Ms. Stewart

1
Mental Math Strategies
For Addition and Subtraction

• Ms. Stewart
• Math 7 and Math 8
• COPY DARK BLUE TEXT INTO EXAMPLE COLUMN OF YOUR
  ORGANIZER

2
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.
• Your turn, try this one using the strategy
• 62 27
• 62 20 is 82 and 7 more is 89

3
Addition

• 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).
• Your turn, try this one using the strategy
• 541 232
• Seven hundred (500 200), seventy (40 30),
  three (1 2)
• 773

4
Addition

• 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.
• Your turn, try this one using the strategy
• 113 796
• 113 796 might be rounded as 100
  800 or 900

5
Addition

• 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) so thats about
  7900.
• Your turn, try this one using the strategy
• 4216 4327
• Eight thousand (4000 4000), five hundred (200
  300) and 16 27 is about another 50 so thats
  about 8550.

6
Addition

• 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.
• Your turn, try this one using the strategy
• 50 59
• Add 50 50 to make 100 and then add 9 to make
  109

7
Addition

• 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.
• Your turn, try this one using the strategy
• 23 62 25 43 10
• 23 25 and 43 10 sum to about 100. Add the
  62. The answer is about 162.

8
Addition

• 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) 125
•  Your turn, try this one using the strategy
• 33 42
• 33 42 becomes 35 40 (add 2 to 33 and take
  2 from 42) 75

9
Addition

• 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)
• Your turn, try this one using the strategy
• 22 18 26
• Notice that the addends cluster around 20.  The
  estimate would be 60 (3 x 20)

10
Addition

• Special Tens Strategy
• In the early grades, you 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.
• For example 500 and 500 1000
• Your turn, try this one using the strategy
• 4000 6000
• 10 000

11
Addition

• 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.
• Your turn, try this one using the strategy
• 32 18
• (32 20) 2
• 52 2
• 50

12
Addition

• Consecutive Number Strategy
• When adding three consecutive numbers, the sum is
  three times the middle number.
• For example 1 2 3 6
• 2 x 3 6
• Your turn, try this one using the strategy
• 5 6 7
• 5 6 7 18
• 6 x 3 18

13
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 and 250 pairing an
  estimate for 1014 766 would be 250
•  Your turn, try this one using the strategy
• 312 157
• Think of the 150 and 150 pairing an estimate
  for 312 157 would be 150

14
Subtraction

• Front-End Strategy
• When there is no need to carry, simply subtract
  from left to right. 
• For example to subtract 368 125 think 300 100
  200, 60 20 40, 8 5 3.  The answer is
  243.
•  Your turn, try this one using the strategy
• 2645 1432
• Think 2000 1000 1000, 600 400 200,
  40 30 10, 5 2 3. The answer is 1213.

15
Subtraction

• 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
• Your turn, try this one using the strategy
• 863.50 234.99
• 863.50 234.99 is about 640.00

16
Subtraction

• 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.
•  Your turn, try this one using the strategy
• 1000 724
• Think what goes with 724 to make 1000. The
  answer is 276.

17
Subtraction

• 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 two to both
  numbers to give 86 60.  This can be done
  mentally.  The answer is 26.
• Your turn, try this one using the strategy
• 57 42
• Add three to both numbers to give 60 45
  which equals 15

18
Subtraction

• 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
• Your turn, try this one using the strategy
• 10.00 3.85
• (10.00 - 4.00) 0.15 6.15

19
Subtraction

• 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 66.

• Your turn, try this one using the strategy
  212 75
• You need 25 to make 100 from 75, then 100 to
  200 and then
  another 12. The answer is 137.

20
Subtraction

• 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.
• Your turn, try this one using the strategy