Lesson 8

Evaluate mentally.

$100 \boldcdot 100$

$\text{-}3 \boldcdot 3$

$\text{-}300 + 300$

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

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.

Complete each diagram. Write some equivalent expressions based on 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