range of media, including written text, spoken
presentation or dialogue, digital media, and multimedia
Write in a range of forms, including notes and messages,
letter, essay, ar ticle, shor t answer, prose, poetr y
Write spontaneously for practical purposes and
enjoyment
Develop a personal voice in writing
Share drafts with ‘critical friends’ (e.g. other students,
teachers, parents) in order to gather ideas for revision
and respond to suggestions
Develop criteria for evaluating own and others’ texts
Improve awareness and master y of the conventions of
language (paragraphs, spelling, punctuation) and the effect
of conventional usage on clarity
Develop a range of strategies for organising ideas and
content prior to writing, including graphic organisers,
concept mapping, note-taking, file system, bibliography
Draw from multiple sources and integrate into own work
with correct citation and no plagiarism
Use word processing, graphics, and publishing as a
medium of exchange
Evolve a personalised style sheet
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Colorado Students Can:
Concepts and skills students
Academic
master: 1. Literary and
Standards
a.
Write narratives to develop real or imagined narrative texts develop a
for Grade 9
experiences or events using effective
controlling idea or theme with
b.
c.
d.
e.
DPMSS Application
technique, well-chosen details, and welldescriptive and expressive
structured event sequences. (CCSS: W.
language
9-10.3)
◦
Engage and orient the reader by
setting out a problem, situation, or
observation, establishing one or
multiple point(s) of view, and
introducing a narrator and/or
characters; create a smooth
progression of experiences or events.
(CCSS: W.9-10.3a)
◦
Use a variety of techniques to
sequence events so that they build
on one another to create a coherent
whole. (CCSS: W.9-10.3c)
Write literary and narrative texts using a
range of poetic techniques, figurative
language, and graphic elements to engage or
entertain the intended audience
Refine the expression of voice and tone in a
text by selecting and using appropriate
vocabulary, sentence structure, and sentence
organization
Review and revise ideas and development in
substantive ways to improve the depth of
ideas and vividness of supporting details
Explain strengths and weaknesses of own
writing and the writing of others using
criteria (e.g., checklists, scoring guides)
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Denver Public Montessori Secondary School
Students Can:
a.
Concepts and skills students
master:
Write arguments to support claims in an
2. Informational and persuasive
analysis of substantive topics or texts, using texts develop a topic and
valid reasoning and relevant and sufficient establish a controlling idea or
evidence. (CCSS: W.9-10.1)
thesis with relevant support
1. Introduce precise claim(s), distinguish the claim
(s) from alternate or opposing claims, and create
an organization that establishes clear
relationships among claim(s), counterclaims,
reasons, and evidence. (CCSS: W.9-10.1a)
2. Develop claim(s) and counterclaims fairly,
supplying evidence for each while pointing out
the strengths and limitations of both in a manner
that anticipates the audience's knowledge level
and concerns. (CCSS: W.9-10.1b)
3. Use words, phrases, and clauses to link the major
sections of the text, create cohesion, and clarify
the relationships between claim(s) and reasons,
between reasons and evidence, and between
claim(s) and counterclaims. (CCSS: W.9-10.1c)
4. Use appropriate rhetorical appeals and genre to
engage and guide the intended audience
5. Anticipate and address readers' biases and
expectations
6. Revise ideas and structure to improve depth of
information and logic of organization
7. Explain and imitate emotional, logical, and
ethical appeals used by writers who are trying to
persuade an audience
8. Establish and maintain a formal style and
objective tone while attending to the norms and
conventions of the discipline in which they are
writing. (CCSS: W.9-10.1d)
9. Provide a concluding statement or section that
follows from and supports the argument
presented. (CCSS: W.9-10.1e)
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Students Can:
a.
b.
c.
d.
Demonstrate command of the conventions
of standard English capitalization,
punctuation, and spelling when writing.
(CCSS: L.9-10.2)
◦
Identify comma splices and fused
sentences in writing and revise to
eliminate them
◦
Distinguish between phrases and
clauses and use this knowledge to
write varied, strong, correct,
complete sentences
◦
Use a colon to introduce a list or
quotation. (CCSS: L.9-10.2b)
Spell correctly. (CCSS: L.9-10.2c)
◦
Produce clear and coherent writing in which
the development, organization, and style are
appropriate to task, purpose, and audience.
(Grade-specific expectations for writing
types are defined in expectations 1 and 2
above.) (CCSS: W.9-10.4)
Develop and strengthen writing as needed
by planning, revising, editing, rewriting, or
trying a new approach, focusing on
addressing what is most significant for a
specific purpose and audience. (CCSS: W.
9-10.5)
Use technology, including the Internet, to
produce, publish, and update individual or
shared writing products, taking advantage of
technology's capacity to link to other
information and to display information
flexibly and dynamically. (CCSS: W.9-10.6)
DPMSS Application
Concepts and skills students
master:
3. Writing for grammar, usage,
mechanics, and clarity requires
ongoing refinements and
revisions
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A core component of Montessori education is that it is integrated. Here are
examples of how Reading, Writing and Communicating are integrated across
all curriculums.
English Across the Curriculum
English is embedded in all areas of the curriculum, wherever language skills are needed to engage
productively with curriculum content. How English is embedded in specific curriculum areas is summarised
in the table below.
The Domain of Intellectual Development
Spoken language
Composing written and
multimodal texts
Citizenship, civics and community life
- use a range of media to
communicate with the wider
community (e.g. telephone,
social networking, video
conference, Skype)
- discuss ideas in conversation
with others within and beyond
the adolescent community
- par ticipate in seminars and
debating
- deliver presentations within and
beyond the adolescent
community
- par ticipate in a council meeting,
conflict resolution conference
Reading
- take notes
- read for pleasure
- summarise reading material
- read to know what surrounding
- present research, analysis and
community and society is
proposals for projects and change
reading and talking about, e.g.
- publish flyers, ar ticles, opinion
positions taken and the opinions
pieces, newsletters and newspapers expressed in the mass media
and popular culture
- incorporate text into char ts,
timelines, and power points
- research primar y and secondar y
sources
- read literar y and philosophical
works
- read non-fiction, including text
books, reference books,
newspapers, journals, websites
- review and respond to the
writing of others
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Mathematics
- demonstrate proofs/problems
- explain problem-solving
strategies
- use the vocabular y of mathematics
effectively
- record the analysis of mathematical
problems and strategies used
- write word problems
- write text to accompany timelines,
graphs, char ts and multimedia
presentations on mathematics
topics
- prepare visual texts including
graphs, diagrams, char ts, timetables
- prepare historical accounts related
to mathematical topics and
biographies of mathematicians
- read stor y/word problems
- research mathematics through
histor y, including the biographies
of mathematicians
- read current texts on topics in
mathematics
English and languages other than English
- read aloud for self or an
audience
- recite poetr y
- engage in stor y-telling to a
variety of audiences
- par ticipate in quizzes,
discussions, book groups and
debates
DPMSS Application
- take notes
- solve puzzles and brainteasers
- keep a journal/diar y
- apply knowledge about grammar
- apply knowledge about grammar to to the analysis of sentences/
clauses
the composition of sentences/
- research primar y and secondar y
clauses
- write effective paragraphs
sources
- draft essays and ar ticles
- read literar y and philosophical
- compose poetr y, fiction, scripts and works
- read non-fiction/factual texts,
other literar y texts
including text books, reference
- write to persuade
materials, newspapers, journals,
- revise, edits and proofread texts
current affairs
- use spelling and punctuation
- apply reading strategies e.g.
effectively
reading for the main idea,
- present/publish written text
skimming, scanning
effectively, including hand-written,
typed, multimodal and digital text - review and respond personally
and critically to the writing of
others
- prepare for assessment
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Denver Public Montessori Secondary School
The Domain of Self-Expression
Spoken language
Written language and
multimedia
Reading
English for self-expression
- follow and give instructions
- take notes on aspects of literar y
- read creative writing across a
related to a range of techniques texts, including setting, character,
range of genres and media
for creative expression
plot, atmosphere, themes, motifs, - read scripts, poetr y and other
- read aloud as performance for a symbols
language for performance
range of audiences
- keep a journal/creative diar y to
- recognise aspects of literary texts,
- par ticipate in acting exercises
record personal responses to
including themes, motifs, symbols,
and the reading of scripts
ar tworks
figurative language (analogy,
- perform in videoed stories,
- write creatively in a range of genres metaphor, simile), characterisation,
plays, dramatis personae
- prepare stor y boards and scripts for imagery, mood and atmosphere,
- perform poetr y and songs
plays and videos
point of view
- discuss ar tworks with others in - write poetr y and song lyrics
- analyse the style of a literar y or
groups and seminars
other ar t work
- write captions and synopses for
- communicate with ar tists,
- read and evaluate responses of
ar tworks and exhibitions
specialists and others involved in - write reviews, analysis, interpretation others to creative expression/
creative industries in the
ar tworks, including own creative
and criticism of artworks
community
- prepare projects related to creative work
- read reference works and
expression, past and present
criticism related to creative
expression, past and present
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The Domain of Preparation for Adult Life and Contemporary Culture
Science (integrated into Occupations)
- follow and give instructions and - use the vocabular y of science
- consult a range of primar y and
demonstrations related to
effectively
secondar y sources
science experiments and
- take notes from talks, lectures and - evaluate the credibility, reliability,
projects
reference material
and accuracy of sources
- par ticipate in discussions and
- write summaries and outlines
- read published reference and
problem-solving exchanges
- record data in journal/diar y
text books and ar ticles as well
- present at seminars and at
- prepare laborator y and research
as work produced by peers
community events
- sur vey and evaluate a range of
repor ts
- communicate with exper ts,
positions and opinions taken on
- write scientific explanations
specialists and others involved in - write analytical essays
issues in science and technology
science and technology in the - prepare multimodal and multimedia
community
project presentations, that include,
- par ticipate in debates and
for example, maps, graphs,
performances related to issues
diagrams, char ts, timelines
in science and technology
- par ticipate in quizzes
History/Humanities
- par ticipate in discussions and
seminars
- deliver spoken presentations at
seminars and community events
- communicate with exper ts,
specialists and members of the
wider community
- par ticipate in debates and
performances related to histor y
topics
- par ticipate in quizzes
DPMSS Application
- take notes
- research a range of primar y and
- keep a journal/diar y
secondar y sources
- write essays, ar ticles and proposals - evaluate the credibility, reliability,
- write to recount and account for
and accuracy of sources
historical events
- read literar y and philosophical
- write to persuade
works related to the study of
- present research/projects in
histor y
written, multimodal and multimedia - read text books, reference
books, newspapers, journals,
form
websites
- review and respond critically to
the historical writing of others
- sur vey and evaluate a range of
positions and opinions taken by
writers on issues in histor y and
current affairs
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Denver Public Montessori Secondary School
Here is a sample lesson plan demonstrating scope and sequence for a
Humanities unit:
Humanities Project: Early Agriculture – The Incas
The project is initiated by a group of students with an adult guide, and the
input of other specialists as needed. The project would span one school term.
Goals
Engagement to inspire wonder in a past civilisation and the relics it leaves behind today
Key
Concepts/
Mastery
Skills
Work
Management
− to experience the Incan culture as an early agricultural, complex social structure
− to understand that the ways in which early agricultural societies developed was affected
by the natural environment and their understanding of their place within the
environment
− to understand that the Incan people made use of limited resources in enterprising ways
in order to meet their fundamental human needs
− take notes from lectures and presentations
− make oral summaries of key ideas for the group
− develop public speaking and presentation techniques
− develop dramatic performance skills
− write summaries of key ideas from readings
− take notes for research using a variety of frameworks
− prepare and draft a research paper
− choose relevant readings from a variety of texts, including multimodal texts
− use referencing conventions and prepare bibliographies effectively
− develop skills in public speaking
− use work time effectively without disturbing others
− manage paperwork effectively
First Period of the Project
In this period students participate in introductory activities that open up the
topic and key concept lessons.
The first period of the Incas project might include introductory activities such
as the following:
• introducing to concepts
• building vocabulary
• initiating the challenge
• eliciting students’ areas of interest and ideas for problem solving
• connecting the project to a micro-enterprise in the adolescent community
• telling an Inca creation story
• watching a DVD: Lost Civilisations: Macchu Picchu
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Students then pose one or more key questions. The key questions for the Inca
project might be:
What was it like to be an everyday Incan?
How was such a large empire so quickly overrun?
What were the similarities and differences between colonization of South
America and colonization of the United States?
The answer to these questions determines the key concept lessons to follow.
Below are a series of key concept lessons that might be presented in the first
period of the Incan project.
Lesson
Lesson 1
Title
Orientation in space and time: South
American
Lesson 2
Incan government & social structures
Lesson 3
Quipu recording system
Lesson 4
Incan agriculture
Lesson 5
Pizarro and the conquest of the Incas
Description
Students design a timeline of the Incan stor y and
create a map to show boundaries of Incan
empire.
Students discuss the running of a large empire, its necessar y structures, its difficulties - and
compare with the running of modern nations.
Students discuss the lack of alphabet and the
use of different systems of recording and
remembering.
Students explore the methods of farming and
the types of domesticated plants and animals of
South America.
Students read accounts of the conquest and
present a seminar to discuss the topic.
Further activities might include:
• making connections with the adolescent community, its land and microenterprises, for example, the growing of vegetables originating from South
America such as corn, potatoes and tomatoes
• cooking using ingredients originating from South America e.g. Quinoa salad,
chocolate
Students will be provided with a range of resources to explore the key concepts
and the discussion question further. These will include a range of reference and
research materials (paper-based, digital, web-based, multimedia).
During the first period of the project students build a shared specialised
vocabulary to talk about the topic. This vocabulary might include:
• Inca, Coya, Amerindians, Sapa Inca
• Quipu, Curaca
• Francisco Pizarro, Atahuallpa, civil war
• Macchu Picchu, Camayoc, Tahuantinsunyu
• llama, alpaca, Quecha, Cuzco
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Denver Public Montessori Secondary School
Second Period of the Project
The second period of the project includes whole group and individual
explorations and activities engaging in enquiry, research, dialogue with
experts, experimentation, field trips and practical activities. Second period
explorations and activities might include the following:
Activity
Title
Description
Activity 1 Map of South America
Activity 2
Activity 3
Activity 4
Activity 5
Students create a 2D or 3D map of South America, showing
topography, current political borders and extent of Incan
empire.
Incan time measurement; IncanStudents measure time taken to boil a potato and use their
number base system
results to recreate their daily timetable in the Incan number
base system.They discuss use of different base systems in
different periods of histor y.
Ar tefact creation
Students create ar tefacts using clay, based on the type of
ar tefacts found in Inca ruins.
Cooking
Students create a salad using corn, quinoa and hot
chocolate.They discuss traditional foods.
Drama
Students are given small scenes to recreate using the
information they have gleaned through research and
concept lessons.
The students then undertake individual research tasks of their own choosing
related to the project.
Third Period of the Project
During the third period of the project students demonstrate their knowledge
and mastery of the topic through tasks such as the following:
Spoken language
• prepare a monologue delivered by Pizzarro, Sapa Inca or an Incan layman
• perform a play or mime recreating the story of the conquest
• perform a play recreating ‘day in the life of’ an Incan
• perform an interview between Pizarro and Sapa Inca
Written language
• end of unit quiz
• providing definitions
• research project on how the Incas met their fundamental needs (e.g. food,
architecture, medicine)
• compose a narrative based on Incan legends and information about Incan
culture
• recreate the journal of a Spanish conquistador or of a vanquished Incan
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Creative expression
• create an archaeological ancient artefact, or musical instrument or artwork
• prepare a dramatic production of conquest or daily life of Incans
DPMSS will require classroom materials including a well stocked
laboratory to handle high school chemistry, biology and physics, reference,
non-fiction research books and fiction books for the library, literacy books, and
classroom materials to allow for the instruction of a wide variety of
Occupations, US history, Civics, Economics, A.P. World History, A.P.
Environmental Science, A.P. Biology, Advanced Algebra, Geometry,
Trigonometry and Calculus, A.P. Spanish and A.P. Language Arts. DPMSS will
also require access to an on-line math program for every enrolled student plus
a wide variety of math resources.
Non-typical expenses will include materials to build and maintain an
urban farm, including a water system. One very successful Occupation in other
Montessori adolescent programs is a culinary arts program that provides lunch.
Compass Montessori is its own School Food Authority and provides lunch for
the entire 330 student Golden campus. If DPMSS is able to work with the DPS
lunch program to create a similar opportunity, that would be ideal. DPMSS will
also require a complete set of Montessori materials equal to one large
classroom in an upper elementary setting at a projected cost of $8,000.
DPMSS will use proceeds from the performance school start up grants (as
evidenced in section V. Finance) to purchase the typical and non-typical
classroom materials and technology. DPMSS will set up a replacement schedule
to make sure that classroom materials are replaced in a methodical manner and
that school technology is updated every three years.
In the September 28, 2006 issue of Science Magazine, Angeline Stoll
Lillard published findings of Montessori education study with the following
conclusion: Comparing outcomes of children at a public inner-city Montessori
school with children who attended traditional schools indicates that Montessori
education leads to children with better social and academic skills.
In 2003, Dr. Kevin Rathunde published a study titled “A Comparison of
Montessori and Traditional Middle Schools: Motivation, Quality of Experience,
and Social Context.” With the help of co-investigator Mihaly Csikszentmihalyi,
Dr. Rathunde compared the experiences and perceptions of 150 middle school
students in Montessori and 150 middle school students in traditional schools
using the Experience Sampling Method (ESM). The ESM statistical procedure
allowed Dr. Rathunde to determine, in an objective manner, whether there were
significant differences between the two groups of students (Montessori and
Traditional) and to adjust or “control” for any differences that were due to other
factors such as background variables.
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Denver Public Montessori Secondary School
The statistical analysis revealed that there were strong differences between the
Montessori and Traditional students. The differences included:
1) Montessori students reported a significantly better quality of experience in
academic work than the traditional students,
2) Montessori students appeared to feel more active, strong, excited, happy,
relaxed, sociable, and proud while engaged in academic work,
3) Montessori students enjoyed themselves more, they were more interested in
what they were doing, and they wanted to be doing academic work more than
the traditional students,
4) Montessori students reported significantly higher percentages of
undivided interest, higher motivation and higher levels of importance with
regard to schoolwork,
5) Montessori students reported more conditions where the challenges and
skills used while doing academic work were above average.
ACARA (Australian Curriculum Assessment and Reporting Authority)
established an extremly rigorous recognition process to determine the extent
to which a well-established alternative national curriclum can deliver
comparable educational outcomes for students to those based on the
Australian National Curriculum. In 2011, ACARA advised that the National
Montessori Curriculum aligns with the Melbourne Declaration on Educational
Goals for Young Australians, meets the particular principles and guidelines in
relation to the Shape of the Australian Curriclum v3 paper, and allows for
broadly comparable educational outcomes in English, mathematics, science and
history by the end of year 10. The complete curriculum alignment has been
published in the NAMTA Journal, Volume 37, Number 1, Winter 2012.
B. Alternative Benchmark Assessment Program
At the beginning of the school year, students’ math skills will be assessed
via the on-line math program’s assessment tools. One example of an on-line
math program is Renaissance math and their STAR assessment. DPMSS will
review the current on-line math offerings during its planning year to
determine which program is the most successful and most compatible with the
Montessori program. Students will take weekly and end of unit on-line
assessments which are summarized within the on-line program. Teachers will
check student progress weekly to determine what math lessons students need
in order to continue making appropriate progress for that particular student.
Teachers will incorporate Montessori math materials along with more
traditional math instruction techniques during math lessons.
Also at the beginning of the year, students will receive the DRA -2 to
determine reading levels. The principal, working with staff, will review this data
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to determine what areas each individual students requires assistance in order
to continue to make adequate progress with reading. Students will be allowed
to choose their own literature books from a list provided by the school. Staff
will then work with students to make adequate progress in all aspects of
reading, including vocabulary, literary technique and structure, reading
elements, and the ability to analyze text. Reading instruction will occur via
literature circle, seminar and book clubs. During the first year, staff will
administer the DRA-2 again half-way through the year and at the end of the
year in order to obtain data on effective reading instruction. Staff will continue
to use the DRA-2 for new students and students who are demonstrating
difficulty with reading as observed in seminar and literature circles, previous
DRA-2 assessments and State assessments.
The third assessment students will complete at the beginning of the year
is a writing assessment. Teachers will review the student’s written work using a
rubric based on Colorado Academic Standards for that grade level. Teachers will
identify what small group instruction each student requires, and place that into
the schedule. Students will be required to complete writing assignments
throughout each Occupations. Teachers will review progress, again based on
the CAS rubric, and continue to develop lessons plans for each individual
student. DPMSS will use the 6 +1 Trait Writing Curriculum as a guide for lesson
development.
At all times, the expectation is that students will be working at or beyond
grade level as determined by the on-line math assessments, the DRA-2, and
the writing rubric. If students are not working at grade level, staff will create a
lesson plan to bring students to grade level. That lesson plan will be a part of
that individual students junior or senior high portfolio.
Every month, the principal will review student portfolios to determine
percentage gained regarding achieved benchmarks. The principal will also
review data compiled from the on-line math program, the DRA-2, the rubric measured writing samples and mastery assessment scores created by each
teacher for their Occupations. Because the school will only have 50 and 65
students in its first two years, the principal will be able to take a very hands on
approach to data review. As the school gets larger, some of these duties
regarding individual student data management will transfer back to the
program directors, and the principal will focus on overall school data trends.
This data will be reviewed monthly with the SAC Committee. Individual student
performance will be presented to parents during two parent/teacher/student
conferences per year. At these conferences, students will walk their families
through their portfolios. Teachers, students and families will then discuss
student achievements, student challenges, and create goals for further
progress.
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Denver Public Montessori Secondary School
Once State assessment data and SPF are released after year one, the
principal will review data based on prioritized benchmarks. The principal will
identify gaps in DPMSS achievement as compared to other DPS schools and
state averages. The principal will work with staff to determine causes for these
gaps and identify small group Montessori lessons to improve student
achievement.
Here is an example of the portfolio that will be used for the junior high
program. This is excerpted from the Compass Montessori Farm School
Portfolio. DPMSS will create similar junior high and senior high portfolios based
on CAS benchmarks.
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Outcome One
Is an experienced thoughtful writer and reader, adjusts use of spoken,
written, and visual language, to respond to the needs of society, to acquire new information and
for personal fulfillment.
Mastery Works
WRITING
! Utilizes effective writing process in a variety
of genres such as:
o Letters
!
Lesson:
!
Work Sample
o Expository essays
!
Lesson:
!
Work Sample
o Process Analysis essays
!
Lesson:
!
Work Sample
o Narrative Essays
!
Lesson:
!
Work Sample
o Experienced research writer
!
Lesson:
!
Work Sample
o Writes detailed papers on topics
relevant to study
!
Lesson:
!
Work Sample
o Uses a variety of reliable sources
and cites appropriately, avoiding
any use of plagiarism, using MLA
format inside text and on
bibliography
!
Lesson:
!
Work Sample
o Writing reflects a scholarly tone
!
Lesson:
!
Work Sample
o Discerns pertinent information
from sources
!
Lesson:
!
Work Sample
o Synthesizes information to form
original thoughts, supports thoughts
with examples
!
Lesson:
!
Work Sample
! Uses journaling/reflective writing for selfexpression
!
Lesson:
!
Work Sample
! Writes in a variety of creative styles such as,
poetry, journalistic, storytelling/fiction
!
Lesson:
!
Work Sample
DPMSS Application
!
Additional Six Trait Skills :
o Writes with voice
!
Lesson:
!
Work Sample
o Extends vocabulary skills
!
Lesson:
! Work
Sample
o Effectively uses the editing process
!
Lesson:
! Work Sample
o Utilizes conventions in writing
(grammar & punctuation)
!
Lesson:
!
Work Sample
READING
! Reads for recreation
o Book List
!
Reads a variety of styles; fiction, nonfiction, autobiography, biography, poetry
o Book List
!
Able to answer factual, interpretive and
evaluative questions based on assigned
reading
!
Lesson:
!
Work Sample
!
Synthesizes information to form own
thoughts/opinions
! Lesson:
! Work Sample
COMMUNICATION
! Write a narrative essay describing a situation
where you used your best communication
skills this year.
o Can communicate effectively in a
variety of settings and situations to
acquire new information, and to selfadvocate
o Open minded, flexible thinker
o Active listener
! Lesson:
! Work Sample:
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Denver Public Montessori Secondary School
C. Alternative Graduation & Promotion Standards
DPMSS high school graduation requirements will reflect the HEAR
requirements including four years of English, four years of Mathematics, three
years of Natural/Physical Science including two lab-based units, three years of
Social Sciences (with at least one unit of U.S. and one unit of World History), one
year of Foreign Language and two years of Academic Electives. Starting in
eighth grade, every DPMSS will develop a personal education plan which will
become part of their junior and then their senior high portfolios. These plans
will be completely integrated with their portfolios to insure students are
receiving 100% of the credits needed to graduate. Occupation curriculum will be
compared to course objectives for traditional classwork to determine
appropriate credit for ninth grade. Tenth through 12th grade classes will have
the same course objectives as traditional schools for the academic areas.
Students will receive grades and transcripts starting in 9th grade.
One additional high school graduation requirement is that all graduates
apply to three colleges or universities. The intention of this requirement is that
all DPMSS graduates are aware that they have the ability to attend college, even
if they are choosing not to attend directly after graduation.
DPMSS is designed to respect stages of adolescent development, and
promotion and retention criteria will reflect this value. Students will be
expected to be promoted within their established class. A key time for
evaluation will occur towards the end of the ninth grade year. If a student is
demonstrating significant gaps in academic achievement, social and/or
emotional growth to the level that they may not thrive in the high school
environment, a conference will be called between the student, their family, the
principal and the student’s advisor to determine if the student should spend an
additional year in the junior high. In high school, if a student is not on track to
meet all DPMSS graduation requirements, the student, their family, the principal
and the student’s advisor will meet to create a plan in order for the student to
graduate. One possible outcome of that plan may be for the student to spend
an additional semester or year at DPMSS until all graduation requirements are
met.
If a student has exceeded graduation requirements before the end of
their 12th grade year, that student will have the option to graduate early or
dually enroll in UCD, Metropolitan State, or another college that offers dual
enrollment. Again, a meeting will be called between the student, their family,
the principal and the student’s advisor to determine the best course of action
for that student.
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Compass Montessori High School created graduation outcomes for its
students. DPMSS will adopt the outcomes as a starting point for creating its own
outcomes reflective of is target population. The outcomes are as follows:
Compass Montessori Student Outcomes
Outcome One
Is an experienced thoughtful writer and reader, adjusts use of spoken,
written, and visual language, to respond to the needs of society, to
acquire new information and for personal fulfillment.
Outcome Two
Has developed a mathematical mind: experienced use of the power of
mathematical thinking in problem solving and paradigm formation.
Outcome Three
Is competent and knowledgeable in life sciences, physical sciences and
advancing technology.
Outcome Four
Is economics literate and an ethical entrepreneur
Outcome Five
Is effective and capable of expressing ideas, contributing to a community
of inquiry, actively listening and collaborating
Outcome Six
Is locally and globally aware, well worldly traveled in fact or through
reading of human encounters; historical minded and historically literate
about human history and the human condition.
Outcome Seven
Is physically active, a participant in activities that create mental / physical
challenges that foster whole person development.
Outcome Eight
Is a developing artist, song writer, poet, musician, actor, etc.through
practice, experience in, appreciation for and understanding of the arts.
Outcome Nine
Is aware and knowledgeable of self-construction and actualization; has
an immense sense of humor and an ingenious love of learning.
When our high school students have achieved these outcomes, the result will be
graduates, regardless of ethnicity or income status, who will be prepared for
college or a career as well as demonstrate ingenuity, adaptability, creativity,
initiative and excellent communication and problem solving skills.
DPMSS Application
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Denver Public Montessori Secondary School
Appendix F
Evidence of Support
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March 19, 2012
N· A· M · T·A
13693 Butternut Road
Burton, Ohio 44021
tel 440.834.4011
fax 440.834.4016
Katy Myers
10923 Magnolia Dr.
Apt. B,
Cleveland, OH 44106.
Dear Katy,
[email protected]
www.montessori-namta.org
Montessori Development Partnerships and the North American Montessori
Teachers' Association have authorized a cash grant of $3000.00 in start-up
funds to be used primarily for Montessori consultancy and services from
Project 2012. Services in kind constitute an additional $5000 in honoraria
donated from David Kahn and Laurie Ewert-Kroeker (and others) in providing
on-site programming and materials for the project. The $3000.00 will be
disbursed in June.
We have elected your program for sponsorship because of our faith in your
history of making Montessori secondary programs work, especially
demonstrated in the viability and authenticity of Compass Montessori School
located in Golden, Colorado. Having had contact with Montessori High
School at University Circle and Hershey Montessori School Farm Program,
we are hoping you adopt some of our successful curriculum design and
orientation creating a unique blend of school cultures that will inevitably lead
the country in Adolescent work.
With best wishes for Denver Public Montessori Secondary School.
k:t..._
0
David Kahn
Si
Executive Director, NAMTA
Executive Director, MDP
e
in affiliation with the Association Montessori In temarionale-Amsterdam, Netherlands
DPMSS Application
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Denver Public Montessori Secondary School
From Katy Mattis, incoming Principal of Denison Montessori.
Montessori Secondary Program
Mattis, Kathryn <[email protected]>
Thu, Mar 1, 2012 at 1:05 PM
To: "[email protected]" <[email protected]>, "Fowler, John"
<[email protected]>, "[email protected]" <[email protected]>,
"Vincent, Frank" <[email protected]>, "Reina-Ayadi, Yamile"
<[email protected]>, "[email protected]"
<[email protected]>
Hi Everyone,
I apologize for not replying sooner, I have been in my own whirlwind of
interviewing to be Denison’s next principal, hopefully, I will know soon if this
dream is to become a reality.
I just wanted to give my feedback on a DPS secondary program and on why Katy
Myers is the perfect person to take this on. As a DPS upper elementary teacher
(Denison--2002-2007) and a Peer Observer (currently), I have seen a very
strong commitment to Montessori within DPS. The size of the program
continues to increase and the Montessori programs that currently exist are
constantly striving to provide authentic Montessori experiences to Denver’s
diverse students.
As an upper elementary teacher, my classroom was significantly impacted
by the loss of 6th graders to middle school
programs with competitive enrollment processes that start in 6th grade. I know
this continues to be a struggle and 2
DPS Montessori schools deal with it by not having 6th graders. Since everyone
in this e-mail is a Montessorian, I will not dive into the challenges that this
presents to authentic Montessori except to say one of my trainers once
described Montessori as creating many dangling ribbons that are neatly tied in
a bow in the 6th grade.
I am so excited about the prospect of there being a true Montessori
secondary program in DPS and I can’t say strongly enough that Katy Myers is
THE person to take on the process of making this happen.
I had the pleasure
of working with Katy at Compass Montessori School, a Jeffco charter that serves
students from age 3-18. Katy is a founding parent of Compass and has vast
experience with taking a Montessori school from its infancy through maturity.
This “growing up” was most profound at the Secondary level, largely because
when she was taking this challenge on, there were no public secondary
Montessori programs. Compass is a world leader in both public and private
Secondary Montessori Education.
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In the years that I was at Compass, I watched the farm school grow into a
program that truly supports Montessori’s vision of an Erdkinder. Katy was
fundamental in this growth. The current program has the students engaged in
authentic occupations with the work on the farm being a vital part of the
students’ learning. The middle school students prepare (the most delicious)
lunch for ALL of the students and staff every day! (I strongly encourage all of
you to visit Compass—Golden and make sure you get a lunch invitation!) This
authentic, purposeful work creates middle school students who are passionate
and focused. I would love if DPS could provide this continuation to its students.
Katy’s knowledge of the successes and (possibly more importantly) the
mistakes that Compass made in creating an occupation based, high achieving,
Erdkinder is what makes her the best person to get this program started in DPS.
Katy has not worked in DPS so will need the support of DPS’s Montessorians.
Unfortunately, Katy isn’t in Colorado, and can’t convene a meeting with all of us
to tell us her vision in person. Katy is in Cleveland working closely with
David Kahn. Katy and David have worked together for many years and has the
support of one of the experts on Montessori secondary education (and public
Montessori education.)
As a leader, Katy is an inspiration. I consider myself lucky to have worked with
her. She has a way of creating a vision and then making it happen, she is not
someone who backs down from a challenge, nothing is impossible! (As I think
we can all see by her willingness to take this on with such a short turn around
time!) Most admirable is her ability to gather her staff around her to create a
common vision. I have spoken to Katy about this project and she is as
passionate about making this happen as I have ever heard her. She has my
support 100%.
Lastly, when I was in the classroom, I had several students go to Compass, even
though it was miles from their homes. I am convinced that if there is a
Montessori middle school offered within DPS, students and parents will leap at
the opportunity. I look forward to working with Katy and you on this project.
Sincerely,
Katy Mattis
Montessori Secondary Program
Spearman, Janice <[email protected]>
Sun, Mar 4, 2012 at 6:22 PM
To: Katy Myers <[email protected]>, "[email protected]"
<[email protected]>, "Trujillo-Hays, JoAnn" <[email protected]>, "Fowler, John" <[email protected]>, "Vincent, Paul"
<[email protected]>, "Hamilton, Beth"
<[email protected]>, Kathryn Mattis <[email protected]>,
"Escalante, Alonso" <[email protected]>, "Vincent, Frank"
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Denver Public Montessori Secondary School
<[email protected]>, Laurie Ewert-Krocker
<[email protected]>, "Reina-Ayadi, Yamile" <[email protected]>
Cc: David Kahn <[email protected]>, "Hairston-Brown, Tunisha"
<[email protected]>
Hi Katy,
Tunisha Hairston-Brown is one of our Primary teachers and she has wonderful
things to say about you and your work at Compass Montessori. Based on her
information about you to our staff, I believe that our Montessori teachers will be
happy to support your efforts. I also offer my support.
Janice
Janice Spearman
Principal Lincoln Elementary School
Secondary Program
Vincent, Frank <[email protected]>
Thu, Mar 1, 2012 at 2:27 PM
To: Katy Myers <[email protected]>, "[email protected]"
<[email protected]>, "Fowler, John" <[email protected]>, Kathryn
Mattis <[email protected]>, "Reina-Ayadi, Yamile" <[email protected]>
Cc: David Kahn <[email protected]>
Katy and all,
I just finished our State of Colorado Review and Interview in preparation for our
Federal Audit coming up soon. TINFL as you know, so we have to have paper
documentation for everything going back two years. That stack took many
hours, is several inches high, and still is not quite complete. Therefore, I have
not been answering all my email lately. We have TCAP testing starting next
week as well, and with all the accommodations it is a scheduling nightmare. I
issued an edict and a prayer that no one is sick next week, child or adult. We’ll
see if that works.
High school could be a strong draw for students and parents who want an
alternative to current offerings, and to those who are concerned about their
child’s continuance in the Montessori program. I am a little concerned
about the potential effect on the 6th grade possibilities at both Gilpin and
Lincoln. Maybe we could transition it backwards in the future and get our 6th
grades that way. In any case, I can’t do anything about it this year. So we
support your work, and are willing to do whatever we can to help.
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(I don’t have a trainer just yet, but am still working on it.)
Frank A. Vincent,
Principal Gilpin Montessori Public School
Montessori Secondary Program
Trujillo-Hays, JoAnn <[email protected]>
Tue, Feb 21, 2012 at 12:33 PM
To: Katy Myers <[email protected]>
While I applaud your efforts, this is not something in which I am able to be
involved. I am retiring at the end of this school year and then working next
school year to assist with the transition to new leadership. My time will be very
limited and I am not willing to take on a new endeavor at this point in my
career. I do wish you the best.
From Dr. Martha Urioste, founding principal of Mitchell (now Denison) Montessori
School.
Montessori Secondary Program
[email protected] <[email protected]>
Sat, Mar 3, 2012 at 10:57 AM Reply-To: [email protected]
To: Katy Myers <[email protected]>, [email protected],
[email protected], Paul Vincent <[email protected]>,
[email protected], Kathryn Mattis <[email protected]>,
[email protected], Frank Vincent <[email protected]>,
[email protected], Laurie Ewert-Krocker
<[email protected]>, "Reina-Ayadi, Yamile" <[email protected]>
Cc: David Kahn <[email protected]>, Deb Silvas <[email protected]>,
Ellie Nichols <[email protected]>
Dear Katy, your positive vision is so encouraging and refreshing! I have been
contacted by AMI Virginia McCue to assist with Colorado Advocacy so it may be
a good idea to include her in the information sharing. Also, monthly, AMI
teachers meet and I gave and ESF presentation there in December-can include
Ellie Nichols-who is leader and with information sharing and meetings-etc. . . I
agree with JoAnn about "dual-language" . (Second language program). Adding
Deb Silvis-Family Star Montessori Coordinator will also work. Shared leadership
and positive vision and action works! Our students will benefit from a holistic
alternative and your efforts-along with David Kahn's support reminds is so
appreciated because it has the potential of greatness of Maria Montessori
vision!
Thank you!
Martha
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Denver Public Montessori Secondary School
Montessori Secondary Program
Escalante, Alonso <[email protected]>
Mon, Feb 20, 2012 at 8:59 PM
To: Katy Myers <[email protected]>
Hi Katy, I believe this is an exciting possibility for our kids. However, at this
time I cannot help out on the committee. I will forward your email to the two
Montessori peer observers who might want to participate on the committee.
Thanks, Alonso
Montessori Secondary Program [email protected]
<[email protected]> Wed, Mar 7, 2012 at 9:04
AM
To: Katy Myers <[email protected]>
Hi Katy, My name is Ellie Willis. About 3.5 years ago,I began a Colorado AMI
support group for all AMI diploma holders. We usually meet about 9-10 times a
year. Some of the meetings are closed to AMI diploma holders and others are
open (most often when we have a tour of a school) for any educator who is
interested in Dr. Montessori's method.
I had heard about your incredible school from a few members of the group
(Lara and Katy) and was fortunate to see some of Compass a little over a year
ago.
I am really excited about your new direction in creating another public
Montessori school for the older "grades" and having it be coupled with the arts.
I have a small start up school in Boulder and would love the opportunity to
meet with you, at any time in the coming year, to ask you some questions
about expanding my school from an IC to also include a Primary. Please
continue to send me information about what you are creating in Denver, I am
happy to pass it along to the members of the support group and would also be
delighted to help in any way possible.
Have a wonderful day,
Ellie
303-882-5468 www.rosemontessori.com
Montessori Secondary Program
Reina-Ayadi, Yamile <[email protected]>
Sat, Mar 3, 2012 at 1:19 PM
To: Katy Myers <[email protected]>
Dear Katy,
Performance School Application Guide
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Page 194
Congratulations on this first step! I will look at data: State and District School
Performance Frameworks, CSAP (TCAP) and enrollment numbers. Also I don’t
know if it would be appropriate I could talk to parents for example at Denison
that have older children (UE) to feel out some key parent engagement from
Denver. Let me know.
Yamile Reina
School Improvement Partner (cell- 720-939-7583) Region 1 - Northwest
Elementary Education Division
From Virginia McHugh, Executive Director of AMI / USA
Montessori Secondary Program
Virginia McHugh <[email protected]>
To: Katy Myers <[email protected]>
Dear Katy, How exciting! Thanks for keeping me in the loop!
Virginia
Association Montessori International/USA
410 Alexander Street Rochester, NY 14607
[email protected] www.montessori-ami.org www.amiusa.org
585.461.5920
From Judith Orion, Director of Training, The Montessori Institute Denver
M. secondary school
Judith Orion <[email protected]>
Sun, Mar 4, 2012 at 2:35 AM
To: [email protected]
Dear Katy,
Though I am not on your email contact list, I heartily support your efforts. I am
out of the country most of the academic year, and training full-on during the
summer at The Montessori Institute (0-3 training). I just wanted to offer my
support though I am unavailable to be actively supportive.
I would love to be on your email list just to remain in touch with what is
happening. I am part of a team that is actively working with DPS to bring AMI
3-6 training to Denver beginning in the summer of 2012 or 2013 (more likely).
Enjoy the remainder of your elementary training. Regards to Greg.
Judi Orion
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Denver Public Montessori Secondary School
Montessori Secondary Program
Hairston-Brown, Tunisha <[email protected]>
Tue, Mar 6, 2012 at 4:47 PM
To: "[email protected]" <[email protected]>
Hello Katy!
I was thrilled to see your email and interest in starting a Secondary Montessori
Progam in DPS!! It was an easy decision to endorse and offer 100 % support for
your efforts. I sent my colleagues an email describing my excitement at the
prospect of an Montessori Secondary Program in DPS, and also expressed my
full confidence in your leadership in this venture.
Thank you for stepping up
to this challenge. If I can help in anyway please let me know. I would love to be
added to your distribution list regarding the application process.
Thanks, Tunisha
Denver Public Montessori Secondary School
Kraft, Debra <[email protected]>
Tue, Apr 3, 2012 at 10:20 AM
To: Katy Myers <[email protected]>
Thank you for your tireless efforts Katy. It is most certainly a huge work and
very much appreciated by all of us. Although I have been extremely busy (I am
in school at night), I am happy to serve the process in the areas of my expertise
and would make myself available to you should you need me. I just finished one
large part of my night school training, so I am a bit more available now if you
should want to request anything from me... Please do not hesitate. My direct
line is listed below and my cell phone is 303-968-9304.
Debra Lucero Kraft Administrative Assistant
Gilpin Montessori Public School
Performance School Application Guide
for schools to open 2013-14
Page 196
Appendix G
Denver Public Montessori Secondary School
Job Descriptions and Self-Governance Model
School Principal Job Description
Qualifications
Montessori Training (AMI or AMS)
Adolescent orientation or Training
Masters Degree in Education Administration and Supervision
Key Responsibilities:
1. Promote School Mission:
•Design, implement and evaluate school-wide policies, programs and
practices, which are consistent with Montessori philosophy
•Create and foster a culture of high expectations regarding behavior and
academic achievement
•Create clear lines of communication and levels of involvement with
committees, staff, students, parents and community members
•Create and foster a welcoming environment
2. Provide Leadership and Long Range Planning:
•Promote a unifying vision
•Establish clear and achievable goals and objectives and evaluate progress
towards goals on a regular basis through a participatory, long range planning
process
•Provide leadership with the School Accountability Committee, teachers, staff,
students, parents, and community members
3. Coordinate and Direct Curriculum and Assessments
•Ensure Authentic Montessori curriculum is established and maintained
•Ensure Denver Public School and Colorado Academic Standards are met and/
or exceeded
•Create, implement and evaluate the use of appropriate classroom, school-
wide, district and state assessments
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Denver Public Montessori Secondary School
•Work closely with school-wide committees, School Accountability Committee,
district and state on issues related to curriculum and assessments
•Review data on an ongoing basis. Create data based monthly reports on
academic progress, achievements and challenges for School Accountability
Committee.
•Create transparency regarding school achievement and mechanisms to
communicate the school’s academic progress, achievements and challenges to
all stakeholders.
4. Develop and Implement Policies
•Develop, implement and evaluate school-wide policies
•Implement District policies and state legal requirements
•Create school policies for any district and state policies and laws that have
been waived.
5. Supervision of Employees
•Ensure that all staff hired are qualified and have appropriate training /
licensure for their position.
•Create and evaluate high quality staff professional development.
•Provide regular, on-going written, evaluations to all professional teachers
that includes monthly observations and is based no less than 50% on
measurable data.
•Provide regular, on-going evaluations to paraprofessional staff
•Ensure clear lines of communication concerning job expectations and
individual performance
•Provide opportunities for professional growth and renewal
6. Manage Financial and Facility Operations
•Develop and maintain an accurate budget and reporting mechanism for the
SAC and School District
•Ensure expenditures are appropriately approved and prioritized
•Maximize revenue sources without compromising policies, programs and
general school wide vision
•Provide leadership and coordination of school facility improvements and
expansions
•Ensure facility maintenance services are arranged
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Program Director (Junior or Senior High)
Qualifications
Montessori Training (AMI or AMS)
Adolescent orientation or Training
Coursework in Master’s Level Education Leadership Program
Responsibilities Overview
Able to strategize with team members and principal on evolution of program.
Create and maintain strong relationships with all members of the self governing
team. Cultivate and maintain the collaborative relationships between the
various school departments and programs. Maintain consistent strong
relationships with parents and students in order to actively manage issues of
behavior and discipline before the point of escalation. Support and develop
governance and autonomous learning of team including discussion with
principal and meetings regarding all aspects of the program.
Support for guides and learning environments
•
Teacher Development
•
Self Assessment
•
Peer Evaluation
•
Defining and developing the role of the adult in this Montessori
environment
•
Aware of the flow in the schedule and building
•
Assessment support
•
Consultation with parents on transitions
•
Monitor effectiveness of parent communication with team
•
Support and mediation for Guides with escalated parents
•
Address student discipline outside of advising
•
Initiate parent follow-up on behavioral issues
Working with the School Principal
•
Communicate all aspects of the program including vision and
sustainability
•
Observe and understand other Montessori secondary program design and
development
•
Report to principal on discipline
•
Referral to principal of all Code of Conduct violations
Actively communicate with and support team members in their work of:
•
Curriculum Development
•
Prepared Environment
•
Community Expectations
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Denver Public Montessori Secondary School
•
•
•
•
•
•
School Culture
High academic expectations
Local overnight trips
Aware of flow in schedule and building
Student Assessment
Staff reflection and accountability
Actively support advisors in
•
Portfolio use and development
•
Consultation for transition
•
Parent communication on classroom and advisory issues
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Denver Public Montessori Secondary School
Self Governance Model
DPMSS will instill a leadership model centered on self-governing teams, program
directors and the school principal. The intention is to allow leadership to manifest from
“the ground up” versus “top down”. This specific model was developed at Compass
Montessori school using best practices from other teacher centered leadership models.
Success of this model depends on creating healthy balance and regular communication
between self-governing teams and the head of school along with utilizing the program
directors to keep our self-governing teams evolving.
Self governing teams always operate in an open welcoming forum. If other staff members
or the principal chooses to join the self governing meeting, they should be able to do so
easily. Our visual on this concept is the perforated circle versus a closed circle. Our proven
experience is that closed circles build walls that become very difficult to tear down.
Perforated circles foster open communication and healthy organization.
Program Director Role:
•
Insure meetings are happening
weekly
•
Set Agenda with input from team
•
Take notes or insure notes are being
taken
Send notes to principal or insure notes are
sent to principal
Keep meeting on track
Insure four focus points are being regularly
addressed by the self governing teams:
Accountability, Logistics, Montessori
Theory, Problem Solving.
Freedoms:
•
To set your own schedule and yearly events
•
To solve problems that are occurring within your level
•
To explore Montessori theory as it applies to your level
•
To determine how to hold each other and students accountable.
•
To participate in the hiring of any new team members.
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Denver Public Montessori Secondary School
Limits:
•
Our core value is creating an
Montessori theory should be a central,
authentic Montessori program. Any consistent part of every self- governing
decision making must have this core meeting.
value at its center.
•
Self-governing teams need to meet DPMSS’ school wide accountability system
is the foundation of student accountability.
at a minimum of once a week in
order to fully realize the benefits of This includes our Student Outcomes,
Student at a Glance Cards, Farm School
this type of school leadership.
•
Any scheduling or events that affect Portfolio, H.S. Albums, and Sub-plane Exit
Outcomes.
other teams have to include
discussion with the other teams and
Holding each other accountable to creating
the program directors / head of
authentic Montessori classrooms along with
school. Scheduling that involves
high expectations of students, ourselves and
hiring people must involve the
each other is a core part of the selfPrincipal early on to see if this
governing team. The team needs to
makes sense from a budget and
determine early in the school year how best
school wide perspective.
to bring up sensitive topics and address
•
Any problem solving that could
concerns.
escalate should include program
directors / principal so that we are
informed and prepared to support
you.
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Appendix H
Resume
Curriculum
Vitae
Katy Myers
1900 East St. Golden, CO 80401 303.431.2385 Cell
Professional Summary
•
•
•
•
Visionary with excellent strategic planning abilities and who can create and execute
tactics that result in success
Demonstrated Leadership
Strong Communication Skills – both written and verbal
Excellent Financial Management Skills
Experience
Head of School, 2005 - 2011
Compass Montessori School; Pre-K through 12th Grade Public Montessori Charter School
Wheat Ridge and Golden CO
Assistant Head of School and Business Manager, 2001 – 2005
Compass Montessori School
Founding Parent and Chairperson of Steering Committee, 1997-1998
Compass Montessori School
Significant Achievements
·
Head of School for public Montessori charter school comprised of two campuses
(Wheat Ridge and Golden), Preschool -12th grade, 80 staff and 600 students
·
Evolved start up to a stellar Montessori program that meets or exceeds Colorado
State Education Standards.
·
Obtained $7.5 million in CECFA facility bond financing and managed the purchase,
design and build of the Golden Campus, which includes a farm, commercial kitchen
and was the first public school facility specifically designed for a Montessori
secondary program. Managed two school expansions including the design, financing
and build process.
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·
Replaced head of school at the Wheat Ridge campus mid-year 2008 due to financial
upheaval and staff turnover. Within two years improved staff and student retention
rates to 95% and significantly improved the campus’ financial stability.
·
Grew Compass Montessori Secondary program from 80 students to 200 students.
Compass High School is currently rated high performing and earned the Governor’s
Award for schools with the highest 2009-2010 academic growth rates in Colorado.
·
Led staff in the design of an outcomes based Montessori pre-k through 12th grade
education accountability system.
·
Created a self-governance leadership model that allows for team decision-making
while maintaining strong partnership and reporting to head of school.
·
Successfully renewed charters at both campuses.
·
Led the Steering Committee responsible for writing the Compass charter, purchasing
the original school facility, hiring founding staff and principal, enrolling 150 founding
students and creating the first year operating budget.
·
Manage finances for both campuses totaling over $4.5 million revenue.
Presentations
Myers, Katy (2010). The Holistic Montessori Environment. NAMTA Adolescent Conference
“The Adolescent and Technology: Find the True Balance in the Montessori Prepared
Environment”, Keynote presented April 17, 2010.
Myers, Katy (2009). Maintaining Adolescent Montessori Programs in the Public Sector,
Montessori Quality and Sustainability – 2009 AMI/USA Public School Forum, November 14,
2009.
Consultations
National Association of Charter School Authorizers – Team Lead Evaluator for the State of
New Jersey 2011 Charter School application evaluation process and for the Louisiana
Department of Education 2011 Charter School application evaluation process. Evaluator for
the State of Florida 2008 Charter school application evaluation process.
Colorado Department of Education Charter School Leadership Mentor Program, 2010-2011.
Great River Montessori High School, Minneapolis, MN, 2005
Education
Masters of Education, Education Administration and Supervision, Arizona State University,
2005
Concentration: Leadership in Entrepreneurial Education
Thesis: Implementing the Montessori Science Curriculum “Occupations” in a Public
Montessori School; Proactive Action Research Study
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Elementary (6-12), Association Montessori Internationale, Montessori Training Center of
New England, Trainer Greg MacDonald.
90% Complete – projected certification date is May, 2012.
A Montessori Orientation to Adolescent Studies, North American Montessori Teachers
Association, 2003
B.S, Speech, Northwestern University, Evanston, IL 1986, Majors: Theatre and Economics
Business Experience
Qwest Communications, 1999-2001.
Real Estate Manager
·
·
·
·
Managed a team of twelve real estate acquisition specialists to lease and zone sites
for wireless communication towers within the Mountain Division.
Worked closely with the construction and engineering teams in order to insure each
project flowed seamlessly from identification to installation
Managed the real estate accounting and property management employees to insure
that all lease payments were paid on time and accurately, and that all lease
requirements were met in order to prevent any default situations.
During the years I managed this team, we were the highest performing Qwest real
estate acquisition team across the United States, as measured by established
company performance metrics.
Beveled Designs, 1992 – 1999
Owner
·
·
Handled the accounting, sales, accounts receivable, accounts payable, payroll, sales
and employment taxes for this stained glass manufacturing company that I co-owned
with my husband.
Grew company from our garage to an established showroom and manufacturing
facility with annual revenues of $300,000.
MCI Telecommunications, 1987 - 1992
Real Estate Manager
·
·
·
·
Managed the acquisition, build out and move in of all MCI sales offices and technical
facilities for the Western Division.
Negotiated commercial leases.
Audited and managed triple net lease expenses, including calculating CPI increases,
for real estate inventory totaling over $1.5 million.
Won Excellence in Service award which recognized the top 2% of employees based
on performance.
References
Tracy McIlrath, Past Board President and Interim Head of School, Compass Montessori
School; [email protected]
Pat Ludick, Montessori Consultant; [email protected]
William Haft, Vice President of Authorizer Development, National Association of Charter
School Authorizers; [email protected].
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Denver Public Montessori Secondary School
Denver Public Montessori Secondary School
Appendix I
School Organization Chart
Denver Public
Schools
School
Accountability
Committee
Principal
Program
Director
Program
Director
Office Staff
Senior High
Teachers
Junior High
Teachers
Instructional
Support Staff
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Exhibit J
Denver Public Montessori Secondary School
Staff Roster
Year 0
Principal
Administrative Assistant
1
0.5
Year 1 - 50 Students, 6th and 7th grade
Principal
0.5
Administrative Assistant
0.5
Teacher who is also ELA-T qualified
1
Teacher who is HQ Spanish and ELA -E qualified 1
Teacher (who is also the Principal)
0.5
Special Education Teacher
0.25
Psychologist / Social Worker
0.2
Nurse
0.1
Farmer (para professional)
300 hours
Wednesday Afternoon Tutors
228 hours
Year 2 - 65 Students, 6th, 7th and 8th grade
Principal
Administrative Assistant
Teacher who is also ELA-E qualified
Teacher who is HQ Spanish and ELA endorsed
Teacher (who is also the Principal)
Special Education Teacher
Psychologist / Social Worker
Nurse
Farmer (para professional)
Wednesday Afternoon Tutors
0.5
0.5
1
1
0.5
0.25
0.2
0.1
300 hours
228 hours
Year 3 - 105 Students, 7th, 8th and 9th grade
Principal
Administrative Assistant
Teacher who is also ELA-E qualified
Teacher who is HQ Spanish and ELA endorsed
Teacher (who is also the Principal)
Special Education Teacher
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0.5
3
1
0.25
0.4
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Psychologist / Social Worker
Nurse
Farmer (para professional)
Wednesday Afternoon Tutors
Para professional (micro-economy)
0.3
0.1
300 hours
342 hours
315 hours
Year 4 - 140 Students, 7th - 10th grade.
Principal
Administrative Assistant
Teacher who is also ELA-T qualified
Teacher who is HQ Spanish and ELA -E
Teacher (who is also the Principal)
Special Education Teacher
Psychologist / Social Worker
Nurse
Farmer (para professional)
Wednesday Afternoon Tutors
Para professional (micro-economy)
0.75
0.75
4.5
1
0.25
0.6
0.5
0.2
300 hours
456 hours
315 hours
Year 5 - 175 Students, 7th - 11th grade.
Principal
Administrative Assistant
Teacher who is also ELA-T qualified
Teacher who is HQ Spanish and ELA-E
Teacher (who is also the Principal)
Special Education Teacher
Psychologist / Social Worker
Nurse
Farmer (para professional)
Wednesday Afternoon Tutors
Para professional (micro-economy)
0.75
1
6
1.5
0.25
0.75
0.5
0.3
300 hours
456 hours
315 hours
Year 6 - 210 Students, 7th - 12th grade.
Principal
Administrative Assistant
Teacher who is also ELA-T qualified
Teacher who is HQ Spanish and ELA-E
Special Education Teacher
Psychologist / Social Worker
Nurse
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1
7.5
1.5
1
0.7
0.3
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Farmer (para professional)
Wednesday Afternoon Tutors
Para professional (micro-economy)
300 hours
456 hours
315 hours
Year 7 - 225 Students, 7th - 12th grade.
Principal
Administrative Assistant
Teacher who is also ELA-T qualified
Teacher who is HQ Spanish and ELA-E
Special Education Teacher
Psychologist / Social Worker
Nurse
Farmer (para professional)
Wednesday Afternoon Tutors
Para professional (micro-economy)
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1
1
8
2
1
0.7
0.3
300 hours
456 hours
315 hours
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Exhibit K
Scope and Sequence
This section is excerpted from A National Montessori Curriculum Report
as published by the NAMTA Journal, Volume 37, Number 1, Winter 2012 and
then adapted to meet the DPMSS programmatic requirements.
Because Montessori education is designed in three year cycles, this scope
and sequence represents 7th - 9th grade science and is not broken out by
grade. All students will be expected to complete all the required benchmarks in
all subject areas as spelled out in the Junior and Senior High portfolio. Ninth
grade students work will be judged against high school standards, and only the
work ninth grade students complete during their ninth grade year will be
counted towards their graduation requirements. In order to comply with the 15
page limit, this document will only show detailed scope and sequence for
Science. Scope and sequence for Language Arts, Math, History and Creative
Expression are available upon request. The high school (10th, 11th and 12th)
will not open until 2016. Prior to opening, a complete scope and sequence
based on college preparatory curriculum will be submitted to DPS for approval.
Science Curriculum for Adolescents Aged from Twelve to Fifteen/Sixteen
Science is significantly embedded in the Occupations, or the work of the
adolescent community, which includes:
•
•
•
practical daily life tasks, including maintenance of the community
environment
working on and being stewards of the land, including, for example, care
of the natural environment, horticulture, agriculture and animal
husbandry
contributing to the micro-enterprises of the community
The concept of embeddedness, sometimes referred to as ‘embodiment’, has
some very specific implications both for the preparation of the teacher and for
the design of Occupations. Each Occupation sets up environmental components
around the activities that are tied to related scientific concepts. Water, plants,
animals, botany, rocks, geology, watershed, thermal dynamics and the
transmission of energy, etc. are all embodied in the Occupation and are
inseparable from it. The work of the Occupation, like the Montessori material of
the classroom, limits the scientific investigations to the task parameters of the
Occupation. One does not exceed the task parameters of the Occupation in
order to make sure the learning of science is precisely reinforced by the work
the Occupation requires. For example the limits or task parameters of a ‘Pig
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Occupation’ include the care of the animal, its vital functions, and its
physical characteristics, making this predominantly a biological study. However,
the market value of the pig invites an economic study. The pig’s habitat
necessitates a study in space and co-habitation. The nature of the task
determines the nature of the study.
The Occupation is holistic, but two main extensions emerge: One is abstract
scientific knowledge usually discussed before and after the task at hand, and
second is the social life of the community. The work of the Occupation is
undertaken collaboratively. The adult working side by side the adolescent is an
exercise in intergenerational cooperation. From the Montessori point of view,
work of this type does not hinder a student’s study; instead, it enhances the
quality of the study as students have the opportunity to apply their knowledge to
solve problems and to contribute to the community. The Occupations enable
students to build independence to the point where they experience what it means
to be economically independent in society. They also learn that collaboration
between humans ‘results in … a happy social life that will facilitate individual
progress’ (Montessori 1976 [1948]: 113). While working collaboratively on
Occupations that contribute to the life of the community, students are also
learning to discipline themselves and to work toward shared goals.
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Denver Public Montessori Secondary School
Occupation Concept Lessons - Delivered over a three year cycle
Zoology
Characteristics of mammals
Characteristics of birds
Systems of mammals: digestive, respiratory, nervous,
reproductive, circulatory, skeletal/muscular (pig, cow, human)
Human digestive system
Basic Biology
Systems of birds: digestive, respiratory, nervous, reproductive,
Metabolism
circulatory, skeletal/muscular (chicken)
Cell structure: organelles
Classification of mammals: cow, chicken
Plant cells
The evolution of mammals: cow, chicken
Animal cells
Genetics: role of chromosomes, dominant and recessive traits,
Types of cells: nerve cell, blood cell, muscle cell, skin cell, bone probability of inheritance, Punnett Square
cell
Botany
Cell division: mitosis/meiosis
Microbiology: yeasts, molds, bacteria
Parts of the plant: leaf, stem, fruit, flower, seed, root
Food chains and food webs
Plant processes: photosynthesis, transpiration, translocation
Plant classification
Chemistry
Genetically modified organisms
Atoms and molecules
Hydroponics
Chemical structure and function of carbohydrates, proteins,
Archeology/Local History
and fats
The history of Huntsburg and Sylvester Clapp
Physical Science
Genealogy of Huntsburg families
Solar radiation and electromagnetic waves
Archeological excavation
Earth’s rotation and tilt
Handling, identifying, cataloguing, and displaying historical
Radiation and matter: reflection, transmission, and absorption artifacts
Thermal mass
Scientists and Scientific Contributions
Water cycle and basic weather principles
Motion, acceleration, and force
Louis Pasteur
Newton’s Laws of Motion
cell biology, pasteurization, disproving spontaneous generation
Simple machines: level, pulley, wheal, axle, inclined plane,
Science and Culture
wedge, and screw
Work, power, and simple machines
The cow in history and mythology
Energy and transformation of energy
Factory farms: mass production of meat animals
World hunger
Economics
Food and body image
Economic models
Healthy diets
Economic math
History of greenhouses
Supply and demand
The biosphere and environmental issues: acid rain, nuclear
Budgeting and forecasting
waste
Profit and feasibility studies
Tools and humanity: the history of tools and the nature of
Business ethics
humans
Scientific Method/Lab Skills
Scientific research and the scientific method
Using a dichotomous key
Using a compound microscope
Using the metric system/unit conversion
In the Montessori view, adolescents learn by doing. Learning by doing is a
feature of the Montessori Science curriculum. Much of the curriculum is aligned
with the Occupations of the Montessori adolescent community. Occupations are
projects, tasks, and courses of study that arise out of needs of the adolescent
community and local environment. They provide real, meaningful work that aims
at developing a sense of worth in the students because their contributions to the
community are real.
Occupations might be understood as a project. Each project is initiated by
a problem that needs a solution. For example, if the class initiates a microenterprise based on keeping poultry, the need to learn about the biology and
!
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needs of poultry is real. This generates meaningful engagement in the process
of scientific inquiry, in which students identify and investigate key questions
and gather and collate evidence-based conclusions. While each project might
be grounded in one area of the curriculum more than others, opportunities for
interdisciplinary studies are also valued. While the main disciplinary focus of a
project might be on science and mathematics, students might also engage with
knowledge and skills related to language, art, history or geography. As the
projects unfold, students have the opportunity to contact scientists working in
relevant fields, as a source of expertise and as a model for how to conduct
scientific enquiry.
While working on projects, students are able to explore particular topics in
depth. Early in the project students participate in main lessons which outline the
key science concepts needed to engage with the project productively. Students
then work to develop their knowledge, skill and understanding to the level
required to complete the project successfully. While engaged on a project,
students are free to explore areas of science and to develop scientific capabilities
that they find relevant and interesting. In addition, because the projects are
undertaken in real life settings to meet real life challenges, the students also
explore ethical issues relevant to the project. For example, if the students are
working on a project that involves keeping poultry, they might apply their
knowledge of poultry biology and behaviour to debate and explore issues relating
to the relative merits of cage-laid, barn laid, free range and/or organic eggs.
As the project unfolds, students have the opportunity take on different
roles. For example, students whose project involves keeping poultry might take
on the roles relating to farming, using video to keep records or bookkeeping. In
this way, students learn to cooperate to achieve goals shared with others, to
experiment with different Occupations and to demonstrate to themselves and
others that they are able to contribute to meaningful and real life ventures. In
addition, they learn to think about the ethics of science and progress and develop
the ability to make informed decisions about issues that relate to the health and
well-being of themselves, their community and their environment.
The project-based approach allows students to develop science
understanding, and inquiry skills because, in order to complete each project,
students must engage in research and experimentation. The project-based
approach also enables students to understand science as human endeavour. For
example, students are encouraged to explore the genesis of scientific
knowledge and understandings by researching the biographies of great
scientists, past and present, as well as the history of scientific concepts and
ideas. As the projects unfold, students engage in seminars, debates and
discussions about not only scientific knowledge, understandings and skills, but
also the cultural and social issues that need to be taken into consideration
when decisions and problem solving involve science.
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Denver Public Montessori Secondary School
As part of the Montessori Science Curriculum for adolescents, students
take part in field trips to observe and collect data and to become familiar with
the ecology of their region. They learn to identify local plants and animals,
whether native, feral or domesticated, and study the ecological systems of the
region, including relations between organic and inorganic elements. Students
also review their knowledge of the systems for organising knowledge in science
and make note of how the knowledge, and terms used are kept current. For
example, they consolidate their knowledge of scientific taxonomies and their
organising principles, as well as features, such as features of anatomy and
physiology, which determine where organisms are placed in a classification
system. Students also use their research skills to track how knowledge about
evolution, and systems such as climate and ecology, is changing and
expanding, and what this might mean for decision makers and humanity in
general.
The aims of the Montessori science curriculum for adolescents aged from
twelve to fifteen/sixteen years include the following:
Science inquiry skills
· to work with scientific data (primary and secondary), including gathering,
recording, storing, collating, interpreting, and repeating investigations
· to represent findings in a variety of forms, including graphs, tables and
diagrams
· to seek elaboration and justification of data and ideas and reflect on
alternative interpretation
· to use principles that will validate and demonstrate personal understanding
of science
· to work collaboratively to undertake laboratory or field science around
reality based activities
· to follow scientific and mathematical procedures to observe, hypothesise,
predict and test in an area of scientific investigation of their own choice.
· to identify potential hazard and design an appropriate investigation to
observe, collect data and present findings
Earth and space sciences
· to create maps and drawings of land-based data (topographical maps).
· to collect, display and interpret data on the geologic and mineral content of
the local soil and through chemical analysis, composition studies and
testing, explaining the historical development of various components
Biological sciences
· to explore and represent patterns and cycles in the natural world
· to create and read biological scale drawings
· to investigate the role of organisms within a variety of ecosystems
· to investigate the local flora and fauna that make up the natural local habitat
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to compare and contrast various ecosystems and their associated functions
in the succession of habitats
· to collect data and track the trends and variability in behaviour of local and
domesticated animals.
Physical sciences
· to investigate physics in the total environment: the Universe, the earth, the
forces that shape the earth, the structure of matter, the transformation of
energy, the motion of things, the forces of nature
· to select and utilise various mechanical devices while testing the models and
patterns of certain scientific laws e.g. conservation of energy
Contemporary sciences
· to design and use apparatus and tools appropriate to meet occupational
challenges
· to maintain small common electrical and mechanical systems, identifying
and eliminating possible causes of malfunctions
· to compare and contrast the design, functionality and structural integrity of
self-designed structures and make appropriate recommendations for
improvement
·
Science (Occupations) Curriculum for the Adolescent Aged Twelve to
Fifteen/Sixteen Years
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Content
Strand
Knowledge, Skills and
Understandings
Typically students will:
Activities and Resources
The study of Earth and living things
Earth and
space sciences:
- cosmology
- astronomy
- geology and
physical
geography
Build knowledge of the stars, galaxies and the universe.
Activities include:
Study the histor y of the exploration of the universe- making models
through visual obser vation, telescopes, unmanned and- reading and making maps
manned space exploration
- creating timelines of
cosmological and
Study the structure of the Ear th and geological histor y
geological eras
- the composition of the Ear th
- conducting experiments
- three states of matter
- interdisciplinar y projects
related to weather and
- different ways of combining
- attraction and gravity
climate e.g. projects that
- geology
integrate scientific,
statistical and historical
knowledge
Study plate tectonics and geological phenomena such as
the formation of mountains
Study the Sun and the Ear th
- rotation of the Ear th and its consequences
- Ear th as a sphere
- tilt of the axis
- seasons
- time zones
Study the Work of Air
- protection of the atmosphere
- rains
- winds
- land and sea breezes
- seasons and the winds
- ocean currents
- the wind as sculptor
Resources include:
- globes
- telescope
- char ts
- maps
- experiment supplies
- non-toxic supplies for
experiments
- almanac
- reference and research
materials (paper-based,
digital, web-based,
multimedia)
Study the Work of Water
- the river
- rain
- ocean waves
- ice
- the water cycle
- water and vegetation
Study of Human Geography
- zones on the Ear th
- interdependencies
- economic geography
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Biological
sciences:
- botany
- zoology
- physiology/
anatomy
- health sciences
Classify living things according to the Linnaean taxonomy Activities will include:
- investigating the life forms
Study and use different classification systems in use today in pond water and their
relations
Study and compare the morphology, or structural features - identifying, recording and
of living things
classifying activities in the
school environment,
Study the cell as the basic unit of life
including both domestic
- the structure of the cell
and natural species
- cell respiration
- creating diagrams, charts,
- cell division/reproduction, meiosis
models, visual data displays
- photosynthesis
and multimedia
- biochemistr y of the cell
representations e.g. of
- DNA/RNA, mitosis, protein synthesis
cells, cell processes, DNA
populations and
relationships in
Introduce and extend knowledge of genetics:
ecosystems, genetic
- Mendel
patterning, natural cycles,
- dominance/recessiveness
biological processes etc
- probability
- projects relating to
- aberration
inherited traits in families
e.g. colour blindness
Review and extend knowledge of natural cycles:
- creating timelines to
- water
illustrate evolutionar y
- nitrogen
time
- carbon
- dissection
- projects that enable
Review and extend knowledge of the vital functions of
students to apply
living things plants and animals:
knowledge of human
- body coverings
physiology to own health
- circulation
and well-being
- respiration
- digestion
- movement
- reproduction
Resources will include:
- microscopes and other
research equipment
- resources for recordIntroduce and extend knowledge of biochemistr y
keeping and displaying
Review and extend knowledge of human physiology, findings
including body functions, hormones and nutrients
- reference and research
materials (paper-based,
Explore the interdependency of life
digital, web-based,
multimedia)
Investigate ecosystems, including populations, interactions - animals
and biodiversity within ecosystems
- garden plants
- natural outdoor
Investigate the extinction of species
environment
Investigate the development of genetic engineering
Investigate animal behaviour :
- reflex
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The study of human progress and civilisation
Physical
sciences:
- physics
- chemistr y
Understand foundation concepts in physics related to
forces and motion, including velocity, acceleration,
iner tia, force, mass and weight, friction, work, power,
effor t, Newton’s three laws of motion, energy
transformation, mechanical advantage, efficiency
Investigate simple machines, including, lever, inclined
plane, wheel and axle, pulleys, gears
Review and extend knowledge of electricity and
magnetism
Investigate forms of energy and energy transfers
Activities include:
- experiments, investigations,
project work
- working with models
Resources include:
- science laborator y
- reference and research
materials (paper-based,
digital, web-based,
multimedia)
Investigate the nature of matter, including atoms and
their structure, par ticle theor y, molecular structure,
ionisation
Review and extend knowledge of elements,
compounds, chemical reactions, acids and bases, salts,
oxidation, valences, the carbon compounds of organic
chemistr y
Identify and use of the periodic table
Compare and contrast metals and non-metals
Understand and describe the carbon, oxygen and
nitrogen cycles
Under take experiments under laborator y conditions
Extend and apply research skills
Reference sources effectively
Contemporary Use and care for basic mechanics tools
Resources include:
sciences
- museum of machines
- mechanics
Repair and maintain the systems of a combustion engine - workshop
- engineering
- tools and equipment
- histor y of science Understand systems for cooling and heating
and technology
Understand electrical systems
Build knowledge of the mechanical and sub-atomic
proper ties of machines that allow them to work
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Synthesising and Integrating Scientific Knowledge and Understanding:
Systems of Interdependency
Scientific understanding and knowledge is synthesised and integrated in the
following ‘learning by doing’ studies of systems of interdependency.
Systems of interdependency
Content
Strand
Knowledge, Skills and Understandings
Activities and
Resources
Typically students will:
Soil
Investigate the composition of soil
Through a study of
soil, students are Relate soil chemistr y to the study of animal and plant
introduced to both life
geological and
Apply knowledge of the carbon, oxygen and nitrogen
biological studies.
cycles
Activities include testing, grading
and mapping soil types
Resources include:
- soil test kit
- mineral sample kit
- range of soil types
- access to internet, e.g.
Understand the role of soil in photosynthesis
Google Ear th, GIS
Recognize soil types, their origins and their suitability - plants, fer tilizers, potting
mix, plant pots
for specific plants
- reference and research
materials (paper-based,
Understand the geological impact of glaciers
digital, web-based,
Describe the causes and effects of erosion
multimedia)
Water
Appreciate the physical proper ties of water
Resources include:
Water is integral to
- water test kit
Identify water forms on ear th
the origin of life
- chemistr y glassware for
and to the Ear th’s
separation of soluble and
Describe the role of water in photosynthesis
histor y. It is studied
insoluble substances.
for its physical and Identify water as the universal solvent
- conductivity meter
chemical
- pH meter
proper ties.
- reference and research
Recall the molecular structure of water
materials (paper-based,
Understand water ionization
digital, web-based,
multimedia)
Understand the water cycle
- local water sources
Test water quality, by obser ving, measuring and
comparing features such as:
- pH
- biological indicators
- turbidity
Comprehend the concept of watershed
Discuss the ethical implications of water use and
management
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Denver Public Montessori Secondary School
Air
Investigate the chemistr y of the air
Air is studied for its
Define meteorology
role in ear th’s
climate and in plant Comprehend the transfer of heat energy Relate
and animal life
cycles
movement of air to climatic patterns Understand
Activities include testing and
analysing air quality
Resources and equipment
include:
- Bunsen burners
- access to Internet e.g.
the role of convection in heating and
Bureau of Meteorology,
cooling
Seabreeze
- Airwatch
Discuss the implications of degrading air quality and the
- air monitor box
relation between air quality and climate change
- reference and research
materials (paper-based, digital,
web-based, multimedia)
Energy
Describe and explain and non-renewable energy
Resources and equipment
Energy is studied as sources including solar power, fossil fuels, geothermal include:
a comprehensive energy, nuclear energy
- bicycles
force that
- timing devices, e.g. video
originated with the Understand energy uses, including work and machines timers, light gates
Big Bang and has Appreciate the nature of energy Explore
- solar panels
global implications
- electronics kits
as a universal
- reference and research
alternative energy systems Understand the
human commodity
materials (paper-based,
role
of
technology
in
energy
and need.
digital, web-based,
production and conser vation
multimedia)
Discuss the ethical implications of energy use
Animals and
Investigate the characteristics of living things
Plants
Animals and plants Understand animal and plant habitats and their
distribution
are studied in
terms of their role Study photosynthesis
in natural
ecosystems and in Har vest plant and animal products
agricultural science,
as well as for their Understand the process photosynthesis and its
anatomical and vital impor tance in ecosystems
functions.
Understand energy flow in food webs and chains
Resources and equipment:
- microscope kit
- anatomical models
- live animals
- plants, fer tilizers, potting
mix, plant pots
- reference and research
materials (paper-based,
digital, web-based,
multimedia)
Understand the concept of genetics
Understand the role of biodiversity in an ecosystem
Study evolution and the diversity of living things
Describe the role of adaptation in evolution
Understand the concept of homeostasis.
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The Human
Research the origins of humans
Organism
The human
Understand the role of humans in animal
organism is studied domestication
in terms of the life
cycle, and for its Explore the use of genetics for science, medicine and
relation with the
agriculture and debate the ethics behind this use
natural world.
Explore the ethics of the uses of natural resources
Resources and equipment
include:
- anatomical models
- medical meters, e.g.
sphygmomanometer,
stethoscope, thermometer
- reference and research
materials (paper-based,
digital, web-based,
multimedia)
Discuss the various systems for food procurement,
processing and distribution.
The sample project below exemplifies how all areas of the curriculum might be
synthesised and integrated in the Occupations of the Montessori adolescent
community.
Science (Occupations) Project: Poultry Farming
The project is initiated by a group of students with an adult guide and the input
of other specialists as needed.
Goals
Engagement
- Students apply scientific knowledge and skills to situations outside of the classroom.
- Students show interest in new or unusual situations.
Key
- Students understand their biology and that of other living things, and recognise the
Concepts/
interdependence of life.
Mastery
- Students understand the structure and function of organisms, from the organisational
level of cells to systems.
- Students understand the need for reproduction in maintaining a species and a
community.
Skills
- Students plan adequate control of variables in a simple experiment.
- Students design a simple controlled experiment to test the effects of one variable.
- Students form inferences based on obser vation.
- Students interpret data in a graphical form.
- Students use correct procedure for handling apparatus.
Work
- Students follow procedures.
Management - Students work cooperatively in a group.
- Students make neat and accurate obser vations.
Methodology
The methodology used to support project-based learning is derived from the
three-period lesson, a lesson structure that is applied at all levels of Montessori
education, from early childhood to teacher education.
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Denver Public Montessori Secondary School
First Period of the Project
In this period students participate in introductory activities that open up the topic
and key concept lessons.
The first period of the poultry farming project might include introductory activities
such as the following:
· a story that demonstrates the interdependence of humans and domesticated
animals and plants
· a reading from the section on ‘domesticates’ from Guns, Germs and Steel by
Jarrad Diamond
· the story of the pavlova
· In 1935, the chef of the Hotel Esplanade in Perth, Western Australia, Herbert
Sachse, created the pavlova to celebrate the visit of the great Russian
ballerina, Anna Pavlova. The dish is based on meringue made from egg
whites. Whilst it has been suggested this dessert was created in New
Zealand, it has become recognized as a popular Australian dish.
· a cooking lesson: how to make pavlova
· a ‘how to’ dissection lesson: dissecting an animal heart
· a ‘how to’ lesson: using a microscope
· an art lesson: painting microscope observation
Students then pose one or more key questions. The key question for the poultry
farming project might be:
What do we need to know to successfully operate a chicken egg farm?
The answer to this question determines the key concept lessons to follow.
Below are a series of key concept lessons that might be presented in the first
period of the poultry farming project. These lessons focus on students
understanding of:
· their own biology and that of other living things
· the interdependence of life
· the structure and function of organisms, from the organisational level of
cells to systems
· need for reproduction in maintaining a species and a community.
Lesson
Title
Lesson 1
Classification of animal kingdom, and the classes of ver tebrate
Lesson 2
Food chains and decomposers
Lesson 3
Circulator y system
Lesson 4
Respirator y system
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Lesson 5
Digestive system
Lesson 6
Structure of egg
Students might also participate in a seminar in which the following question is
researched and discussed:
How do our actions on a farm affect the balance of nature?
Students will be provided with a range of resources to explore the key concepts
and the discussion question further. These will include a range of reference and
research materials (paper-based, digital, web-based, multimedia).
During the first period of the project students build a shared specialised
vocabulary to talk about the topic. This vocabulary might include:
· Kingdom, Phylum, Class, Order, Family, Genus, Species
· autotroph, heterotroph, producer, consumer, decomposer
· poultry, fowl, hen, rooster, chicken, hatchlings
· free range, battery
· mould, fungus, bacteria, compost
· food chain, food web
· reproduction system: egg, sperm, mitosis, penis, vagina
· circulatory system: heart, blood, artery, vein
· respiratory system: lungs, diaphragm, intercostal muscles, bronchi,
bronchioles, alveoli
· digestive system: mouth, oesophagus, stomach, small intestine, large
intestine, anus
Second Period of the Project
The second period of the project includes whole group and individual,
explorations, and activities in which students actively explore, research,
experiment, discuss, and take part in hands-on practical tasks relevant to the
project. In the context of the poultry farming project these, explorations and
activities might focus on the students developing the following knowledge,
skills and understandings:
· Plan adequate control of variables in a simple experiment
· Design a simple controlled experiment to test the effects of one variable
· Follow a procedure
· Work cooperatively in a group
· Make neat and accurate observations
· Use correct procedure for handling apparatus
· Understand the structure and function of organisms, from the organisational
level of cells to systems
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Denver Public Montessori Secondary School
Whole group lessons and activities might include the following:
Lesson
Title
Lesson 1
Investigating the needs of poultr y
Lesson 2
Making a chicken coop
Lesson 3
Setting up a bread mould experiment
Lesson 4
Setting up a compost decomposition experiment
Lesson 5
Creating photo identification cards of school plants and animals
Lesson 6
Conducting a hear t dissection
Lesson 7
Conducting step test for fitness
Lesson 8
Calculating lung volume
Lesson 9
Creating ar t work based on microscope obser vations of tissues
The students then undertake individual research tasks related to the project. In
the context of the poultry farming project these might include the following:
·
·
·
·
·
·
growth of poultry
business policy and guidelines for poultry farming
ethical rearing of poultry
avian diseases
uses of poultry products: meat, eggs, feathers
history of poultry and poultry farming
Third Period of the Project
In the third period of the project students complete a variety of tasks for
assessment, including spoken and written presentations and creative
expression. A spoken presentation might be used to present results of
observations and experiments and a written assignment or report might be
used to present research findings. Students might also be quizzed or tested on
the knowledge, skills and understandings they have gained. Students would
also present creative work, such as illustrations based on microscope
observations.
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Appendix L
School Calendar and School Day Schedule
These dates are estimated and will be adjusted once the official DPS 2013/2014
School Calendar is Released.
August 8,9
August 5-16
August 19
September 2
September 20
October 18
October 21 - 25
October 28 - Nov. 1
November 11
November 27-29
December 20
December 23 January 3
January 6
January 20
February 17
February 18
March 14
March 17 - 21
March 24 - April 3
April 4
May 9
May 23
May 26
June 10
June 11
June 12,13
Walk in registration
Planning / Professional Days (no class for students)*
First Day of School
Labor Day Holiday - No School
Assessment Day - No Classes
Quarter progress reports sent home
Parent / Student / Teacher conferences held after
school
Fall Break - No School
Planning / Professional Day (no class for students)
Thanksgiving Holiday - No School
Assessment Day - No Classes, Semester progress
reports sent home.
Winter Holiday - No School
Planning / Professional Day (no class for students)
Martin Luther King Holiday - No School
President Day Holiday - No School
Planning / Professional Days (no class for students)
Quarter Progress reports sent home
Parent / Student / Teacher conferences held after
school
Spring Break Holiday - No School
Planning / Professional Days (no class for students)
Planning / Professional Days (no class for students)
Assessment Day - No Classes
Memorial Day Holiday - No Classes
Last Day of School
Planning / Professional Day; Final semester reports
sent home
Planning / Professional Day
Student Report Days: 171 Total Days
Teacher Report Days: 191 Total Days
*The first year we will have 10 planning/professional days prior to the first day of school.
Subsequent years we will have 5 planning/professional days prior to the first day of school with
Teacher Report Days at 186.
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Denver Public Montessori Secondary School
DPMSS Junior High Daily Schedule
Monday , Tuesday, Thursday, Friday
Wednesday
8:00 –
8:30
Morning Meeting, advisor check in, daily schedule
check, announcements
Community Meeting
8:30 –
11:30
Academic Work Time.
Academic Work Time; small group lessons in math,
Spanish, ELL, key lessons for Occupations including
reading, writing, history, civics, and science. Students
are doing independent and small group work when not
in lessons. There will also be time for art and microeconomy.
11:30- Lunch / Outdoor recreation time
12:30
Lunch / Outdoor
recreation time.
12:30 – Reading and Journal time. Advisors are conducting
portfolio checks and having one on one advising time.
1:15
Reading and Journal
time, ending with
restoration of
environment
1:15 –
3:10
Academic Work Time; small group lessons in math,
Spanish, ELL, key lessons for Occupations including
reading, writing, history, civics and science. Students
are doing independent and small group work when not
in lessons. There will also be time for art and microeconomy.
1:30 – Students are
released to leave or
attend supervised
study hall.
3:10 –
3:30
Advisement Check-In and restoration of environment.
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DPMSS High School Schedule
Tuesday
Core Class
Lessons &
Work
Wednesday
Community
Meeting
Advising
Often other
follow up
meetings: SIP,
Intl. Trip, ACT
Prep, etc.
Thursday
Core Class
Lessons &
Work
Friday
Core Class
Lessons &
Work
11:40 – Lunch
12:25
Lunch
A.W.O.L
Lunch
Lunch
12:301:30
Elective
Classes
Elective
Classes
A.W.O.L
Elective
Classes
Elective
Classes
Practice time
for Athletics,
performance.
Advisors
available for
tutoring
Practice time A.W.O.L.
for Athletics,
performance.
Advisors
available for
tutoring
Practice time
for Athletics,
performance.
Advisors
available for
tutoring
Practice time
for Athletics,
performance.
Advisors
available for
tutoring
8:00 –
11:40
1:35
-2:35
2:40 –
3:30
Monday
Core Class
Lessons &
Work
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