1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Coherence – Fractions Across the Grades

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives 2 Explore the development of fractions across the grade levels. Examine and study the PK–5 standards and related modules foundational to fractions. Examine the K–5 progressions documents with particular emphasis on Number and Operations—Fractions. Explore how content knowledge directed by the standards and progressions documents supports the implementation of coherence in the classroom. Consider how G3—M5 supports the fraction progression.

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 Standards of Grade 3—Module 5 4 Develop understanding of fractions as numbers.  3.NF.1, 3.NF.2, 3.NF.3 Reason with shapes and their attributes.  3.G.2

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundational Understanding and Skills 5 Review the standards of G3—M5. What understanding and skills are needed before learning these standards?

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundational Standards 6 What Grade 2 standards are foundational to the G3—M5 standards?

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

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Foundational Standards 8 Continue to map backwards noting the understanding, skills and related standards from Grades 1, K, and PK.

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 9 A Progression of Foundational Standards

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Fraction Standards 10 The G3—M5 standards are foundational to what standards in grades 4 and 5?

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

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

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Demonstration – A Progression of Concrete and Visual Models 13

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 14

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Techniques for a Study of Progressions: 15 Denote your reactions to the text with a personalized coding system. For example: Light bulb moment ? Questions about this Important – revisit this portion

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Collaborative Study – Number and Operations— Fractions 16

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Techniques for a Study of Progressions: 17 Create a visual link (brackets, arrows, or color coded highlights) between standards in the margin and related text.

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Selected Excerpts from the Progressions: 18 Words / sentences to use when defining or describing content: For example, we “partition” the shape, not “divide.” Connection to mathematical practices Models and representations High level goals for this content in a given grade Areas of possible student misconceptions

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Techniques for a Study of Progressions: 19 Read the first five paragraphs of page 5 in the Number and Operations—Fractions progression is a line by line fashion. Check for comprehension at every component of each sentence. Mark anything that ties back to Grade 3 with a “3,” and anything that is new content with a “4.”

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Studying Progressions of Topics 20 Reflections: How does what is gained from a study of the progressions differ from what is gained from a study of the standards? What do these two essential documents offer to our profession?

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps 21 How can you increase coherence in your school’s delivery of topics? How can you initiate a study of progressions with your colleagues?