1. EngageNY.org Adopt or Adapt in Math: Support for Districts and Schools on Curriculum Decision Making

2. EngageNY.org2 Necessary Tools for Assessing Quality of Common Core Math Curriculum Common Core Mathematics Standards Standards for Mathematical Practices The Shifts for Mathematics Math Content Emphases Key Fluencies by Grade Level Learning Progressions Publishers’ Criteria for Mathematics EQUIP Rubric for Mathematics

3. EngageNY.org3 These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. … It is time to recognize that standards are not just promises to our children, but promises we intend to keep. CCSSM, p. 5

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5. 5 6 Shifts in Mathematics Focus Coherence Fluency Deep Understanding Applications Dual Intensity 5 Instructional Shifts in Mathematics Demanded by the Core EngageNY.org5

6. 6 Shifts in Assessments Six Shifts in Mathematics Assessments

7. EngageNY.org7 Six Shifts  Three Shifts

8. EngageNY.org8 Mathematics topics intended at each grade by at least two- thirds of A+ countries Mathematics topics intended at each grade by at least two- thirds of 21 U.S. states The shape of math in A+ countries 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002). 8

9. 9 K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability Traditional U.S. Approach 9EngageNY.org9

10. 10 Focusing Attention Within Number and Operations Operations and Algebraic Thinking Expressions and Equations Algebra →→ Number and Operations—Base Ten → The Number System → Number and Operations —Fractions → K12345678 High School 10EngageNY.org10

11. EngageNY.org11 Math Content Emphases

12. EngageNY.org12 Math Content Emphases

13. EngageNY.org13 Math Content Emphases For Grade 3

14. EngageNY.org14 Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within 10 2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single- digit products from memory) Add/subtract within 1000 44.NBT.4Add/subtract within 1,000,000 55.NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations

15. EngageNY.org15 http://ime.math.arizona.edu/progressions/ Learning Progressions

16. EngageNY.org16 Publishers’ Criteria

17. EngageNY.org17 The K–8 Publishers’ Criteria I.Focus, Coherence, and Rigor in the Common Core State Standards for Mathematics II. Criteria for Materials and Tools Aligned to the K–8 Standards III. Appendix: “The Structure is the Standards”

18. EngageNY.org18 II. Criteria for Materials and Tools Aligned to the K–8 Standards 1. Focus on Major Work: In any single grade, students and teachers using the materials as designed spend the large majority of their time on the major work of each grade.

19. EngageNY.org19 II. Criteria for Materials and Tools Aligned to the K–8 Standards 2. Focus in Early Grades: Materials do not assess any of the following topics before the grade level indicated.

20. EngageNY.org20 II. Criteria for Materials and Tools Aligned to the K–8 Standards 3. Focus and Coherence through Supporting Work: Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 4. Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by (all of the following, in the case of comprehensive materials; at least one of the following for supplemental or targeted resources):

21. EngageNY.org21 II. Criteria for Materials and Tools Aligned to the K–8 Standards 4. Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by (all of the following, in the case of comprehensive materials; at least one of the following for supplemental or targeted resources): a. Developing students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. b. Giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. c. Using the materials as designed to spend sufficient time working with engaging applications, without losing focus on the major work of each grade.

22. EngageNY.org22 II. Criteria for Materials and Tools Aligned to the K–8 Standards 5. Consistent Progressions: Materials are consistent with the progressions in the Standards, by (all of the following): a. Basing content progressions on the grade-by-grade progressions in the Standards. b. Giving all students extensive work with grade-level problems. c. Relating grade level concepts explicitly to prior knowledge from earlier grades.

23. EngageNY.org23 II. Criteria for Materials and Tools Aligned to the K–8 Standards 6. Coherent Connections: Materials foster coherence through connections at a single grade, where appropriate and where required by the Standards, by (all of the following): a. Including learning objectives that are visibly shaped by CCSSM cluster headings. b. Including problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. c. Preserving the focus, coherence, and rigor of the Standards even when targeting specific objectives.

24. EngageNY.org24 II. Criteria for Materials and Tools Aligned to the K–8 Standards 7. Practice-Content Connections: Materials meaningfully connect content standards and practice standards. 8. Focus and Coherence via Practice Standards: Materials promote focus and coherence by connecting practice standards with content that is emphasized in the Standards. 9. Careful Attention to Each Practice Standard: Materials attend to the full meaning of each practice standard.

25. EngageNY.org25 II. Criteria for Materials and Tools Aligned to the K–8 Standards 10. Emphasis on Mathematical Reasoning: Materials support the Standards’ emphasis on mathematical reasoning, by (all of the following): a. Prompting students to construct viable arguments and critique the arguments of others concerning key grade-level mathematics that is detailed in the content standards b. Engaging students in problem solving as a form of argument. c. Explicitly attending to the specialized language of mathematics.

26. EngageNY.org26 Collaboratively built tools informed and approved by the authors of the CCSS, which evaluate the Common Core alignment of curricular materials Actualize the Publishers Criteria Collaboratively built tools informed and approved by the authors of the CCSS, which evaluate the Common Core alignment of curricular materials Actualize the Publishers Criteria

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29. EngageNY.org29 Dimension I Alignment to The Depth of the CCSS

30. EngageNY.org30 Dimension II Key Shifts In the CCSS

31. EngageNY.org31 Dimension III Instructional Supports

32. EngageNY.org32 Dimension IV Assessment

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34. EngageNY.org34 Overall Rating

35. EngageNY.org35 Rating Procedures for Rubric

36. EngageNY.org36 Rating Procedures for Rubric

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41. EngageNY.org41 Dimension I Alignment to The Depth of the CCSS

42. EngageNY.org42 Dimension I

43. EngageNY.org43 Dimension II Key Shifts In the CCSS

44. EngageNY.org44 Dimension II

45. EngageNY.org45 Dimension II

46. EngageNY.org46 Dimension III Instructional Supports

47. EngageNY.org47 Dimension III

48. EngageNY.org48 Dimension III

49. EngageNY.org49 Dimension IV Assessment

50. EngageNY.org50 Dimension IV

51. EngageNY.org51 Overall Rating

52. Context for Curriculum Work Vendor Partners: $26 MM (RttT)  P-2 ELA: Core Knowledge  3-8 ELA: Expeditionary Learning  9-12 ELA: PCG & Odell Education  P-12 Math: Common Core, Inc. Regents Research Fund/ SED = 3 FTE + 2 Mgrs Teacher Reviewers = 50 teachers @ 10 hrs/wk Intensive Review Cycles with SAP SAP calibration and gradual release to RRF/ SED EngageNY.org52

53. EngageNY.org53 What we’ve learned… Highly Qualified Writers and Reviewers take up to 6 months to calibrate  Devotion to/ experience in a content area does not a CCSS writer/ reviewer make  A good teacher does not a curriculum writer/ reviewer make  Much of what must shift is sacred Rhetorical alignment and actual alignment are two different things CCSS stickers are easy to produce; true quality, rigor, and alignment are not It often takes 6-8 revision cycles to get to necessary levels of quality/ rigor/ alignment Deep understanding of the documents presented is critical