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  

Summary