A Story of Ratios

1. A Story of Ratios Grade 6 – Module 3

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

4. Curriculum Overview of A Story of Ratios

5. 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 aand –aare located an equal distance from zero, in opposite directions. • Rational numbers represent real-world situations.

6. G6-M3: Module Overview

7. G6-M3: Vocabulary and Representations

8. 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. Topic A: Understanding Positive and Negative Numbers on the Number Line

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

11. 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. Positive and Negative Numbers on the Number Line: Opposite Direction and Value Lesson 1 • 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…

13. 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. Real World Positive and Negative Numbers and Zero Lessons 2-3 • Outcomes: • Students use positive and negative numbers to indicate a change (gain or loss) in elevation with a fixed reference point, temperature, and the balance in a bank account.   • Students use vocabulary precisely when describing and representing situations involving integers; for instance, an elevation of feet is the same as feet below the fixed reference point. • Students will choose an appropriate scale for the number line when given a set of positive and negative numbers to graph.

15. Real World Positive and Negative Numbers and Zero Lessons 2-3 • 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.

16. Real World Positive and Negative Numbers and Zero Lesson 3 /Exit Ticket

17. The Opposite of a Number’s Opposite Lesson 5 • Outcomes: • Students understand that, for instance, the opposite of is denoted and is equal to . In general, they know that the opposite of the opposite is the original number; e.g., . • Students locate and position opposite numbers on a number line.

18. The Opposite of a Number’s Opposite Lesson 5/Example

19. The Opposite of a Number’s Opposite Lesson 5/Activity

20. Rational Numbers on the Number Line Lesson 6

21. Rational Numbers on the Number Line Lesson 6/Exercise 1

22. Rational Numbers on the Number Line Lesson 6/Exercise 1

23. Rational Numbers on the Number Line Lesson 6/Exit Ticket

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

25. Topic B: Order and Absolute Value

26. 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, then -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. Ordering Integers and Other Rational Numbers Lesson 7 • What is the Value of Each Number and Which is Larger? • The first number is 8 ½ units to the right of -5. The second number is 3 units to the right of 0. • First Number: Second Number:; is larger than . • 2) The first number is ¼ unit to the left of -7. • The second number is 8 units to the left of 1. First Number: Second Number: is larger than . • 3) The opposite of the first number is 2 units to the right of 3. • The opposite of the second number is 2 units to the left of -3. First Number: Second Number: is larger than

28. Ordering Integers and Other Rational Numbers Lesson 8 • Outcomes: • Students write, interpret, and explain statements of order for rational numbers in the real-world. • Students recognize that if , then , 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.

29. Writing and Interpreting Inequality Statements Involving Rational Numbers Lesson 10 Inequalities Fluency Builder

30. Absolute Value – Magnitude and Distance Lesson 11/Exercises • 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.

31. Mid-Module Assessment Question3

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

33. Topic C: Rational Numbers and the Coordinate Plane

34. 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. End-of-Module Assessment Questions 1 and 5

36. Agenda Introduction to the Module Concept Development Module Review

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

38. 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.