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 \(97 \boldcdot 103 = (1003)(100+3)\)
100  3  
100  10,000  300 
3  300  9 
 Explain how this diagram is used to compute \(97 \boldcdot 103 = 9,\!991\).
 Draw a similar diagram that helps you mentally compute \((30+1)(301)\). What is the result? What multiplication problem did you just solve?
 Use this method to compute:
 \(7 \boldcdot 13\)
 \(102 \boldcdot 98\)
 \(995 \boldcdot 1,\!005\)
 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. Write some equivalent expressions based on the diagram.

10 5 10 100 45 
7 10 7 70 
\(x\) 8 \(x\) 8 
\(a\) 9 \(\text{}9a\) 9 
\(b\) \(\frac12\) \(b\) \(b^2\) \(\text{}\frac{1}{4}\) 
7 \(c\) \(\text{}c^2\) 7 49