1 / 103

PARCC Model Content Frameworks for High School Mathematics: Analysis and Implementation Guide

This guide provides an analysis of the PARCC Model Content Frameworks for High School Mathematics, including course-specific overviews, examples, and recommendations for implementing the standards. It also offers guidance on making connections among standards and integrating mathematical content and practices.

anthonyd
Download Presentation

PARCC Model Content Frameworks for High School Mathematics: Analysis and Implementation Guide

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mississippi Department of EducationCommon Core State Standards (CCSS) and Assessments Grades 9 - 12 Mathematics Training of the Trainers July 2012

  2. PARCC Model Content Frameworks for High School Mathematics

  3. PARCC Model Content Frameworks for Mathematics Purpose: • To serve as a bridge between the CCSS and the PARCC Assessments • The PARCC Assessment will be designed to measure conceptual understanding, procedural skill, fluency, application and problem solving • Questions will measure student learning across various mathematical domains and practices • To inform the development of item specifications and the assessment blueprints

  4. PARCC Model Content Frameworks for Mathematics High School Standards Analysis Structure: (June 2012 version)

  5. PARCC Model Content Frameworks for Mathematics Course-specific Analyses: • Individual End-of-Course Overviews • Examples of Key Advances from Previous Grades or Courses • Discussion of Mathematical Practices in Relation to Course Content • Fluency Recommendations • Pathway Summary Tables (Table 1 and Table 3) • Assessment Limit Tables (Table 2 and Table 4)

  6. PARCC Model Content Frameworks for Mathematics General Analysis • Examples of Opportunities for Connections among Standards, Clusters, Domains or Conceptual Categories • Examples of Opportunities for Connecting Mathematical Content and Mathematical Practices

  7. PARCC Model Content Frameworks for Mathematics (page 46) Additional Note on Modeling (MP.4):

  8. PARCC Model Content Frameworks for Mathematics (Appendices) Appendix A: Lasting Achievements in K-8 (p. 47) Appendix B: Starting Points for Transition to the CCSS (p. 49) • Gives special attention to how well current materials address the suggested starting points. • Organizes implementation work according to progressions. Appendix C: Rationale for the Grades 3-8 and High School Content Emphases by Cluster (p. 51) Appendix D: Considerations for College and Career Readiness (p. 55)

  9. *All page references are from this document unless otherwise noted.

  10. Design and Organization of the Common Core State Standards (CCSS) for Mathematics • Introduction • Standards for Mathematical Content • Standards for Mathematical Practice • Glossary

  11. Introduction: Where was American education before CCSS?(Refer to CCSS pp 3-4)

  12. Standards for Mathematical Content Grade Level Domains K – 5 • Counting and Cardinality • Operations and Algebraic Thinking • Number and Operations in Base Ten • Number and Operations – Fractions • Measurement and Data • Geometry 6 – 8 • Ratios and Proportional Relationships • The Number System • Expressions and Equations • Functions • Geometry • Statistics and Probability

  13. Standards for Mathematical Content High School Conceptual Categories N = Number and Quantity A = Algebra F = Functions G = Geometry S = Statistics and Probability Modeling

  14. High School Conceptual Categories • Number and Quantity • The Real Number System N-RN • Quantities N-Q • The Complex Number System N-CN • Vector and Matrix Quantities N-VM • Algebra • Seeing Structure in Expressions A-SSE • Arithmetic with Polynomials & Rational Functions A-APR • Creating Equations A-CED • Reasoning with Equations and Inequalities A-REI

  15. High School Conceptual Categories continued • Functions • Interpreting Functions F-IF • Building Functions F-BF • Linear, Quadratic, and Exponential Models F-LE • Trigonometric Functions F-TF • Geometry • Congruence G-CO • Similarity, Right Triangles, and Trigonometry G-SRT • Circles G-C • Expressing Geometric Properties with Equations G-GPE • Geometric Measurement and Dimension G-GMD • Modeling with GeometryG-MG

  16. High School Conceptual Categories continued • Statistics and Probability • Interpreting Categorical & Quantitative Data S-ID • Making Inferences & Justifying Conclusions S-IC • Conditional Probability & the Rules of Probability S-CP • Using Probability to Make Decisions S-MD

  17. High School Conceptual Category: Modeling (Refer to CCSS page 72)

  18. Directions:Using the Promethean device on your table, respond to the following statement: “There are a total of six domains in the High School CCSS for Mathematics.”

  19. Mississippi Mathematics Framework (MMF) Content Strands vs. CCSS High School Conceptual Categories Numbers Algebra Geometry Statistics and Data MMF Content StrandsCCSS High School Conceptual Categories

  20. Structure Sample from Grade 3 (Refer to CCSS page 5) Cluster Heading (According to PARCC)

  21. Structure Sample from High School(Refer to CCSS page 71) Conceptual Category Domain Trigonometric Functions F - TF Extend the domain of trigonometric functions using the unit circle. Cluster Heading Standard Cluster Plus Standard

  22. Reading the Grade Level Standards • Conceptual Categories are larger groups of relateddomains that portray a coherent view of high school mathematics. * Note: Standards from different conceptual categories may sometimes be closely related. • Domains are larger groups of relatedstandards. *Note: Standards from different domains may sometimes be closely related. • Cluster Heading is indicated in bold and summarizes the major skills and concepts taught in a group of standards. • Clustersare groups of related standards. *Note: Standards from different clusters may sometimes be closely related.

  23. Reading the High School Standards • Standards define what students should understand and be able to do. • Plus Standardsrepresent additional standards that students should learn in order to take advanced courses. *Note: These standards will not be tested in Grades 9-11. They will, however, appear in the 4th year course: Common Core Plus. Courses without a (+) symbol should appear in the common math curriculum for all students (Algebra I, Algebra II, and Geometry).

  24. Referencing the CCSS for Mathematics F-BF.2 F-BF.2 - Functions Conceptual Category F-BF.2 - Building Functions Domain F-BF.2- Standard Number N-CN.5 N-CN.5 - Numbers and Quantity Conceptual Category N-CN.5 - The Complex Number System Domain N-CN.5- Standard Number

  25. Referencing the CCSS for Mathematics (Refer to CCSS page 71) What is the reference for the following standard? “Interpret the parameters in a linear or exponential function in terms of a context.” Answer: ____________

  26. Referencing the CCSS for Mathematics (Refer to CCSS page 71) F-LE.5 • What is the conceptual category? • What is the domain? • What is the standard number? • What is the cluster heading? Functions Linear, Quadratic, and Exponential Models (*) 5 Interpret expressions for functions in terms of the situation they model

  27. Referencing the CCSS for Mathematics Using F-LE.5,the facilitator will model how to use the PARCC Model Content Frameworks for High School Mathematics to inform implications for instruction.

  28. Referencing the CCSS for Mathematics Directions: • LocateF-IF.4 and N-VM.5 in the CCSS and the PARCC Model Content Frameworks for Mathematics. • As a group, briefly discuss the implications for instruction for both of these standards.

  29. Referencing the CCSS for Mathematics Facilitator will discuss implications for instruction for F-IF.4 and N-VM.5

  30. Work Session 1CCSS K-12 Mathematics Progression of Domains Directions: • Locate Work Session 1 Activity Sheet. • Complete Work Session 1 Activity Sheet as a group.

  31. Work Session 1continued The facilitator will select several groups to report out.

  32. Work Session 1 continued

  33. Reviewing the CCSS for Mathematics Glossary Directions: • Locate pages 85-90 of the CCSS for Mathematics. • Note the following: • List of Terms: (pp 85 – 87) • Table 1: (p. 88) • Table 2: (p. 89) • Tables 3, 4, and 5: (p. 90)

  34. A Snapshot of the Glossary(Refer to List of Terms CCSS page 85) Glossary Additive inverses. Two numbers whose sum is 0 are additive inverses of one another. Example: 3/4 and – 3/4 are additive inverses of one another because 3/4 + (– 3/4) = (– 3/4) + 3/4 = 0. Associative property of addition. See Table 3 in this Glossary. Associative property of multiplication. See Table 3 in this Glossary. Bivariate data. Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team. Box plot. A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.1

  35. A Snapshot of the Glossary(Refer to Table 1 CCSS page 88)

  36. A Snapshot of the Glossary(Refer to Table 2 CCSS page 89)

  37. A Snapshot of the Glossary(Refer to Table 3 CCSS page 90) Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system.

  38. Work Session 2: CCSS for Mathematics “Scavenger Hunt” Directions: • Locate Work Session 2 Activity Sheet. • Knowing where to find information in the Standards is just as important as knowing the information itself. Using the CCSS for Mathematics, work in pairs to find the answers to the questions.

  39. Work Session 2 continued Facilitator will discuss answers for Work Session 2.

  40. PARCC Model Content Frameworks for Mathematics (page 43) (Work Session 2, item #14) Examples of Opportunities for Connections among Standards, Clusters, Domains or Conceptual Categories: Connections among Statistics, Functions and Modeling. Functions may be used to describe data; if the data suggest a linear relationship, the relationship can be modeled with a regression line, and its strength and direction can be expressed through a correlation coefficient.

  41. The Heart of the CCSS for Mathematics: Standards for Mathematical Practice

  42. Standards for Mathematical Practice (Refer to CCSS pp 6 - 8) The Standards for Mathematical Practice describe ways in whichdevelopingstudent practitioners of the discipline of mathematics increasingly ought to engagewith the subject matter as they grow in mathematical maturityand expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connectthe mathematical practices to mathematicalcontentin mathematics instruction.

  43. Standards for Mathematical Practice The Role of the Teacher The Role of the Student The Learning Environment

  44. Standards for Mathematical Practice Directions: • Locate CCSS pages 6 – 8. • Review the eight Standards for Mathematical Practice. • As a group, create a list of three words that capture the essence of each Standard for Mathematical Practice.

  45. Standards for Mathematical Practice The facilitator will select several groups to report out.

  46. Standards for Mathematical Practice (Refer to CCSS pp. 6 - 8) • 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. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

  47. Standards for Mathematical Practice The Standards for Mathematical Practice should not be used as a checklist nor should they be used in isolation. Rather, the Mathematical Practices should be interwoven into every lesson where they overlap and interact with each other constantly.

  48. Work Session 3:Connecting Mathematical Practices to Instruction Directions: • Locate Work Session 3. • Locate the large “card” on your table. The number on the front indicates the Mathematical Practice your group will discuss. • Complete Work Session 3 as a group.

  49. Work Session 3 continued The facilitator will select several groups to report out on their responses to item #3 of the Work Session Activity.

More Related