Operations with Rational Numbers

Lesson 13

Math

Unit 2

7th Grade

Lesson 13 of 18

Objective


Multiply signed rational numbers and interpret products in real-world contexts.

Common Core Standards


Core Standards

  • 7.NS.A.2.A — Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
  • 7.NS.A.2.C — Apply properties of operations as strategies to multiply and divide rational numbers.

Criteria for Success


  1. Apply the rules of multiplying signed numbers to find the products of rational numbers.
  2. Given a product, find factors that multiply to get the product.
  3. Write multiplication problems with signed rational numbers to represent contexts.

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Anchor Problems


Problem 1

Your dog’s veterinarian recommends that you put your dog on a diet to lose some weight. You change your dog’s food and feeding schedule and keep a log of his weight. On average, you notice that your dog’s weight changes by $$-0.8$$ pounds per month. Write an expression to represent the total change in your dog's weight after $$6$$ months. What number represents the change in your dog’s weight?

Guiding Questions

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Problem 2

List three factors that have a product of $${-{3\over5}}$$? Can you think of another set of three factors? 

Guiding Questions

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Problem 3

On the number line below, $${|a| < |b|}$$. Which expressions are negative? Select all that apply.

 

A.   $${ab}$$

B.     $$-({ab})$$

C.     $${(-a)(-b)}$$

D.      $${2a}$$

E.   $${2b-a}$$

F.     $${2a}-b$$

Guiding Questions

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Problem Set

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Target Task


Problem 1

On Thursday, the temperature was 64 ℉. Since Monday, three days earlier, the temperature had decreased consistently by 2 degrees each day. What multiplication expression represents the change in temperature from Thursday to Monday? Explain what each factor in your expression represents.

Problem 2

Find the product:

$${1{1\over2} \times \left( -{7\over8} \right )}$$

Problem 3

Determine if the statement is always, sometimes, or never true: The product of any two numbers is the product of their opposites.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include procedural practice multiplying signed rational numbers, including integers, fractions, and decimals
  • Include problems with real-world contexts or have students write contexts to represent multiplication problems.
  • Include problems where students identify equivalent expressions.
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Lesson 12

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Lesson 14

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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