Ms. StewartMs. StewartMath 7 and Math 8Math 7 and Math 8

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AdditionAdditionBreak Up the Numbers StrategyBreak Up the Numbers Strategy This strategy is used when regrouping This strategy is used when regrouping

is required.  One of the addends is is required.  One of the addends is broken up into its expanded form and broken up into its expanded form and added in parts to the other addend.  added in parts to the other addend. 

For example 57 + 38 might be For example 57 + 38 might be calculated in this way: 57 + 30 is 87 calculated in this way: 57 + 30 is 87 and 8 more is 95.and 8 more is 95.

Your turn, try this one using the Your turn, try this one using the strategy:strategy:62 + 27 62 + 27

62 + 20 is 82 and 7 more is 8962 + 20 is 82 and 7 more is 89

Front-End (left to right) StrategyFront-End (left to right) Strategy This commonly used strategy involves This commonly used strategy involves

adding the front-end digits and proceeding adding the front-end digits and proceeding to the right, keeping a running total in your to the right, keeping a running total in your head.  head. 

For example, 124 + 235 might be calculated For example, 124 + 235 might be calculated in the following way: Three hundred (200 + in the following way: Three hundred (200 + 100), fifty (20 + 30) nine (4 + 5).100), fifty (20 + 30) nine (4 + 5).

Your turn, try this one using the strategy:Your turn, try this one using the strategy:

541 + 232541 + 232

Seven hundred (500 + 200), seventy (40 + Seven hundred (500 + 200), seventy (40 + 30), three (1 + 2)30), three (1 + 2)

= 773= 773

AdditionAddition

AdditionAddition Rounding for EstimationRounding for Estimation Rounding involves substituting one Rounding involves substituting one

or more numbers with “friendlier” or more numbers with “friendlier” numbers with which to work.  numbers with which to work. 

For example, 784 + 326 might be For example, 784 + 326 might be rounded as 800 + 300 or 1100.rounded as 800 + 300 or 1100.

Your turn, try this one using the Your turn, try this one using the strategy:strategy:

113 + 796 113 + 796

113 + 796 might be rounded as 113 + 796 might be rounded as 100 + 800 or 900 100 + 800 or 900

AdditionAddition Front-End EstimationFront-End Estimation This strategy involves adding from the left This strategy involves adding from the left

and then grouping the numbers in order to and then grouping the numbers in order to adjust the estimate.  adjust the estimate. 

For example 5239 + 2667 might be For example 5239 + 2667 might be calculated in the following way: Seven calculated in the following way: Seven thousand (5000 + 2000), eight hundred thousand (5000 + 2000), eight hundred (600 +200) – no, make that 900 (39 and (600 +200) – no, make that 900 (39 and 67 is about another hundred) so that’s 67 is about another hundred) so that’s about 7900.about 7900.

Your turn, try this one using the strategy:Your turn, try this one using the strategy:4216 + 43274216 + 4327Eight thousand (4000 + 4000), five Eight thousand (4000 + 4000), five hundred (200 + 300) and 16 + 27 is about hundred (200 + 300) and 16 + 27 is about another 50 so that’s about 8550.another 50 so that’s about 8550.

AdditionAddition Compatible Number StrategyCompatible Number Strategy Compatible numbers are number pairs that go Compatible numbers are number pairs that go

together to make “friendly” numbers.  That is, together to make “friendly” numbers.  That is, numbers that are easy to work with.  numbers that are easy to work with. 

To add 78 + 25 for example you might add 75 To add 78 + 25 for example you might add 75 + 25 to make 100 and then add 3 to make 103.+ 25 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:

50 + 5950 + 59

Add 50 + 50 to make 100 and then add 9 Add 50 + 50 to make 100 and then add 9 to make 109to make 109

AdditionAddition Near Compatible EstimationNear Compatible Estimation Knowledge of the compatible numbers that are Knowledge of the compatible numbers that are

used for mental calculations is used for used for mental calculations is used for estimation.  estimation. 

For example, in estimating 76 + 45 + 19 +26 For example, in estimating 76 + 45 + 19 +26 +52, one might do the following mental +52, one might do the following mental calculation: 76 + 26 and 52 + 45 sum to about calculation: 76 + 26 and 52 + 45 sum to about 100.  Add the 19.  The answer is about 219.100.  Add the 19.  The answer is about 219.

Your turn, try this one using the strategy:Your turn, try this one using the strategy:23 + 62 + 25 + 43 + 1023 + 62 + 25 + 43 + 10

23 + 25 and 43 + 10 sum to about 100. 23 + 25 and 43 + 10 sum to about 100. Add the 62. The answer is about 162.Add the 62. The answer is about 162.

AdditionAddition Balancing StrategyBalancing Strategy A variation of the compatible number strategy, A variation of the compatible number strategy,

this strategy involves taking one or more from this strategy involves taking one or more from one addend and adding it to the other.  one addend and adding it to the other. 

For example, 68 + 57 becomes 70 + 55 (add 2 For example, 68 + 57 becomes 70 + 55 (add 2 to 68 and take 2 from 57) = 125to 68 and take 2 from 57) = 125

  Your turn, try this one using the Your turn, try this one using the strategy:strategy:

33 + 4233 + 42

33 + 42 becomes 35 + 40 (add 2 to 33 33 + 42 becomes 35 + 40 (add 2 to 33 and take 2 from 42) = 75and take 2 from 42) = 75

AdditionAddition Clustering in EstimationClustering in Estimation Clustering involves grouping addends and Clustering involves grouping addends and

determining the average.  determining the average.  For example, when estimating 53 + 47 + 48 For example, when estimating 53 + 47 + 48

+ 58 +52, notice that the addends cluster + 58 +52, notice that the addends cluster around 50.  The estimate would be 250 (5 x around 50.  The estimate would be 250 (5 x 50)50)

Your turn, try this one using the strategy:Your turn, try this one using the strategy:

22 + 18 + 2622 + 18 + 26

Notice that the addends cluster around 20.  Notice that the addends cluster around 20.  The estimate would be 60 (3 x 20)The estimate would be 60 (3 x 20)

AdditionAddition Special Tens Strategy Special Tens Strategy In the early grades, you learn the In the early grades, you learn the

number of pairs that total ten – 1 and 9, number of pairs that total ten – 1 and 9, 2 and 8, 3 and 7, and so on.  These can 2 and 8, 3 and 7, and so on.  These can be extended to such combinations as be extended to such combinations as 10 and 90, 300 and 700, etc.10 and 90, 300 and 700, etc.

For example 500 and 500 = 1000For example 500 and 500 = 1000 Your turn, try this one using the Your turn, try this one using the

strategy:strategy: 4000 + 60004000 + 6000 = 10 000= 10 000

AdditionAddition Compensation StrategyCompensation Strategy In this stage, you substitute a compatible In this stage, you substitute a compatible

number for one of the numbers so that number for one of the numbers so that you can more easily compute mentally.  you can more easily compute mentally. 

For example, in doing the calculation 47 + For example, in doing the calculation 47 + 29 one might think (47 + 30) – 1.29 one might think (47 + 30) – 1.

Your turn, try this one using the strategy:Your turn, try this one using the strategy:32 + 1832 + 18(32 + 20) – 2(32 + 20) – 2

= 52 – 2 = 52 – 2 = 50= 50

AdditionAddition Consecutive Number StrategyConsecutive Number Strategy When adding three consecutive numbers, When adding three consecutive numbers,

the sum is three times the middle number.the sum is three times the middle number. For example 1 + 2 + 3 = 6For example 1 + 2 + 3 = 6

2 x 3 = 62 x 3 = 6 Your turn, try this one using the strategy:Your turn, try this one using the strategy:

5 + 6 + 75 + 6 + 7

5 + 6 + 7 = 185 + 6 + 7 = 18

6 x 3 = 186 x 3 = 18

SubtractionSubtraction Compatible Number EstimationCompatible Number Estimation Knowledge of compatible numbers can be Knowledge of compatible numbers can be

used to find an estimate when subtracting.  used to find an estimate when subtracting.  Look for the near compatible pairs.  Look for the near compatible pairs. 

For example when subtracting 1014 – 766, For example when subtracting 1014 – 766, one might think of the 750 and 250 pairing; one might think of the 750 and 250 pairing; an estimate for 1014 – 766 would be 250an estimate for 1014 – 766 would be 250

  Your turn, try this one using the strategy:Your turn, try this one using the strategy:

312 – 157312 – 157

Think of the 150 and 150 pairing; an Think of the 150 and 150 pairing; an estimate for 312 – 157 would be 150 estimate for 312 – 157 would be 150

SubtractionSubtraction Front-End StrategyFront-End Strategy When there is no need to carry, simply When there is no need to carry, simply

subtract from left to right. subtract from left to right.  For example to subtract 368 – 125 think 300 For example to subtract 368 – 125 think 300

– 100 = 200, 60 – 20 = 40, 8 – 5 = 3.  The – 100 = 200, 60 – 20 = 40, 8 – 5 = 3.  The answer is 243.answer is 243.

  Your turn, try this one using the strategy:Your turn, try this one using the strategy: 2645 – 14322645 – 1432 Think 2000 – 1000 = 1000, 600 – 400 = 200, Think 2000 – 1000 = 1000, 600 – 400 = 200,

40 – 30 = 10, 5 – 2 = 3. The answer is 1213. 40 – 30 = 10, 5 – 2 = 3. The answer is 1213.

SubtractionSubtraction Front-End EstimationFront-End Estimation For questions with no carrying in the highest For questions with no carrying in the highest

two place values, simply subtract those place two place values, simply subtract those place values for a quick estimation.  values for a quick estimation. 

For example, the answer to For example, the answer to $465.98 - $345.77 is about $120.00$465.98 - $345.77 is about $120.00 Your turn, try this one using the strategy:Your turn, try this one using the strategy: $863.50 – $234.99$863.50 – $234.99 $863.50 – $234.99 is about $640.00$863.50 – $234.99 is about $640.00

SubtractionSubtraction Compatible Numbers StrategyCompatible Numbers Strategy This works well for powers of 10.  Think This works well for powers of 10.  Think

what number will make the power of 10.  what number will make the power of 10.  For example, to subtract 100 – 54, think For example, to subtract 100 – 54, think

what goes with 54 to make 100.  The what goes with 54 to make 100.  The answer is 46.answer is 46.

  Your turn, try this one using the strategy:Your turn, try this one using the strategy:

1000 – 7241000 – 724

Think what goes with 724 to make 1000. Think what goes with 724 to make 1000. The answer is 276.The answer is 276.

SubtractionSubtraction Equal Additions Strategy for SubtractionEqual Additions Strategy for Subtraction This strategy avoids regrouping.  You add This strategy avoids regrouping.  You add

the same number to both the subtrahend the same number to both the subtrahend and minuend to provide a “friendly” and minuend to provide a “friendly” number for subtracting, then subtract.  number for subtracting, then subtract. 

For example, to subtract 84 – 58, add two For example, to subtract 84 – 58, add two to both numbers to give 86 – 60.  This can to both numbers to give 86 – 60.  This can be done mentally.  The answer is 26.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 57 – 42 Add three to both numbers to give 60 – 45 Add three to both numbers to give 60 – 45

which equals 15which equals 15

SubtractionSubtraction Compensation Strategy for SubtractionCompensation Strategy for Subtraction As with addition, subtract the “friendly” As with addition, subtract the “friendly”

number and add the difference.  number and add the difference.  For example, $3.27 - $0.98 For example, $3.27 - $0.98

($3.27 - $1.00) + $0.02 = $2.29($3.27 - $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$10.00 – $3.85

($10.00 - $4.00) + $0.15 = $6.15 ($10.00 - $4.00) + $0.15 = $6.15

SubtractionSubtraction ““Counting On” Strategy for SubtractionCounting 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, For example, 110 – 44.  You need 6 to make 50 from 44,

then 50 to make 100, then another 10.  The answer is 66.then 50 to make 100, then another 10.  The answer is 66.

Your turn, try this one using the strategy: Your turn, try this one using the strategy: 212 – 75 212 – 75

You need 25 to make 100 from 75, then 100 to 200 You need 25 to make 100 from 75, then 100 to 200 and then another 12. The and then another 12. The answer is 137.answer is 137.

SubtractionSubtraction ““Counting On” EstimationCounting On” Estimation ““Counting On” can also be used for Counting On” can also be used for

estimation.  estimation.  For example, to estimate 894 – 652, For example, to estimate 894 – 652,

think that 652 + 200 gives about 850.  think that 652 + 200 gives about 850.  Then another 50 gives about 900.  The Then another 50 gives about 900.  The difference is about 250.difference is about 250.

Your turn, try this one using the Your turn, try this one using the strategy:strategy: