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A Story of Ratios

A Story of Ratios. Grade 7 – Module 2. Session Objectives. Examine the development of mathematical understanding across the module using a focus on concept development within the lessons.

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A Story of Ratios

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  1. A Story of Ratios Grade 7 – Module 2

  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: 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. G7-M2: Module Overview

  7. G7-M2: Vocabulary and Representations

  8. 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. Topic A: Addition and Subtraction of Integers and Rational Numbers

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

  11. Opposite Quantities Combine to Make Zero Lesson 1 • 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.

  12. Opposite Quantities Combine to Make Zero Lesson 1/Example 3

  13. Opposite Quantities Combine to Make Zero Lesson 1, Concept Development The Integer Game

  14. Opposite Quantities Combine to Make Zero Lesson 1, Concept Development Let’s Play the Integer Game!

  15. Using the Number Line to Model the Addition of Integers Lesson 2/Example 1

  16. Using the Number Line to Model the Addition of Integers Lesson 2/Example 3

  17. Understanding Addition of Integers Lesson 3 • Outcomes: • Students understand addition of integers as putting together or counting up, where counting up a negative number of times is counting down. • Students use arrows to show the sum of two integers, , on a number line and to show that the sum is distance from to the right if is positive and to the left if is negative. • Students refer back to the Integer Game to reinforce their understanding of addition.

  18. Understanding Addition of Integers Lesson 3/Exit Ticket

  19. 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. Understanding Subtraction of Integers and Other Rational Numbers Lesson 5/Example

  21. The Distance Between Two Rational Numbers Lesson 6/Closing

  22. The Distance Between Two Rational Numbers Lesson 6/Exit Ticket

  23. The Distance Between Two Rational Numbers Lesson 6/Problem Set

  24. Addition and Subtraction of Rational Numbers Lesson 7

  25. Applying the Properties of Operations to Add and Subtract Rational Numbers Lessons 8 and 9 • 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

  26. Applying the Properties of Operations to Add and Subtract Rational Numbers Lessons 8 and 9

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

  28. Topic B: Multiplication and Division of Integers and Rational Numbers

  29. Understanding the Multiplication of Integers Lesson 10/Example 3

  30. Develop Rules for Multiplying Signed Numbers Lesson 11 • Outcomes: • Students understand the rules for multiplication of integers and that multiplying the absolute values of integers results in the absolute value of the product. The sign, or absolute value, of the product is positive if the factors have the same sign and negative if they have opposite signs. • Students realize that and see that it can be proven to be true mathematically through the use of the distributive property and the additive inverse. • Students use the rules for multiplication of signed numbers and give real-world examples.

  31. Develop Rules for Multiplying Signed Numbers Lesson 11/Example 1

  32. Develop Rules for Multiplying Signed Numbers Lesson 11

  33. Converting Rational Numbers to Decimals Using Long Division Lesson 14/Example 2

  34. Mid-Module Assessment Question 6

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

  36. Topic C: Applying Operations with Rational Numbers to Expressions and Equations

  37. Comparing Tape Diagram Solutions to Algebraic Solutions Lesson 17

  38. Comparing Tape Diagram Solutions to Algebraic Solutions Lesson 17/Exit Ticket

  39. If-Then Moves with Integer Cards Lesson 21/ Exercises 1

  40. If-Then Moves with Integer Cards Lesson 21/ Exercises 1

  41. Solving Equations Using Algebra Lesson 23/Exercise 2

  42. Solving Equations Using Algebra Lesson 23/Exit Ticket

  43. End-of-Module Assessment Questions 2 and 3

  44. Agenda Introduction to the Module Concept Development Module Review

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

  46. 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.

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