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

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. 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 might be calculated in this way: is 87 and 8 more is 95. For example might be calculated in this way: is 87 and 8 more is 95. Your turn, try this one using the strategy: Your turn, try this one using the strategy: is 82 and 7 more is is 82 and 7 more is 89

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. This commonly used strategy involves adding the front-end digits and proceeding to the right, keeping a running total in your head. For example, might be calculated in the following way: Three hundred ( ), fifty ( ) nine (4 + 5). For example, might be calculated in the following way: Three hundred ( ), fifty ( ) nine (4 + 5). Your turn, try this one using the strategy: Your turn, try this one using the strategy: Seven hundred ( ), seventy ( ), three (1 + 2) = 773 Addition

Addition Rounding for Estimation Rounding for Estimation Rounding involves substituting one or more numbers with “friendlier” numbers with which to work. Rounding involves substituting one or more numbers with “friendlier” numbers with which to work. For example, might be rounded as or For example, might be rounded as or Your turn, try this one using the strategy: Your turn, try this one using the strategy: might be rounded as or 900

Addition Front-End Estimation Front-End Estimation This strategy involves adding from the left and then grouping the numbers in order to adjust the estimate. This strategy involves adding from the left and then grouping the numbers in order to adjust the estimate. For example might be calculated in the following way: Seven thousand ( ), eight hundred ( ) – no, make that 900 (39 and 67 is about another hundred) so that’s about For example might be calculated in the following way: Seven thousand ( ), eight hundred ( ) – no, make that 900 (39 and 67 is about another hundred) so that’s about Your turn, try this one using the strategy: Your turn, try this one using the strategy: Eight thousand ( ), five hundred ( ) and is about another 50 so that’s about 8550.

Addition Compatible Number Strategy Compatible Number Strategy Compatible numbers are number pairs that go together to make “friendly” numbers. That is, numbers that are easy to work with. Compatible numbers are number pairs that go together to make “friendly” numbers. That is, numbers that are easy to work with. To add for example you might add to make 100 and then add 3 to make 103. To add for example you might add to make 100 and then add 3 to make 103. Your turn, try this one using the strategy: Your turn, try this one using the strategy: Add to make 100 and then add 9 to make 109 Add to make 100 and then add 9 to make 109

Addition Near Compatible Estimation Near Compatible Estimation Knowledge of the compatible numbers that are used for mental calculations is used for estimation. Knowledge of the compatible numbers that are used for mental calculations is used for estimation. For example, in estimating , one might do the following mental calculation: and sum to about 100. Add the 19. The answer is about 219. For example, in estimating , one might do the following mental calculation: and sum to about 100. Add the 19. The answer is about 219. Your turn, try this one using the strategy: Your turn, try this one using the strategy: and sum to about 100. Add the 62. The answer is about and sum to about 100. Add the 62. The answer is about 162.

Addition Balancing Strategy 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. 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, becomes (add 2 to 68 and take 2 from 57) = 125 For example, becomes (add 2 to 68 and take 2 from 57) = 125 Your turn, try this one using the strategy: Your turn, try this one using the strategy: becomes (add 2 to 33 and take 2 from 42) = becomes (add 2 to 33 and take 2 from 42) = 75

Addition Clustering in Estimation Clustering in Estimation Clustering involves grouping addends and determining the average. Clustering involves grouping addends and determining the average. For example, when estimating , notice that the addends cluster around 50. The estimate would be 250 (5 x 50) For example, when estimating , notice that the addends cluster around 50. The estimate would be 250 (5 x 50) Your turn, try this one using the strategy: Your turn, try this one using the strategy: Notice that the addends cluster around 20. The estimate would be 60 (3 x 20)

Addition Special Tens Strategy 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. 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 For example 500 and 500 = 1000 Your turn, try this one using the strategy: Your turn, try this one using the strategy: = =

Addition Compensation Strategy Compensation Strategy In this stage, you substitute a compatible number for one of the numbers so that you can more easily compute mentally. 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 one might think ( ) – 1. For example, in doing the calculation one might think ( ) – 1. Your turn, try this one using the strategy: Your turn, try this one using the strategy: ( ) – 2 = 52 – 2 = 52 – 2 = 50 = 50

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

Subtraction Compatible Number Estimation Compatible Number Estimation Knowledge of compatible numbers can be used to find an estimate when subtracting. Look for the near compatible pairs. 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 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: 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

Subtraction Front-End Strategy Front-End Strategy When there is no need to carry, simply subtract from left to right. 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. 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: 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 Think 2000 – 1000 = 1000, 600 – 400 = 200, 40 – 30 = 10, 5 – 2 = 3. The answer is 1213.

Subtraction Front-End Estimation Front-End Estimation For questions with no carrying in the highest two place values, simply subtract those place values for a quick 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 For example, the answer to $ $ is about $ $ $ is about $ Your turn, try this one using the strategy: Your turn, try this one using the strategy: $ – $ $ – $ $ – $ is about $ $ – $ is about $640.00

Subtraction Compatible Numbers Strategy Compatible Numbers Strategy This works well for powers of 10. Think what number will make the power of 10. 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. 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: Your turn, try this one using the strategy: 1000 – – 724 Think what goes with 724 to make The answer is 276. Think what goes with 724 to make The answer is 276.

Subtraction Equal Additions Strategy for 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. 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. 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: Your turn, try this one using the strategy: 57 – – 42 Add three to both numbers to give 60 – 45 which equals 15 Add three to both numbers to give 60 – 45 which equals 15

Subtraction Compensation Strategy for Subtraction Compensation Strategy for Subtraction As with addition, subtract the “friendly” number and add the difference. As with addition, subtract the “friendly” number and add the difference. For example, $ $0.98 For example, $ $0.98 ($ $1.00) + $0.02 = $2.29 ($ $1.00) + $0.02 = $2.29 Your turn, try this one using the strategy: Your turn, try this one using the strategy: $10.00 – $3.85 ($ $4.00) + $0.15 = $6.15 ($ $4.00) + $0.15 = $6.15

Subtraction “Counting On” Strategy for Subtraction “Counting On” Strategy for Subtraction Visualize the numbers on a number line. 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. 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 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. You need 25 to make 100 from 75, then 100 to 200 and then another 12. The answer is 137.

Subtraction “Counting On” Estimation “Counting On” Estimation “Counting On” can also be used for estimation. “Counting On” can also be used for estimation. For example, to estimate 894 – 652, think that gives about 850. Then another 50 gives about 900. The difference is about 250. For example, to estimate 894 – 652, think that gives about 850. Then another 50 gives about 900. The difference is about 250. Your turn, try this one using the strategy: Your turn, try this one using the strategy: