1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 6 – Module 5

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Objectives Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons. Introduction to mathematical models and instructional strategies to support implementation of A Story of Ratios.

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

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Curriculum Overview of A Story of Ratios

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module’s Foundation Standards: Pages 18-20 in the Progressions Document (K-6,Geometry,) serves as a foundation.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M5: Module Overview

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M5: Module Overview

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M5: Vocabulary and Representations

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M5 Topic Overview Topic A: Area of Triangles, Quadrilaterals, and Polygons Topic B: Polygons on the Coordinate Plane Topic C: Volume of Right Rectangular Prisms Topic D: Nets and Surface Area

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

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

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

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

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lessons 1 – 10 Lesson Study

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mid-Module Assessment Complete Question 4 from the Mid-Module Assessment. Share your completed task with a table partner. With your partner, refer to the rubric and sample student work for this question and compare your own findings. Which standards relate to this question? Which Mathematical Practices are embodied in this task? What challenges might students face as they complete this task? How does students’ work in Topics A and B prepare them for this task?

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C:

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

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic D:

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lessons 11 – 19a Lesson Study

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End-of-Module Assessment Count off at your tables 1, 2, 1, 2…. so that half of you will answer question 1 and the other half will answer question 5. Complete Questions 1 or 5. When everyone at your table is finished, the 1’s will discuss their question and then the 5’s will discuss their question. Whole group share: What is the progression from Topic A through Topic D?

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Biggest Takeaway Turn and Talk: What questions were answered for you? What new questions have surfaced?

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Key Points Students utilize and build upon their previous understanding of composition and decomposition from Grades 1 – 5. Area and volume are additive. Students determine the formulas for area from their knowledge of the area of a rectangle and how it can be composed and decomposed. Students use their prior knowledge of Module 2 to calculate the volume of right rectangular prisms with unit cubes with fractional lengths. Students use their prior knowledge of Module 3 to determine area and surface area of polygons through distance calculations. Students use their prior knowledge of Module 4 to use equations to determine missing angles, as well as to use formulas for area, volume, and surface area. Students apply formulas to real-life contexts and distinguish between the need to find surface area or volume within contextual situations.