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2. How to Use the “Compensation” Strategy to Multiply
Dawn Galente, Arlington CSD 2012
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The “compensation” strategy can help us multiply numbers because it’s easier to multiply by tens.
EXAMPLE: 4 x 9 = ?
Step 1: Pick a factor that is close to a ten. Here we’ll use 9.
+ 1 9 4
Step 2: Add to EACH GROUP to make groups of ten. (We now have 4 groups of ten instead of 4 groups of 9)
+ 1
+ 1
+ 1
Step 3: Multiply the new numbers. 10
Step 4: Adjust the answer to “compensate” for the addition of 1 cube TO EACH GROUP.
4 x 10 = 40
40 – 4 = 36
I added 1 to each of 4 groups, so I subtract 4.
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4 x 10 = 40

4. + 2
+ 2
+ 2
EXAMPLE 2: 18 x 3 =
Step 1: Pick a factor that is close to a ten. Add to that number to reach a ten. (In this case we will add 2 to 18 to get 20).
Step 2: Multiply the new numbers.
20 x 3 = 60
Step 3: Adjust the answer to “compensate” for the addition of 2 to EACH group.
Hmm, I added 2 to EACH group, so now I need to subtract 2 from EACH group.
+ 2 18 x 3 20 x
3 = 60 60 -
6 = 54

5. Example 3: 37 x 12 =
Step 1: Pick an addend that is close to a ten. (We’ll use 37).
Step 2: Add to that number to reach a ten. (In this case we add 3 to 37 to get 40 in EACH of the 12 groups).
Step 3: Multiply the new numbers.
Step 4: Adjust the answer to “compensate” for the addition of 3 to EACH group.
Hmm, I added 3 to EACH group so I need to subtract 3 from EACH group.
+ 3 37 x
12 = 40 x
12 = 480
480 -
36 = 444

6. The End