1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 8 – Module 7

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session 5 Objectives Understand the mathematical concepts developed within Grade 8 Module 7. Practice collecting evidence of effective instruction using exemplar transcripts of classroom instruction. Uncover strategies for supporting teachers with their implementation of the Standards for Mathematical Practice.

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios What’s In a Module? Teacher Materials Module Overview Topic Overviews Daily Lessons Assessments Student Materials Daily Lessons with Problem Sets Copy Ready Materials Exit Tickets Fluency Worksheets / Sprints Assessments

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Types of Lessons 1.Problem Set Students and teachers work through examples and complete exercises to develop or reinforce a concept. 2.Socratic Teacher leads students in a conversation to develop a specific concept or proof. 3.Exploration Independent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge. 4.Modeling Students practice all or part of the modeling cycle with real-world or mathematical problems that are ill-defined.

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios What’s In a Lesson? Teacher Materials Lessons Student Outcomes and Lesson Notes (in select lessons) Classwork General directions and guidance, including timing guidance Bulleted discussion points with expected student responses Student classwork with solutions (boxed) Exit Ticket with Solutions Problem Set with Solutions Student Materials Classwork Problem Set

6. © 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

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

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

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

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

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

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

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Square and Cube Roots Learning is motivated by the Pythagorean Theorem and need to get a precise length of a side of a right triangle. Square roots are defined. Square and cube roots exist and are unique. Students simplify square roots (optional). Students solve equations using roots.

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Before Beginning the Module: Pythagorean Theorem Lessons from Modules 2 and 3 must be taught: Module 2, Lesson 15 Module 2, Lesson 16 Module 3, Lesson 13 Module 3, Lesson 14 Lessons contain proofs and practice.

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

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 1 Example 4 Consider the math that students needed to know in order to answer this question: Knowledge/Properties of Equilateral Triangle Understanding of Congruence (M2) Triangle Sum Theorem (M2) Laws of Exponents (M1) Properties of Equality/Solving Equations (M4) Estimating Square Roots (M7)

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 1 Example 4 – alternate method

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

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

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Turn and Talk Rational numbers are defined as numbers whose decimal expansions eventually repeat. Irrational numbers are defined as numbers that are not rational. Focus of Topic B is writing decimal expansions of numbers. Students learn why the long division algorithm leads to the decimal expansion of a number. Students learn how to determine the decimal expansion of irrational numbers, including pi. Topic B: Decimal Expansion of Numbers

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

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios In your table groups, share the observations you made using the CCSS Instructional Practice Guide. Each group member shares one observation and the supporting evidence. Then the group member to his/her right shares. Continue this process until all observations have been shared. Round Robin Activity

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 7

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Locating a number with a finite number of decimal digits on the number line.

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Locating a number with a infinite number of decimal digits on the number line.

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

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

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

36. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

38. © 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?