Teacher’s Guide to the PARCC Model Content Frameworks for High School Mathematics October 16, 2012 Heather Brown Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Poll #1 Find the mean of 18, 18, 20, 21 and 28 10 18 19 20 21 Range Mode Nothing Median Mean Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Poll #1 Find the mean of 18, 18, 20, 21 and 28 10 18 19 20 21 Range Mode Nothing Median Mean Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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? Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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? Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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 ) Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Slide from PARCC 2012 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

PARCC adopted these concepts to five major claims to drive the design of the assessment. Slide from PARCC 2012 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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.

Things to Consider Appendix A vs. PARCC MCF 2011 MCF Draft vs. 2012 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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Supporting clusters are designed to strengthen the areas of major emphasis. Connections of supporting to the major clusters are provided. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Additional are those clusters that do not connect tightly or explicitly to the major work. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Key Advances from the Previous Grades or Courses Highlights grade-to-grade steps in the progression of knowledge and skill Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

How would you assess practices and content? http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation 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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

How would you assess practices and content? http://www.parcconline.org/samples/mathematics/high-school-functions 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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Pathway Summary Tables Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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Brainstorm ideas on how you could use this with your schools to assist in the implementation of the CCSSM. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Slide from PARCC 2012 Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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Progressions Avoid Crosswalks http://ime.math.arizona.edu/progressions/ Avoid Crosswalks Refer to the progression documents for more information regarding sequence of instruction. http://ime.math.arizona.edu/progressions/ 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. http://www.corestandards.org/the-standards 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. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License