1. Teacher’s Guide to the PARCC Model Content Frameworks for High School Mathematics October 16, 2012
Heather Brown
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2. Objectives To discover the elements of the Model Content Frameworks
To use the Model Content Frameworks to aid in the implementation of the Common Core State Standards for Mathematics.
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3. The problems are on slide 4 and 6
The problems are on slide 4 and 6. If you are doing a live presentation, give participants a handout with both problems. Have the participants work through the actual problems.
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4. Poll #1 Find the mean of 18, 18, 20, 21 and 28 10 18 19 20 21 Range
Mode
Nothing
Median
Mean
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5. Poll #1 Find the mean of 18, 18, 20, 21 and 28 10 18 19 20 21 Range
Mode
Nothing
Median
Mean
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6. Poll #2
What statistical measurement would most closely represent the potential pay of a new clerk if there are ten clerks who all make about the same amount and a manager who makes ten times as much?
Range
Mean
Median
Mode
How would this change if the ten clerks made exactly the same amount?
What would the range represent, the mode?
When would mode be more useful?
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7. Poll #2
What statistical measurement would most closely represent the potential pay of a new clerk if there are ten clerks who all make about the same amount and a manager who makes ten times as much?
Range
Mean
Median
Mode
How would this change if the ten clerks made exactly the same amount?
What would the range represent, the mode?
When would mode be more useful?
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8. When working with the first task there is a clear answer.
When working with the second task, there are options. Multiple choice leads to frustration because there is no room to explain WHY you choose your answer.
The tasks are overlapping, but one is deeper than the other (like the spoons )
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9. Key Advances of the Common Core
MATHEMATICS
Focus, coherence and clarity: emphasis on key topics at each grade level and coherent progression across grades
Balance between procedural fluency and understanding of concepts and skills
Promote rigor through mathematical proficiencies that foster reasoning and understanding across discipline
The Common Core demands new things. Focus, coherence, balance and rigor are major points that the CC promotes and PARCC has adopted
ANCHORED IN COLLEGE AND CAREER READINESS
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Slide from PARCC 2012
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10. Time Discussion Interactions Connections NOT a checklist
Focus and Coherence
Time Discussion Interactions Connections NOT a checklist
Talk about what focus and coherence are.
The standards are based on focus and coherence. Focus allows time for deep, rich discussions and interactions, so students have sufficient time to think, practice and integrate new ideas into their growing knowledge structure.
Coherence requires connections both in grade and across grade level progressions. Coherence also needs to occur between the content and practice standards.
Focus and coherence recognize that the standards are not a checklist, nor should they be fragmented to meet mastery.
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11. PARCC adopted these concepts to five major claims to drive the design of the assessment.
Slide from PARCC 2012
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12. High School Pathways
Offers recommendations for both Traditional and Integrated Pathways
Both ways students end up with the exact same standards.
There are a couple differences between major and supporting, but the vast majority are the same.

13. Things to Consider Appendix A vs. PARCC MCF
2011 MCF Draft vs Final MCF
Standards don’t change
More functions are specified at the Algebra 1 and Math 1 level in the MCF. Algebra 1 focuses on linear, quadratic, and exponential functions with domain in the integers. It also suggests work with the piecewise functions (including step and absolute value), square root and cube root in several standards, unlike Appendix A.
The PARCC MCF does state, “In Algebra 1, students will master linear and quadratic functions. Students encounter other kinds of functions to ensure that general principles are perceived in generality” (MCF p. 8). This implies that despite the exposure to some of the more advanced functions, the longer amount of time will be spent on linear and quadratic.
The unit on probability has moved from Algebra 1 in Appendix A to Geometry in the PARCC MCF.
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14. PARCC Model Content Frameworks
Purpose
Support implementation
Inform development of item specifications and PARCC assessments
Audience
Curriculum directors
Teachers and administrators
They created the MCF to connect the ccssm to the assessment as a tool for teachers and other stakeholders to use.
Purpose
Support implementation of the Common Core State Standards
Inform development of item specifications and blueprints for the PARCC assessments in grades 3–8 and high school
Audience
Primary audience is state and local curriculum directors
Frameworks are a resource for teachers and building administrators
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15. Key Elements of the PARCC Model Content Framework
Advances
Fluency
Recommendations
Individual
End of Course Overviews
Pathway Summary
Tables
High School
Course
Assessment Limits Tables for Standards Assessed in More than One Course
PARCC Model Content Framework seems to be the clearest and most well-defined resource when it comes to defining HS courses.
Helpful for teachers because it is aligned to what students will see on PARCC assessments.
Figure shows all components that are available for each HS course (Traditional and Integrated are both included in PARCC as well)
Mathematical Practices in Relation to Course Content

16. Individual End of Course Overviews
Green – major Blue – supporting Yellow – additional
Individual
End of Course Overviews
The chart at the end of each grade level description lists each of the clusters and an emphasis to encourage focus.
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18. Supporting clusters are designed to strengthen the areas of major emphasis. Connections of supporting to the major clusters are provided.
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19. Additional are those clusters that do not connect tightly or explicitly to the major work.
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20. This chart lists the specific standards as a numerical list of standards in parentheses.
Note that an entire cluster may not be included in one course.
Standards that are underlined will be assessed on more than one end-of-course assessment.
Delineation on what the scope of that standard per course will be is available in the Assessment Limit Sections
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21. Key Advances from the Previous Grades or Courses
Highlights grade-to-grade steps in the progression of knowledge and skill
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22. Key Advances to Geometry
Because concepts such as rotation, reflection, and translation were treated in the grade 8 standards mostly in the context of hands-on activities, and with an emphasis on geometric intuition, high school Geometry will put equal weight on precise definitions.
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23. Discussion of Mathematical Practices in Relation to Course Content
In my opinion, this should be earlier in the standards. Practice standards are one of the largest shift in the CCSSM.
Highlights opportunities to connect content and practice within the context of working a problem.
Separating the practices from the content is not what the standards require.
The Standards for Mathematical Practice should be embedded in classroom instruction, discussions, and activities.
Mathematical Practices in Relation to Course Content
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24. Connecting Content and Practice: Algebra II
MP7 Look for and make use of structure
Delve deeper into transforming expressions that reveal meaning
Students need the opportunity to experience designed standards-based mathematical tasks that vary in difficulty, context and type.
The practice standards interact and overlap with each other. Like the content standards, the practice standards should not be used as a checklist, but placed where organic connections can be made between the content and practices
The structure theme in Algebra 1 centered on seeing and using algebraic expressions.
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25. How would you assess practices and content?
Claim A Students solve problems involving the major content for their grade level with connections to practices.
A.SSE Seeing structure in expressions
Note that you can fill in the blank, making guessing nearly impossible.
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26. How would you assess practices and content?
Claim A Students solve problems involving the major content for their grade level with connections to practices.
F.IF.9 Compare properties of two functions each represented in a different way.
Computer gradeable, innovative approach
Note that F.IF.9 has more details in it.
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27. Fluency Recommendations
Highlights standards that set expectations for fluency and culminating masteries.
Fluency is an outcome of a progression of learning and thoughtful practice and does not come at the expense of understanding.
Whenever the word fluently appears in a content standard, the word means quickly and accurate, to work with flow.
Fluency isn’t halting, stumbling or reversing oneself.
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28. Fluency
F.IF.3 Fluency in translating between recursive definitions and closed forms is helpful when dealing with many problems involving sequences and series, with applications ranging from fitting functions to tables to problems in finance.
Also,
Claim A Students solve problems involving the major content for their grade level with connections to practices.
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29. Pathway Summary Tables
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31. Assessment Limits Tables for Standards Assessed on More than One End-of-Course Test
Assessment Limits Tables for Standards Assessed in More than One Course
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33. Brainstorm ideas on how you could use this with your schools to assist in the implementation of the CCSSM.
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34. Slide from PARCC 2012
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36. MAJOR, SUPPORTING and ADDITIONAL
Inform instructional resources
Evaluate instructional materials
Do NOT sort and teach in order
Use the major, supporting and additional clusters to inform instructional decisions on time and resources.
Use the supporting clusters and Standards for Mathematical Practice to highlight the focus on the major work through sense-making, reasoning, critiquing, modeling, etc.
Evaluate instructional materials and professional development opportunities based on the major, supporting and additional clusters.
Do NOT simply sort clusters from major to supporting and teach them in that order. Coherence is one of the key shifts of the CCSSM.
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38. Progressions Avoid Crosswalks
Avoid Crosswalks
Refer to the progression documents for more information regarding sequence of instruction.
Use in conjunction with the CCSSM. Despite the fact that only the clusters are listed in the MCF, the individual wording of each content standard is important.
Don’t use the MCF or the CCSSM to do cross-walk exercises. The analysis of curricular materials is more than just topic-matching. Each standard is very specific and needs to be addressed with precision.
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