1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundations to Fraction Operations

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Quiet Work Complete problem 1 on the G5 assessment in your packet. G5-M3 Mid-Module Assessment

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Map for A Story of Units

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives 1.Geometry 2.Measurement 3.Study the big idea of one arithmetic for whole numbers and fractions. 4.Deliberately practice teaching key concepts in A Story of Units.

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Geometry standards provide the foundation for: Decomposing a whole into equal parts and naming the parts as fractional units and equivalent fractions using the tape diagram and area model.

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Introduction to Decomposing a Whole Decompose flat shapes into two or more shapes GK-M6-L6

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decomposing a Whole into Equal Parts Name and count shapes as parts of a whole, recognizing relative sizes of the parts. G1-M5-L7

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units How many triangles can you find? G2-M8-L2 Application Problem

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decomposing a Whole into Equal Parts and Name Equal Parts as Fractional Units Partition shapes and identify halves and quarters of circles and rectangles. G1-M5-L9

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decomposing a Whole into Equal Parts and Name Equal Parts as Fractional Units Partition shapes and identify halves and quarters of circles and rectangles. G2-M8-L10

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decomposing a Whole into Equal Parts and Name Equal Parts as Fractional Units G2-M8-L11

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decomposing a Whole into Equal Parts and Name Equal Parts as Fractional Units G3-M5-L3 How does the work in K-2 prepare students for success with 3.NF.1?

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Measurement standards provide the foundation for: Defining a fraction as a number using the number line. The big idea that more iterations of a unit are required to cover the same length when the iterated unit is shorter.

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundations for Fractions on a Number Line and Iterations of Units Compare the length of linking cube sticks to various objects. Compare the weight of an object with sets of different objects on a balance scale. GK-M3-L6 and L12

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundations for Fractions on a Number Line and Iterations of Units The Number Path GK-M1-L15 and G1-M1-L26

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundations for Fractions on a Number Line and Iterations of Units How would a first grader describe how to measure length? G1-M3-L4

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundations for Fractions on a Number Line and Iterations of Units Connect measurement with physical units by using multiple copies of the same physical unit to measure. Solve addition and subtraction word problems using the ruler as a number line. G2-M2-L1 and G2-M2-L8

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 1. Select a lesson to study G2-M2-L3G2-M7-L15 G2-M8-L12G3-M5-L21 2.Share the key concept of each lesson and how it relates to the standards 3.Discuss how the Grade 2 lessons build foundation for Grade 3 equivalents on the number line. Lesson Study

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units How does the common misconception that 8 is more than 3 so 8 cm must be longer than 3 in relate to a student who thinks ⅙ is greater than ⅓ 2

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Operations standards provide the foundation to: Compose a higher value unit to add fractions. Add and subtract like units. Decompose a higher value unit to subtract fractions.

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add Find partners of 10 using 5-groups. GK-M4-L40

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add How does 1.OA.3 relate to the Make Ten strategy? G1-M2-L6

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add Make a Hundred What are the new complexities in G2- M7-L12 Problem 3? G2-M5-L5 and G2-M7-L12

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add How Many More to Make a Meter? 2.MD.4 G2-M2-L8

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add How are these drawings related? GK-M4-L9 and G3-M5-L8

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add What higher value unit are we composing? G4-M5-L18

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Compose a Higher Value Unit to Add Does one arithmetic apply to decimals? How does the algorithm fit in? DELIBERATE PRACTICE: 1 hundred 8 ones + 2 tens 4 ones G5-M1-L9

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Add and Subtract Like Units G1-M4-L11

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Add and Subtract Like Units What strategies might students use to solve the problems on the G1-M6-L11 Problem Set? How does this strategy support the idea of adding like units? G1-M6-L11

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Add and Subtract Like Units 1. How is money used as a way of understanding place value concepts? 2. How does G2-M3-L19 Problem Set relate to 2.NBT.5? G2-M3-L8 and L19

36. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Add and Subtract Like Units How many units are in a mixed number? How can you make like units to add or subtract fractions? G4-M5-L22

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Add and Subtract Like Units What misconception is evident in this student’s work? G5-M3-L3

38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA

39. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose a Higher Value Unit to Subtract Match the standard to the problem. K.OA.3 K.OA.4 K.NBT.1 GK-M5-L20, GK-M4-L7, and GK-M4-L27

40. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose a Higher Value Unit to Subtract To use the make ten or take from ten strategies, students must know: Partners of 10 (K.OA.4) Decompositions of 1-9 (K.OA.3) Teen numbers are composed of 10 ones and some more ones (K.NBT.1) G1-M2-L13 and L19

41. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose a Higher Value Unit to Subtract Subtract from 100 Demonstrate the subtract-from- 100 strategy to a parent who wants to help with homework. G2-M4-L23

42. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose a Higher Value Unit to Subtract What higher value unit are we decomposing? G4-M5-L22

43. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose a Higher Value Unit to Subtract Does one arithmetic apply to decimals? How does the algorithm fit in? DELIBERATE PRACTICE: 92 – 6 tens 4 ones G5-M1-L10

44. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units One Arithmetic Composing a Higher Value Unit to Add Adding and Subtracting Like Units Decomposing a Higher Value Unit to Subtract

45. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units What have you learned about the foundation for fraction operations in K-2? How can K-2 teachers embed the understanding of manipulating units in our students? How can this information be used to improve instruction? Reflection