Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 12

Operations with Rational Numbers

Lesson 12

Math

Unit 2

7th Grade

Lesson 12 of 18

Objective

Determine the rules for multiplying signed numbers.

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.

Foundational Standards

  • 3.OA.B.5

Criteria for Success

  1. Use properties of operations as a model to understand multiplication of integers.
  2. Understand that a negative number times a positive number results in a negative number.
  3. Understand that a negative number times a negative number results in a positive number.

Tips for Teachers

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Anchor Problems

25-30 minutes

Problem 1

Model each situation using a number line and the walking character shown below.

a.   How can you model $${3 \times 2}$$ on the number line? [Watch Video #1 on slide 1.]

b.   Model $${4 \times 3}$$ in the same way on the number line. [Watch Video #2 on slide 2.]

c.   What about $${(-4) \times 3}$$? What about $${4 \times (-3)}$$? [Watch Video #3 and Video #4 on slides 3 and 4.]

d.   What does this mean about $${(-4) \times (-3)}$$? [Watch Video #5 on slide 5.]

Guiding Questions

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Student Response

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References

SERP Poster Problems Walking the Line

Walking the Line from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed Aug. 14, 2017, 2:10 p.m..

Problem 2

Investigate the properties of operations with negative numbers. Use Diagram 1 to answer parts A - F, and Diagram 2 to answer parts G - L.

a.   What types of numbers are shown in the parentheses in expression A? What happens when you add them together?

b.   What value goes in box B?

c.   What is the product of 3 and the value in box B?

d.   What property says that expression A and expression D are equal?

e.   If expression A and expression D are equal, then what is the value of box E?

f.   Knowing the value of expression D, what must go in box F? What is the product of 3 and -5?

g.   What is the value of box G? Where does it come from? What property is it?

h.   What is the value of box H? Why?

i.   What property says that the two expressions are equal?

j.   From what you know about box F in Diagram 1, what is the value of box J?

k.   What is the value of box K? Why?

l.   Knowing the values of boxes J and K, what must go in box L? What is the product of -5 and -3?

Guiding Questions

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Student Response

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References

Mathematical Musings Why Is a Negative Times a Negative a Positive?

Why Is a Negative Times a Negative a Positive? by Bill McCallum is made available on Mathematical Musings. Accessed Aug. 14, 2017, 2:21 p.m..

Problem 3

Which expressions below have a positive value? Select all that apply.

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Guiding Questions

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Student Response

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Problem Set

15-20 minutes

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Target Task

5-10 minutes

Problem 1

Explain or show in your own words or in an example why $${(-1) \times (-1) = 1}$$.

Student Response

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Problem 2

Rewrite the expression as a multiplication problem: $${(-5) + (-5) + (-5) + (-5)}$$.

Student Response

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Problem 3

Evaluate:

a.   $${-5(6)}$$

b.   $${-6(5)}$$

c.   $${-6 \times (-5)}$$

d.   $${-8 \cdot (2+4)}$$

e.   $${(2-4) \times 8}$$

f.   $${(-7)(-10)(-3)}$$

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.

Next

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

Lesson 13
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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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