1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 6 – Module 3

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: 6.NS.C.5, 6.NS.C.6, 6.NS.C.7, 6.NS.C.8 Pages 7 – 8 in the Progressions Document (The Number System, 6-8) serves as a foundation. Directed measurement --- a rational number’s position on the number line is found using length and direction. The opposite of a number a, is –a. Both a and –a are located an equal distance from zero, in opposite directions. Rational numbers represent real-world situations.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M3: Module Overview

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M3: Vocabulary and Representations

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G6-M3 Rational Numbers – Topic Overview Topic A: Understanding Positive and Negative Numbers on the Number Line Topic B: Order and Absolute Value Topic C: Rational Numbers and The Coordinate Plane

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Understanding Positive and Negative Numbers on the Number Line

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 Positive and Negative Numbers on the Number Line: Opposite Direction and Value Lesson 1 Outcomes: Students extend their understanding of the number line, which includes zero and numbers to the right, that are above zero, and numbers to the left, that are below zero. Students use positive integers to locate negative integers, moving in the opposite direction from zero. Students understand that the set of integers is the set of whole numbers and their opposites, and understand that zero is its own opposite.

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Positive and Negative Numbers on the Number Line: Opposite Direction and Value The number line extends to include negative numbers. Lengths on the right-side and left-side of zero are the same for a number and its opposite. (Use a compass for the construction.) The set of whole numbers and their opposites (zero is its own opposite) are called integers. The order of the set of integers is: …-5,-4,-3,-2,-1,0,1,2,3,4,5… Lesson 1

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Positive and Negative Numbers on the Number Line: Opposite Direction and Value Lesson 1/Activity Draw a horizontal line. Place a point on the line and label it 0. Use a compass to locate and label the next point 1, thus creating a scale. (Continue to locate other whole numbers to the right of zero using the same unit measure.) Using the same process, locate the opposite of each number on the left side of zero. Label the first point to the left of zero, -1.

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Real World Positive and Negative Numbers and Zero Lessons 2-3

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Real World Positive and Negative Numbers and Zero Use positive and negative numbers and zero to represent situations. Graph integers on a number line, using an appropriate scale and relating points to real-world situations. Explain the meaning of zero in the context of a situation. Lessons 2-3

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Real World Positive and Negative Numbers and Zero Lesson 3 /Exit Ticket

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Opposite of a Number’s Opposite Lesson 5

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Opposite of a Number’s Opposite Lesson 5/Example

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Opposite of a Number’s Opposite Lesson 5/Activity

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Rational Numbers on the Number Line Lesson 6

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Rational Numbers on the Number Line Lesson 6/Exercise 1

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Rational Numbers on the Number Line Lesson 6/Exercise 1

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Rational Numbers on the Number Line Lesson 6/Exit Ticket

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Order and Absolute Value

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Ordering Integers and Other Rational Numbers Lesson 7 Outcomes: Students write, interpret, and explain statements of order for rational numbers in real world contexts. Students recognize that if a -b, because a number and its opposite are equal distances from zero; and moving along the horizontal number line to the right means the numbers are increasing.

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Ordering Integers and Other Rational Numbers Lesson 7

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Ordering Integers and Other Rational Numbers Lesson 8

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Writing and Interpreting Inequality Statements Involving Rational Numbers Inequalities Fluency Builder Lesson 10

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Absolute Value – Magnitude and Distance Complete Exercises 1- 3 How do we want Grade 6 students to conceptualize absolute value? Complete Exercises 6 – 19 Discuss how students display an understanding of absolute value as magnitude and distance. Lesson 11/Exercises

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mid-Module Assessment Question 3

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

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Rational Numbers and the Coordinate Plane

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios You’re the Expert! Lessons 14 - 19 Go to the appropriate table as designated by the number on your card. You will have ten minutes to discuss with your group the following: Lesson Study Modeling of an Essential Portion of the Lesson Concerns/Scaffolding Beyond Teacher’s Edition Each group will have ten minutes to model essential portion During the ten minutes please address: Lesson progression Prerequisite/Foundation Skills

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End-of-Module Assessment Questions 1 and 5

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

37. © 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?

38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Key Points Directed measurement --- a rational number’s position on the number line is found using length and direction. The opposite of a number a, is –a. Both a and –a are located an equal distance from zero, in opposite directions. Rational numbers represent real-world situations. We can write and explain statements of order for rational numbers in real-world contexts. The absolute value of a number is its distance from zero; and can be used in the context of a situation to show magnitude. We can use absolute value and the symmetry of the coordinate plane to solve problems related to distance.