 # Develop Rules for Multiplying Signed Numbers

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Examples, videos, and solutions to help Grade 7 students learn how to develop rules for multiplying signed numbers.

### New York State Common Core Math Module 2, Grade 7, Lesson 11

Download worksheets for Grade 7, Module 2, Lesson 11

Lesson 11 Student 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.

Lesson 11 Summary

To multiply signed numbers, multiply the absolute values to get the absolute value of the product. The sign of the product is positive if the factors have the same sign and negative if they have opposite signs.

Example 1: Extending Whole Number Multiplication to the Integers

Part A: Complete quadrants 1 and 4 of the table below to show how sets of matching integer cards will affect a player’s score in the Integer Game. For example, three 2’s would increase a player’s score by 0 + 2 + 2 + 2 = 6 points.

a. What patterns do you see in the right half of the table?
b. Enter the missing integers in the left side of the middle row, and describe what they represent.
c. What relationships or patterns do you notice between the produtcs (values) in quadrant two and the products (values) in quadrant 1?
d. What relationships or patterns do you notice between the products (values) in quadrant two and the products (values) in quadrant four?
e. Use what you know about the products (values) in quadrants one, two, and four to describe what quadrant three will look like when its products (values) are entered.
f. Is it possible to know the sign of a product of two integers just by knowing in which quadrant each integer is located? Explain.
g. Which quadrants contain which values? Describe an integer game scenario represented in each quadrant.

Exercise 1: Multiplication of Integers in the Real-World

Generate real-world situations that can be modeled by each of the following multiplication problems. Use the Integer Game as a resource.

a. -3 × 5
b. -6 × (-3)
c. 4 × (-7)

Lesson 11 Problem Set
3. Each time that Samantha rides the commuter train, she spends \$4 for her fare. Write an integer that represents the change in Samantha’s money from riding the commuter train to and from work for 13 days.

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