KCCRS – Mathematics ~ ~ ~ ~ ~ ~ Curriculum Planning

1. KCCRS – Mathematics ~ ~ ~ ~ ~ ~Curriculum Planning September 15, 2014

2. Goal: • To learn the 4 step process for curriculum planning • To provide resources to support your district with this process

3. Outcomes: • To have a deeper understanding of the KCCRS and resources • To understand the role of the learning progressions and examine implementation needs • To know and be able to use the resources that align with the intent of the KCCRS • To walk away with ideas and resources to assist with implementation of the KCCRS

4. Step 1 Standards for Math Practice & Content Standards KSDE Training September 8, 2014

6. Fewer, Clearer, Higher… What Does this Mean? Critical Areas Where do you find…? Where do you find the…? Coherence Focus Progressions Rigor Where do you find the…?

7. Structure for Math Practices

8. Implementing the Practices

9. Using evidence from the text, why might the practices be categorized in this way?

10. How do the Math Practices impact Curriculum Planning? Discuss this with your table group.

11. Step 2 Learning Progressions KSDE 2014

12. How should educators increase their understanding of the content within the Kansas College and Career Ready Standards for Mathematics?

13. Learning Progressions http://ime.math.arizona.edu/progressions/

14. Number sense ~ Subitizing Pg 4

15. Where is this in the standards? Look in the Kindergarten and First Grade standards. This particular concept is not specifically stated within the standards but it is a critical concept that all students are to be able to perform and understand.

16. Decomposition of Number Students then need to extend this concept into decomposition of number which is the foundation for the fundamental properties of operations. The ability to be able to decompose numbers in intuitive ways leads to the flexible use of the properties of operations.

17. Learning Progression 1st Grade Pg 15

18. 3rd Grade ~ Fraction Understanding (NF pg. 3)

19. Ratios Pg 3 Pg 4

20. Functions 8-12 Pg 6

21. Why are the Learning Progressions important for Curriculum Planning?Talk with your table partners.

22. Learning Progressions KSDE 2014

23. Step 3 Curriculum Mapping KSDE 2014

24. Common definition: What is curriculum mapping? • Curriculum mapping is the process of indexing or diagraming to • identify and address academic gaps, • redundancies, and • misalignments for purposes of improving the overall coherence of a course of study and, by extension, its effectiveness http://edglossary.org/curriculum-mapping/

25. Coherent curriculum is… • Well organized and purposefully designed to facilitate learning, • Free of academic gaps and needless repetitions • Aligned across lessons, courses, subject areas, and grade levels. http://edglossary.org/curriculum-mapping/

26. Phil Daro: Common Core Lead Author • Not a mile wide-inch deep, stop adding your own things.

27. Steps 3: Curriculum Mapping Process • Vertical coherence • What comes before and after? • Academic gaps • Sequence coherence • Major/supporting/additional • Order and time emphasis

28. Vertical Coherence Example:

29. Line of Concept Development • Elementary- Number and Operations- Fractions • Middle- Ratios and Proportional Reasoning • High- Functions

30. VISUAL MODELS Multiple Representations • 3rd Grade • Understand part/whole relationships • Generate equivalent fractions • 4th/5th • Multiply fractions by whole numbers and fractions • 6th • Distinguish between part/part and part/whole ratios and rates • Generate equivalent ratios • 7th /8th • Unit rate • Graph proportional relationships • Use the unit rate as a slope • Generate equations • High School • Linear Functions • Constant rate of change • Multiple representations

31. Vertical Coherence in Progressions • K-5 Geometry Progression • Changing definition of trapezoid

32. Vertical Coherence- Academic Gaps • Bridging the old with the new • Different paths for each cohort of students • Acceleration • Intervention focus

33. 7th grade math 8th grade math Algebra 1 Rational and Irrational Numbers Integer computation Proportional thinking Exponential Functions Solving equations One/two step equations Complete the square Linear graphs/slope Rational signed numbers Prove solution method Systems of Equations Sequences Quadratics/Non-linear functions Standard deviation Functions Functions Bivariate data Sampling methods Probability

34. Shift in content: Statistics example 5th grade

35. Vertical Coherence- Academic Gaps • Bridging the old with the new • Different paths for each cohort of students • Acceleration • Intervention focus

36. Sequence Coherence • Zimba’s documents • Sequence Worksheets • SBAC for HS Depth Opportunities NOT Delta Indicators!

38. Step 3: Curriculum Mapping • How will your district create and sustain opportunities for teachers to collaborate vertically? • How will your district ensure sequence coherence as more than delta indicators?

39. Step 4 Unit Planning

40. Step 4: Unit CoherenceGrain Size • Standards aren’t a discrete checklist • Shift to thinking about units • Across topics, across domains

41. Unit Coherence • 3.NBT.A • Place value understanding and properties of operations • 3.OA.D • Solving problems, identifying and explaining patterns in arithmetic

42. Unit Coherence • 7. SP.C (Probability) • Finding relative frequencies • 7.RP (Proportional Thinking) • Solve percent problems

43. Unit Coherence • F.BF.B • Transforming functions • F.IF.C • Graph by hand

46. Example:

47. Non-example

48. Step 4: Unit Planning • Describe why the smallest grain size should be a coherent unit. • How do all four steps of the curriculum mapping process support utilizing the rubric?

49. Using the Rubric • Select Instructional Material • Physical Book • Websites: map.mathshell.org, engageNY, Illustrative Math, k-5mathteachingresources.com, Illuminations • Select one unit You are not evaluating a textbook, you are evaluating a materials for a unit.

50. KSDE Follow-up • Progressions • Curriculum Mapping • Evaluating Units