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

Mental Math Strategies. For Addition and Subtraction. Ms. Stewart Math 7 and Math 8 COPY DARK BLUE TEXT INTO EXAMPLE COLUMN OF YOUR ORGANIZER. Addition. Break Up the Numbers Strategy

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

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  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 that’s 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 that’s 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:

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