# Lesson 8

Multiplying Expressions

• Let’s explore multiplication strategies.

### 8.1: Math Talk: Combining the Similar Numbers

Evaluate mentally.

$$100 \boldcdot 100$$

$$\text{-}3 \boldcdot 3$$

$$\text{-}300 + 300$$

$$1,\!279 + \text{-}1,\!279$$

### 8.2: A Method for Multiplying

Here is a method for multiplying 97 and 103:

97 is $$100 - 3$$

103 is $$100 + 3$$

So $$97 \boldcdot 103 = (100-3)(100+3)$$

 100 -3 100 10,000 -300 3 300 -9
1. Explain how this diagram is used to compute $$97 \boldcdot 103 = 9,\!991$$.
2. Draw a similar diagram that helps you mentally compute $$(30+1)(30-1)$$. What is the result? What multiplication problem did you just solve?
3. Use this method to compute:
1. $$7 \boldcdot 13$$
2. $$102 \boldcdot 98$$
3. $$995 \boldcdot 1,\!005$$
4. Create a challenge problem for your partner, that could use this method. Create a diagram that shows the answer before giving the problem to your partner.

### 8.3: Find the Missing Pieces

Complete each diagram. Use the diagram to write some equivalent expressions that could be solved using the diagram.

1.  10 5 10 100 45
2.  7 10 -7 -70
3.  $$x$$ 8 $$x$$ -8
4.  $$a$$ -9 $$\text{-}9a$$ 9
5.  $$b$$ $$\frac12$$ $$b$$ $$b^2$$ $$\text{-}\frac{1}{4}$$
6.  7 $$c$$ $$\text{-}c^2$$ 7 49