Mental Math: Subtraction Strategies

Show your work for each problem.

1.
Which strategy is best for calculating ?
1. a)Standard algorithm
2. b)Breaking apart by place value
3. c)Counting up (since 58 and 63 are close together)
4. d)Compensation (round 58 to 60)
Answer: Counting up (since 58 and 63 are close together)
Counting up is ideal when numbers are close: , . Total: . Quick and simple!
2.
Calculate using the counting up strategy. What is the answer?
Answer: 27
Count up: , then . Total: . So .
3.
Use compensation to calculate . What is the answer?
Answer: 45
. Since 30 is 1 more than 29, add 1 back: .
4.
Calculate using the breaking apart strategy.
Answer: 43
1. Break apart 43 into tens and ones: 40 + 3
2. Subtract the tens: 46
3. Subtract the ones: 43
5.
When using compensation for , you first calculate . What do you do next?
1. a)Add 2 to get 37
2. b)The answer is already 35
3. c)Add 30 to get 65
4. d)Subtract 2 to get 33
Answer: Add 2 to get 37
Since 30 is 2 more than 28, you subtracted 2 too many. Add 2 back: .
6.
Calculate using the complement strategy (9 minus tens, 10 minus ones).
Answer: 53
Tens: . Ones: . Together: . Check: ✓
7.
Calculate using the counting up strategy.
Answer: 45
1. Start at 47. Jump to the next ten: 3
2. From 50, jump to 90: 40
3. From 90, jump to 92: 2
4. Add all jumps: 45
8.
A book costs 38 euros. You pay with a 50 euro note. Using mental math, how much change should you receive?
1. a)18 euros
2. b)12 euros
3. c)22 euros
4. d)8 euros
Answer: 12 euros
Using compensation: . Since 38 is 2 less than 40, add 2: euros.
9.
Calculate mentally.
Answer: 28
(tens), (ones). Answer: . Check: ✓
10.
Calculate using the compensation strategy.
Answer: 34
1. Round 49 to the nearest ten: 50
2. Subtract the rounded number: 33
3. Did you subtract too much or too little? By how much? 1
4. Adjust: 34
11.
Your team scored 91 points. The opponent scored 67 points. What is the point difference?
Answer: 24
Using compensation: . Since 70 is 3 more than 67, add 3: points.
12.
A movie is 95 minutes long. You've watched 58 minutes. How many minutes are left?
Answer: 37
1. Choose a strategy. Round 58 to what friendly number? 60
2. Calculate 35
3. You rounded 58 up by 2. Should you add or subtract 2? add
4. Final answer: 37
13.
Which calculation shows the correct use of compensation for ?
1. a), then
2. b), then
3. c), then
4. d), then
Answer: , then
Round 38 to 40. Calculate . Since 40 is 2 more than 38, you subtracted 2 too many. Add 2 back: .
14.
Calculate using any mental math strategy.
Answer: 16
Using the complement to 100: (tens), (ones). Answer: . Check: ✓
15.
You have 75 euros. After buying a gift for 48 euros, how much money do you have left?
Answer: 27
1. Which strategy will you use? Round 48 to the nearest ten: 50
2. Subtract the rounded amount: 25
3. How much did you round up by? 2
4. Adjust by adding back: 27