Mental Math Strategies
Mental Math Fun :)
Addition
Break Up the Numbers Strategy
This strategy is used when regrouping is required. One of the addends is broken
up into its expanded form and added in parts to the other addend. For example
57 + 38 might be calculated in this way: 57 + 30 is 87 and 8 more is 95.
Front-End (left to right) Strategy
This commonly used strategy involves adding the front-end digits and proceeding
to the right, keeping a running total in your head. For example, 124 + 235 might
be calculated in the following way: Three hundred (200 + 100), fifty (20+30) nine
(4 + 5).
Rounding for Estimation
Rounding involves substituting one or more numbers with “friendlier” numbers
with which to work. For example, 784 + 326 might be rounded as 800 + 300 or
1100.
Front-End Estimation
This strategy involves adding from the left and then grouping the numbers in
order to adjust the estimate. For example 5239 + 2667 might be calculated in the
following way: Seven thousand (5000 + 2000), eight hundred (600 +200) – no,
make that 900 (39 and 67 is about another hundred). That’s about 7900
Compatible Number Strategy
Compatible numbers are number pairs that go together to make “friendly”
numbers. That is, numbers that are easy to work with. To add 78 + 25 for
example you might add 75 + 25 to make 100 and then add 3 to make 103.
Near Compatible Estimation
Knowledge of the compatible numbers that are used for mental calculations is
used for estimation. For example, in estimating 76 + 45 + 19 +26 +52, one might
do the following mental calculation: 76 + 26 and 52 + 45 sum to about 100. Add
the 19. The answer is about 219.
Balancing Strategy
A variation of the compatible number strategy, this strategy involves taking one
or more from one addend and adding it to the other. For example, 68 + 57
becomes 70 + 55 (add 2 to 68 and take 2 from 57)
Clustering in Estimation
Clustering involves grouping addends and determining the average. For
example, when estimating 53 + 47 + 48 + 58 +52, notice that the addends cluster
around 50. The estimate would be 250 (5 x 50)
Special Tens Strategy
In the early grades, students learn the number of pairs that total ten – 1 and 9, 2
and 8, 3 and 7, and so on. These can be extended to such combinations as 10
and 90, 300 and 700, etc.
Compensation Strategy
In this stage, you substitute a compatible number for one of the numbers so that
you can more easily compute mentally. For example, in doing the calculation 47
+ 29 one might think (47 + 30) – 1.
Consecutive Number Strategy
When adding three consecutive numbers, the sum is three times the middle
number.
Subtraction
Compatible Number Estimation
Knowledge of compatible numbers can be used to find an estimate when
subtracting. Look for the near compatible pairs. For example when subtracting
1014 – 766, one might think of the 750 – 250 pairing.
Front-End Strategy
When there is no need to carry, simply subtract from left to right. To subtract 368
– 125 think 300 – 100 = 200, 60 – 20 = 40, 8 – 5 = 3. The answer is 234.
Front-End Estimation
For questions with no carrying in the highest two place values, simply subtract
those place values for a quick estimation. For example, the answer to $465.98 $345.77 is about $120.00
Compatible Numbers Strategy
This works well for powers of 10. Think what number will make the power of
10. For example, to subtract 100 – 54, think what goes with 54 to make
100. The answer is 46.
Equal Additions Strategy for Subtraction
This strategy avoids regrouping. You add the same number to both the
subtrahend and minuend to provide a “friendly” number for subtracting, then
subtract. For example, to subtract 84 – 58, add too to both numbers to give 86 –
60. This can be done mentally. The answer is 26.
Compensation Strategy for Subtraction
As with addition, subtract the “friendly” number and add the difference. For
example, $3.27 - $0.98 – ($3.27 - $1.00) + $0.02 = $2.29
“Counting On” Strategy for Subtraction
Visualize the numbers on a number line. For example, 110 – 44. You need 6 to
make 50 from 44, then 50 to make 100, then another 10. The answer is 56.
“Counting On” Estimation
“Counting On” can also be used for estimation. For example, to estimate 894 –
652, think that 652 + 200 gives about 850. Then another 50 gives about
900. The difference is about 250.