1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 7 – Module 2

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Objectives Examine the development of mathematical understanding across the module using a focus on concept development within the lessons. Identify the big idea within each topic in order to support instructional choices that achieve the lesson objectives while maintaining rigor within the curriculum.

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: 7.NS.A.1, 7.NS.A.2, 7.NS.A.3, 7.EE.A.2, 7.EE.B.4 Pages 9 – 13 in the Progressions Document (The Number System, 6-8) serves as a foundation. Using vectors to represent the addition of rational numbers on the number line; arriving at the additive inverse: p + (-p) = 0. Representing subtraction as distance on the number line; and |p – q | is the distance between p and q on the number line. Students use the properties of operations to justify multiplication and division of rational numbers.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G7-M2: Module Overview

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G7-M2: Vocabulary and Representations

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G7-M2 Rational Numbers – Topic Overview Topic A: Addition and Subtraction of Integers and Rational Numbers Topic B: Multiplication and Division of Integers and Rational Numbers Topic C: Applying Operations with Rational Numbers to Expressions and Equations

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Addition and Subtraction of Integers and Rational Numbers

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 Opposite Quantities Combine to Make Zero Outcomes: Students add positive integers by counting up and negative integers by counting down (using curved arrows on the number line). Students play the Integer Game to combine integers, justifying that an integer plus its opposite add to zero. Students know the opposite of a number is called the additive inverse because the sum of the two numbers is zero. Lesson 1

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make Zero Lesson 1/Example 3

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make Zero The Integer Game Lesson 1, Concept Development

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make Zero Let’s Play the Integer Game! Lesson 1, Concept Development

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Using the Number Line to Model the Addition of Integers Lesson 2/Example 1

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Using the Number Line to Model the Addition of Integers Lesson 2/Example 3

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Addition of Integers Lesson 3

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Addition of Integers Lesson 3/Exit Ticket

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Subtraction of Integers and Other Rational Numbers Lesson 5 Outcomes: Students justify the Rule for Subtraction: Subtracting a number is the same as adding its opposite. Students relate the subtraction to the Integer Game. Students justify the Rule for Subtraction for all rational numbers, using the inverse relationship between addition and subtraction.

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Subtraction of Integers and Other Rational Numbers Lesson 5/Example

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Distance Between Two Rational Numbers Lesson 6/Closing

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Distance Between Two Rational Numbers Lesson 6/Exit Ticket

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Distance Between Two Rational Numbers Lesson 6/Problem Set

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Addition and Subtraction of Rational Numbers Lesson 7

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Applying the Properties of Operations to Add and Subtract Rational Numbers Outcomes: Students use properties of operations to add and subtract rational numbers without the use of a calculator. Students recognize that any problem involving addition and subtraction of rational numbers can be written as a problem using addition and subtraction of only positive numbers. Students use the commutative and associative properties of addition to rewrite numerical expressions in different forms. They know the opposite of a sum is the sum of its opposites: -(3 + (-4)) = -3 + 4. the opposite Lessons 8 and 9

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Applying the Properties of Operations to Add and Subtract Rational Numbers Lessons 8 and 9

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Multiplication and Division of Integers and Rational Numbers

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding the Multiplication of Integers Lesson 10/Example 3

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Develop Rules for Multiplying Signed Numbers Lesson 11

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Develop Rules for Multiplying Signed Numbers Lesson 11/Example 1

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Develop Rules for Multiplying Signed Numbers Lesson 11

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Converting Rational Numbers to Decimals Using Long Division Lesson 14/Example 2

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mid-Module Assessment Question 6

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

36. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Applying Operations with Rational Numbers to Expressions and Equations

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Comparing Tape Diagram Solutions to Algebraic Solutions Lesson 17

38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Comparing Tape Diagram Solutions to Algebraic Solutions Lesson 17/Exit Ticket

39. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios If-Then Moves with Integer Cards Lesson 21/ Exercises 1

40. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios If-Then Moves with Integer Cards Lesson 21/ Exercises 1

41. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Solving Equations Using Algebra Lesson 23/Exercise 2

42. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Solving Equations Using Algebra Lesson 23/Exit Ticket

43. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End-of-Module Assessment Questions 2 and 3

44. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

45. © 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?

46. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Key Points The additive inverse is the opposite of a number because, when added to a number, the sum is zero. We can use arrows on a number line to show the sum, p + q, on a number line. The sum is the distance|q|from p to the right of p if p is positive, and to the left of p if p is negative. Subtracting a number is the same as adding its opposite. The properties of operations justify the rules for multiplication and division of integers. (-1)(-1) = 1 can be justified using the distributive property and additive inverse. The opposite of a sum is the sum of its opposites. Ex.: –(-3 + 4) = 3 + (-4). Distance between 2 rational numbers p and q on a number line is |p - q| Every rational number can be written as a decimal that either terminate s in zeros or repeat.