Name: ___________________ Date: ______________________ 7th grade Accelerated Unit I Lesson 2-1 Multiplying Integers

Focus Question: How does knowing to add positive and negative integers help you multiply positive and negative integers? How do properties of addition and multiplication help you multiply positive and negative integers?

Examples/Key ConceptsPart 1 IntroYou know that multiplication is repeated addition.

Because multiplication is commutative, you can also find the value of – 2 • 3: – 2 • 3 = 3 • ( – 2) = – 6 Part 1 ExampleIf a glacier is retreating at a rate of 7 feet per year, then the product of 4 ( – 7) represents the retreat, in feet, of the glacier over 4 years.

Complete a number line model to find the product of 4 ( – 7).

Name: ___________________ Date: ______________________ Part 2 Intro You know that 1 and – 1 are additive inverses. 0 = 1 + ( – 1)You can use the properties of operations to show that – 1 ( – 1) and – 1 are also additive inverses.

You can use – 1 ( – 1) to find the product of any two negative integers.

Part 2 ExampleYou can use the product – 4 ( – 7) to represent where the glacier’s positive was 4 years ago.use – 1 ( – 1) = 1 to show that the product – 4 ( – 7) is 28.

Name: ___________________ Date: ______________________ Key ConceptYou can use the signs of the factors to determine the sign of a product of integers.

Different Signs = Negative Same Signs = Positivepositive × negative = negative positive × positive = positive

+ • – = – + • + = +6 • (– 5) = – 30 6 • 5 = 30

negative × positive = negative negative × negative = positive– • + = – – • – = +

– 5 • 6 = – 30 – 6 • (– 5) = 30Part 3 ExampleSort these products into two groups.

Note that expressions have not been sorted correctly.

Additional Practice

1.

Name: ___________________ Date: ______________________ 2.

3.

4.

5.

6.