# Understanding Multiplication of Integers

Video solutions to help Grade 7 students learn learn how to develop rules for multiplying signed numbers.

## New York State Common Core Math Module 2, Grade 7, Lesson 10

Lesson 10 Student Outcomes

• Students practice and justify their understanding of multiplication of integers by using the Integer Game. For example, 3 x 5 corresponds to what happens to your score if you get three 5 cards; 3 x (-5) corresponds to what happens to your score if you get three -5 cards; (-3) x 5 corresponds to what happens to your score if you lose three 5 cards; and (-3) x (-5) corresponds to what happens to your score if you lose three -5 cards.

• Students explain that multiplying by a positive integer is repeated addition and that adding a number multiple times has the same effect as removing the opposite value the same number of times (e.g. 5 x 3 = (-5) x (-3) and 5 x (-3) = (-5) x 3.)

• Students use the properties and facts of operations to extend multiplication of whole numbers to multiplication of integers.

Lesson 10 Summary

Multiplying integers is repeated addition and can be modeled with the Integer Game. If 3 x a corresponds to what happens to your score if you get three cards of value a, then (-3) x a corresponds to what happens to your score if you lose three cards of value a. Adding a number multiple times has the same effect as removing the opposite value the same number of times (e.g. a x b = (-a) x (-b) and a x (-b) = (-a) x b.)

Example 1: Product of a Positive Integer and a Negative Integer

Example 2: Product of a Negative Integer and a Positive Integer

Example 3: Product of Two Negative Integers

This video gives some context clues.

This video gives some sample solutions.

Lesson 10 Problem Set

2. You have the integer cards shown at the right when your teacher tells you to choose a card to multiply four times. If your goal is to get your score as close to zero as possible, which card would you choose? Explain how your choice changes your score.