Download define algebra

The Common Core:
A Challenge & an Opportunity
Summer Conference
Sara Wright
STEM Division,ODCTE
[email protected]
Information compiled from
Dr. Eric Milou
http://ericmilou.com
And many CCSS resources
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Common Core State Standards
 http://www.CoreStandards.org/
 The Council of Chief State School Officers and The National Governors
Association Center for Best Practices
 Fewer, clearer, and higher, to best drive effective policy and practice;
 But definitely not fewer for grades 9-12!
 Clearer? Have you read these things?
 Aligned with college and work expectations, so that all students are
prepared for success upon graduating from high school;
 Does math for college = math for work?
 Inclusive of rigorous content and application of knowledge through high-
order skills, so that all students are prepared for the 21st century;
 Internationally benchmarked, so that all students are prepared for
succeeding in our global economy and society; and
 Singapore. Singapore. Singapore.
 Research and evidence-based.
 The research they liked.
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Key Instructional Shifts in Mathematics
The Common Core State Standards emphasize coherence at each grade
level – making connections across content and between content and
mathematical practices in order to promote deeper learning.
The standards focus on key topics at each grade level to allow educators
and students to go deeper into the content.
The standards also emphasize progressions across grades, with the end
of progression calling for fluency – or the ability to perform calculations or
solving problems quickly and accurate.
The Standards for Mathematical Practice describe mathematical “habits of
mind” or mathematical applications and aim to foster reasoning, problem
solving, modeling, decision making, and engagement among students.
Finally, the standards require students to demonstrate deep conceptual
understanding by applying them to new situations.
Source:
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Overview of K-8 Mathematics
Standards
The K- 8 standards:
The K-5 standards provide students with a solid foundation
in whole numbers, fractions and decimals
The 6-8 standards describe robust learning in geometry,
algebra, and probability and statistics
Modeled after the focus of standards from high-performing
nations, the standards for grades 7 and 8 include significant
algebra and geometry content
Students who have completed 7th grade and mastered
the content and skills will be prepared for algebra, in 8th
grade or after
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CCSS Domain Progression
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Overview of High School
Mathematics Standards
The high school mathematics standards:
 Call on students to practice applying mathematical ways of
thinking to real world issues and challenges
 Require students to develop a depth of understanding and
ability to apply mathematics to novel situations, as college
students and employees regularly are called to do
 Emphasize mathematical modeling, the use of mathematics and
statistics to analyze empirical situations, understand them
better, and improve decisions
 Identify the mathematics that all students should study in order to
be college and career ready
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People are the next step
 • If people just swap out the old
standards and put the new CCSS
- in the old boxes
– into old systems and procedures
– into the old relationships
– Into old instructional materials formats
– Into old assessment tools,
• Then nothing will change
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What mathematics do we want
students to walk away with from
this chapter?
 • Content Focus of professional learning
communities should be at the chapter level
 • When working with standards, focus on
clusters. Standards are ingredients of
clusters.
Coherence exists at the cluster level
across grades
 • Each lesson within a chapter or unit has the
same objectives….the chapter objectives
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Big Bang Theory
 http://youtu.be/TIYMmbHik08
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Mathematical Practices
 http://www.okcareertech.org/educato
rs/science-technology-engineeringand-mathematics-stem1/mathematics-1/mathematicalpractices-information-examples
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Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
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The Other Mathematical Practices
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning.
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Mathematical Practices
Explained
 http://www.okcareertech.org/educato
rs/science-technology-engineeringand-mathematics-stem1/mathematics-1/mathematicalpractices-unpacked
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Illustrative Mathematics
 Algebra 2 Information
 http://www.okcareertech.org/educato
rs/science-technology-engineeringand-mathematics-stem1/mathematics-1/algebra-2information
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National Assessments
(Center for K–12 Assessment & Performance Management at ETS)
 Two Comprehensive Assessment Consortia: the
Partnership for Assessment of Readiness for College and
Careers (PARCC) and the Smarter Balanced
Assessment Consortium (Smarter Balanced)
 Two Alternate Assessment Consortia: the Dynamic
Learning Maps (DLM) Consortium and the National
Center and State Collaborative (NCSC) Consortium
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National Assessments 2014-15
 Partnership for Assessment of Readiness for College
and Careers (PARCC)
 24 states + DC, Achieve
 SMARTER Balanced Assessment Consortium
(SBAC)
 26 states, West Ed
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PARCC & SBAC
 Online assessments for Grades 3-8 and high school
 Use of a mix of item types, including selected response, constructed
response, technology enhanced and complex performance tasks.
 Two components, both given during final weeks of the school year.
 Use of both electronic and human scoring, with results expected within
two weeks.
 Approximately $20 per pupil per year for all summative assessment
components
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CRD score from Jr. year tests
 Level 5-Superior Command, Academically well prepared for
entry level credit bearing college course, Exempt from
placement tests
 Level 4-Solid command, academically prepared / exempt
 Level 3-partial command, will likely need academic
support, not exempt
 Level 2-Limited command, will need academic support,
not exempt
 Level 1-very limited command, will need extensive
academic support, not exempt
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What's next:
•Prototype tasks will be released at the end
of August
•Math assessment will be about 4 hours
in two parts due to need for constructive response
not just multiple choice
•The face of English 101 and college algebra
will change as students come in more prepared.
More content less remediation – exciting time
for higher ed.
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Bill Daggett Assessment
Example for 8th grade math
 Ms. J had new insulation installed and
windows sealed $600
 Contractor told Ms. J that heating bill
would decrease by at least 10%
 In 2007 spent $1500 on heating
 Expected to save $150 each winter
 January bill in 2008 was $235
compared to last year of $240
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Assessment question
continued
 Assess the cost-effectiveness of Ms. J’s new insulation and




window sealing. You will need to research “heating degree
days” on the internet. In your response, you must do the
following:
Compare Ms. J’s gas bills from Jan. 2007 and Jan 2008
Explain Ms. J’s savings after the insulation and sealing
Identify circumstances under which M. J’s Jan 2008 would have
been at least 10% less than 2007
Decide if insulation and sealing was cost-effective and provide
evidence for this decision.
 Full problem provided on your flash-drive
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Differences
 PARCC
 SMARTER
Fixed-form delivery
Adaptive delivery
(students take one of
(students see an
several fixed, equated
individually tailored set
sets of items)
of items and tasks)
Optional – K-2
A retake option is
formative performance
available for the endtasks.
of-year component
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Suggested Practice for
Assessments
 http://map.mathshell.org.uk/material
s/tasks.php
 http://nces.ed.gov/nationsreportcard/
itmrlsx/landing.aspx
 Free benchmark tests available from
SDE in September (CCSS content)
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Big Ideas
Elementary K-2: Place Value & 10
Grades 3-6+: Fractions!
Grades 7-8: Transition to Algebra
High School: Modeling
Modeling links classroom mathematics and
statistics to everyday life, work, and decisionmaking.
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Dan Meyer
 The formulation of a problem is often
more essential than its solution, which
may be merely a matter of
mathematical or experimental skill—
Albert Einstein
 TED Talks video by Dan Meyer
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High School
 The high school standards specify the mathematics that all
students should study in order to be college and career ready.
 Additional mathematics that students should learn in order to
take advanced courses such as calculus, advanced statistics, or
discrete mathematics is indicated by (+), as in this example:
 Represent complex numbers on the complex plane in rectangular and
polar form (including real and imaginary numbers).
 The high school standards are listed in conceptual categories:
 Number and Quantity, Algebra, Functions, Modeling, Geometry,
Statistics and Probability
 Appendix A
 Updated PARCC Framework included on flash drive
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Appendix A
 Four model course pathways are included:
 1. An approach typically seen in the U.S. (Traditional) that consists of two
algebra courses and a geometry course, with some data, probability and
statistics included in each course;
 2. An approach typically seen internationally (Integrated) that consists of a
sequence of three courses, each of which includes number, algebra, geometry,
probability and statistics;
 3. A “compacted” version of the Traditional pathway where no content is
omitted, in which students would complete the content of 7th grade, 8th
grade, and the High School Algebra I course in grades 7 and 8
 4. A “compacted” version of the Integrated pathway where no content is
omitted, in which students would complete the content of 7th grade, 8th
grade, and the Mathematics I course in grades 7 and 8.
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Intended Uses of the Model Content
Frameworks
 Assist in transitioning to the CCSS
–Help inform curriculum, instruction, and
assessment
–Educator engagement and awareness
 Assist in evaluating resources; provide
awareness and quality of other resources
 Provide awareness on the balance of tasks
 Help educators think more deeply about the
standards, especially foundational structures
 Grade level analyses
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Releasing the Content Frameworks
 Frameworks are available on
http://www.parcconline.org/sites/parcc/files/PARCCMCFforHi
ghSchoolMathematicsDraftSummer2012.pdf
 •Frameworks intended to be dynamic and responsive to
evidence and on-going input
–PARCC collected feedback until July 11,2012 and will refine
frameworks as necessary
 •PARCC will develop additional model instructional tools and
supports that build on the frameworks
–Model Instructional Units
–Educator Leader Cadres
–Item specifications
–Item and task prototypes
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Algebra 2
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Timeline of Implementation
Oklahoma C3 Standards
Date of Full
Implementation
Common Core Language
Arts
Standards
2013-2014
PARCC Assessed 2014-2015
PASS Assessed 2013-2014
Common Core
Mathematics
Standards
2013-2014
PARCC Assessed 2014-2015
PASS Assessed 2013-2014
High School Modeling
 10 mg Zrytec daily
 50% of Zrytec is eliminated daily
 What % is in the body
after 7 days
10 days
n days?
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10mg Daily of Zrytec
Day
1
2
3
4
5
6
Mg. of Zyrtec
10
15
17.5
18.75
19.375
19.6875
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iGeneration
They have NEVER known a
world without the internet or
cell phones.
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Engage me
Virtual Games (online play)
http://www.arcademicskillbuilders.com/
Videos & Music (youtube)
Clickers & Cell Phones
http://www.polleverywhere.com/
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Resources
 http://www.edutopia.org/common-core-state-
standards-resources
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http://ericmilou.com/
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Fact #1
A
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Fact #2
B
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Fact #3
C
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Fact #4
D
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Fact #5
E
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Fact #6
F
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Fact #7
G
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Fact #8
H
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Fact #9
I
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What is this?
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What is this?
F
A
C
E
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What If?
A
B
C
D
E
F
G
H
I
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Try Again
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Try Again
DECA D E
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What’s the Point?
Do NOT:
Isolate Skills
Do:
Connect mathematics
Model mathematics
Engage students with Technology
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Things to Consider in Summary
Is modeling and contexts a part of daily
instruction?
Depth of content.
Be wary of extraneous context.
Embedded Mathematical Practices
including discourse, scaffolding, and
reasoning. (Not word problems at the end
of the lessons.)
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Thank You
If you have never received
information from me:
Please send me an email:
[email protected]
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