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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 Innovation Plan Denver Montessori Junior/Senior HS Page 2 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 Page 3 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 Innovation Plan 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. Innovation Plan Denver Montessori Junior/Senior HS Page 5 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. Innovation Plan Denver Montessori Junior/Senior HS Page 6 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 Page 7 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 Page 8 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 Page 11 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 Page 13 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. Page 15 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. Page 29 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 Page 30 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 Page 31 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 Policy 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 Policy 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 Replacement 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. Page 32 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 Replacement 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 Replacement 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. Page 33 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 Policy 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 Policy 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 Policy 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 Replacement 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, Policy 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 Page 34 Policy 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 Policy 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 Page 35 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. Page 36 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 Policy 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 Replacement 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 Page 38 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 Policy 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 Replacement determinations will be made by the school principal as deemed appropriate to minimize Policy 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 Policy (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 Replacement 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 Page 39 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 • • MM: Number Line, Signed Numbers. • • • • • • • • • Apply and extend previous understandings • of operations with fractions to add, subtract, • multiply, and divide rational numbers • • • • • • 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 • 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 • 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: • • • • Work with radicals and integer exponents • • • • • • Use square root and cube root symbols to represent solutions to equations of the form • • x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of • small perfect squares and cube roots of • small perfect cubes. Know that _2 is • irrational. • • 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 • • • • • • • • • • • • • • • • • • 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 • 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 • • • • 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 • • • • • • • • • Solve real-world and mathematical problems leading to two linear equations in • • two variables. For example, given coordinates for two pairs of points, • determine whether the line through the first • pair of points intersects the line through the • second pair. • • 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 • • • • • • • • • • • Understanding function notation • • • • • • • • • • • • • • • • 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 • 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. • • • • • • • • 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 s ednetssctroibeesta bsleiqshuefnacets Usmeeinsfioornmaal lfiagrugruem • • • • • • • • • • • • • • • Parallel lines 1 Congruent triangles 1 Congruent triangles 2 Shifting and reflecting functions • MM: Constructive Triangles, Geometric Cabinet, Blue Triangles. • • • • • • • • • 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 • • • 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 • • • • • 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 hic Usceim raatiloenxaplaanpspioronxw im atihornespoefatisrreavtieonntaulally • 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 • • • • • • • • 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) • • • • • • • 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 • • • • 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) DPMSS Application for performance school Page 113 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 114 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 DPMSS Application for performance school Page 115 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 116 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 DPMSS Application for performance school Page 117 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 118 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. DPMSS Application for performance school Page 119 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 120 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. DPMSS Application for performance school Page 121 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 122 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 DPMSS Application for performance school Page 123 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 124 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 DPMSS Application for performance school Page 125 Denver Public Montessori Secondary School “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 Performance School Application Guide for schools to open 2013-14 Page 126 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. DPMSS Application for performance school Page 127 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 128 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 DPMSS Application for performance school Page 129 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 130 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 DPMSS Application for performance school Page 131 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 132 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. DPMSS Application for performance school Page 133 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 134 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 DPMSS Application for performance school Page 135 Denver Public Montessori Secondary School 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. DPMSS Application for performance school Page Page136 139 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 DPMSS Application for performance school Page139 137 Page 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 DPMSS Application for performance school Page138 139 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. DPMSS Application for performance school Page 139 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 140 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. DPMSS Application for performance school Page 141 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 142 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. DPMSS Application for performance school Page 143 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 144 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 DPMSS Application for performance school Page 145 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 146 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. Performance School Application Guide for schools to open 2013-14 Page 148 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. Performance School Application Guide for schools to open 2013-14 Page 148 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 DPMSS Application for performance school Page 149 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 150 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 DPMSS Application for performance school Page 151 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 Performance School Application Guide for schools to open 2013-14 Page 152 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 DPMSS Application for performance school Page 153 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 154 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 for performance school Page 155 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. . Performance School Application Guide for schools to open 2013-14 Page 156 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 DPMSS Application for performance school Page 157 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. Performance School Application Guide for schools to open 2013-14 Page 158 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 DPMSS Application for performance school Page 159 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 160 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 DPMSS Application for performance school Page 161 Denver Public Montessori Secondary School 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. Performance School Application Guide for schools to open 2013-14 Page 162 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. DPMSS Application for performance school Page 163 Denver Public Montessori Secondary School 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) Performance School Application Guide for schools to open 2013-14 Page 164 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 for performance school Page 165 Denver Public Montessori Secondary School - 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) Performance School Application Guide for schools to open 2013-14 Page 166 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) for performance school Page 167 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) Performance School Application Guide for schools to open 2013-14 Page 168 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 DPMSS Application for performance school Page 169 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 170 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) for performance school Page 171 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) Performance School Application Guide for schools to open 2013-14 Page 172 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 for performance school Page 173 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 174 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 for performance school Page 175 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 Performance School Application Guide for schools to open 2013-14 Page 176 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 for performance school Page 177 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 Performance School Application Guide for schools to open 2013-14 Page 178 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 DPMSS Application for performance school Page 179 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 Performance School Application Guide for schools to open 2013-14 Page 180 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. DPMSS Application for performance school Page 181 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 Performance School Application Guide for schools to open 2013-14 Page 182 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. DPMSS Application for performance school Page 183 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. Performance School Application Guide for schools to open 2013-14 Page 184 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: for performance school Page 185 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. Performance School Application Guide for schools to open 2013-14 Page 186 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 for performance school Page 187 Denver Public Montessori Secondary School Appendix F Evidence of Support Performance School Application Guide for schools to open 2013-14 Page 188 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 for performance school Page 189 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. Performance School Application Guide for schools to open 2013-14 Page 190 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" DPMSS Application for performance school Page 191 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. Performance School Application Guide for schools to open 2013-14 Page 192 (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 DPMSS Application for performance school Page 193 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 for schools to open 2013-14 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 DPMSS Application for performance school Page 195 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 DPMSS Application for performance school Page 197 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 Performance School Application Guide for schools to open 2013-14 Page 198 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 DPMSS Application for performance school Page 199 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 Performance School Application Guide for schools to open 2013-14 Page 200 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. DPMSS Application for performance school Page 201 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. Performance School Application Guide for schools to open 2013-14 Page 202 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. DPMSS Application for performance school Page 203 Denver Public Montessori Secondary School · 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 Performance School Application Guide for schools to open 2013-14 Page 204 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]. DPMSS Application for performance school Page 205 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 Performance School Application Guide for schools to open 2013-14 Page 206 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 DPMSS Application 0.75 0.5 3 1 0.25 0.4 for performance school Page 207 Denver Public Montessori Secondary School 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 Performance School Application Guide 1 1 7.5 1.5 1 0.7 0.3 for schools to open 2013-14 Page 208 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) DPMSS Application 1 1 8 2 1 0.7 0.3 300 hours 456 hours 315 hours for performance school Page 209 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 210 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. DPMSS Application for performance school Page 211 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 ! Performance School Application Guide for schools to open 2013-14 Page 212 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. DPMSS Application for performance school Page 213 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 Performance School Application Guide for schools to open 2013-14 Page 214 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 DPMSS Application for performance school Page 215 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 216 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 DPMSS Application for performance school Page 217 Denver Public Montessori Secondary School 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 Performance School Application Guide for schools to open 2013-14 Page 218 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 DPMSS Application for performance school Page 219 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. Performance School Application Guide for schools to open 2013-14 Page 220 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. DPMSS Application for performance school Page 221 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 Performance School Application Guide for schools to open 2013-14 Page 222 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 DPMSS Application for performance school Page 223 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. Performance School Application Guide for schools to open 2013-14 Page 224 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. DPMSS Application for performance school Page 225 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. Performance School Application Guide for schools to open 2013-14 Page 226 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 DPMSS Application for performance school Page 227