1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Coherence Across the Grades in Number and Operations—Base Ten

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives Examine the sequence of standards that comprise the Number and Operations—Base Ten domain. Examine the sequence of base ten models employed in A Story of Units. Examine and practice the algorithms employed in A Story of Units. 2

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

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 4 Card Sort!

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 5 Compose and decompose numbers 11–19 into 10 ones and some further ones… Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Compose and decompose numbers 11–19 into 10 ones and some further ones… (K.NBT.1) Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. (1.NBT.5) Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. (2.NBT.8)

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 6 Use place value understanding to round whole numbers to the nearest 10 or 100. Use place value understanding to round multi-digit whole numbers to any place. Use place value understanding to round decimals to any place. Use place value understanding to round whole numbers to the nearest 10 or 100. (3.NBT.1) Use place value understanding to round multi-digit whole numbers to any place. (4.NBT.3) Use place value understanding to round decimals to any place. (5.NBT.4)

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 7

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units NBT Standards Across PK-5 8 Take a moment to reflect on the curriculum map. What role does your grade play in the development of Number and Operations—Base Ten? How does it rely on the previous grade and prepare students for the subsequent grade?

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 9 A Story of UnitsA Story of RatiosA Story of Functions Number and Operations— Base Ten The Number System Algebra Number and Operations— Fractions K-56-89-12

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 10

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 11

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Visual Models 12

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 13

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Visual Models 14 What did you notice about the sequence of visual models? In what ways will students benefit from this sequence? How does it compare with other models that you currently use?

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

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Demonstration – A Progression of Algorithms 16

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Algorithms 17 What did you notice about the sequence of algorithms? In what ways will students benefit from this sequence? How does it compare with other algorithms that you currently use?

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 18

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Study of the Progression 19 Pick a grade and read the appropriate section of the Progressions document, highlighting evidence in support of this morning’s demonstrations. Do the same with the previous and subsequent grades.

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Study of the Progression 20 What connections did you find between the Progressions document and this morning’s demonstrations? Think about the modules that you explored yesterday. How are they relevant in the coherence of the NBT domain?

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 21 Card Sort!

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps 22 How will this information impact instruction in your classroom/school/district? How will you continue to use the Progressions documents as you implement A Story of Units? How can you initiate a study of the Progressions with your colleagues?

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 23 While work in NBT is dependent on understanding of the meanings and properties of operations, it also fosters a deeper understanding of them. The NBT standards include a deliberate trajectory from reasoning about quantities, the base-ten system, and the meanings of operations to mastery of standard algorithms. The Standards and Progressions provide valuable insight that enables educators to meet their students’ needs in a way that also maintains coherence across the curriculum.