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A Story of Ratios

This module explores the development of mathematical understanding in grade 6 using a focus on concept development within the lessons. It introduces mathematical models and instructional strategies to support the implementation of A Story of Ratios. The module covers topics such as area of triangles, quadrilaterals, and polygons, polygons on the coordinate plane, volume of right rectangular prisms, and nets and surface area.

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A Story of Ratios

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  1. A Story of Ratios Grade 6 – Module 5

  2. 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. Agenda Introduction to the Module Concept Development Module Review

  4. Curriculum Overview of A Story of Ratios

  5. Module’s Foundation • Standards: • Pages 18-20 in the Progressions Document (K-6,Geometry,) serves as a foundation.

  6. G6-M5: Module Overview

  7. G6-M5: Module Overview

  8. G6-M5: Vocabulary and Representations

  9. 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. Agenda Introduction to the Module Concept Development – Topic A Module Review

  11. Topic A:

  12. Agenda Introduction to the Module Concept Development – Topic B Module Review

  13. Topic B:

  14. Lessons 1 – 10Lesson Study

  15. 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. Agenda Introduction to the Module Concept Development – Topic C Module Review

  17. Topic C:

  18. Agenda Introduction to the Module Concept Development – Topic D Module Review

  19. Topic D:

  20. Lessons 11 – 19aLesson Study

  21. 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. Agenda Introduction to the Module Concept Development Module Review

  23. Biggest Takeaway • Turn and Talk: • What questions were answered for you? • What new questions have surfaced?

  24. 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.

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