mental arithmetic strategies

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Strategy 1: Subtract in two parts 53 8 = 53 3 5 = 50 5 = 45 72 6 = 72 2 4 = 70 4 = 66 Subtract 8 in two parts: first 3, then 5. Subtract 6 in two parts: first 2, then 4. In other words, first subtract to the previous whole ten, then the rest. 1. Subtract the elevated number in parts first subtract to the previous whole ten; then the rest. − 5 / \ a. 51 1 4 = ______ 7 / \ b. 62 ____ − ____ = ______ 4 / \ c. 33 ____ − ____ = ______ 5 / \ d. 92 ____ − ____ = ______ 6 / \ e. 75 ____ − ____ = ______ − 7 / \ f. 63 ____ − ____ = ______ 7 / \ 5 / \

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EXERCISE ON MENTAL ARITHMETIC STRATEGIES

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Strategy 1: Subtract in two parts

53 8

=53 35

= 505= 45

72 6

=72 24

= 704= 66

Subtract 8 in two parts: first 3, then 5.Subtract 6 in two parts: first 2, then 4.

In other words, first subtract to theprevious whole ten, then the rest.

1. Subtract the elevated number in partsfirst subtract to the previous whole ten; then the rest. 5/ \

a.51 1 4= ______

7/ \

b.62____ ____= ______

4/ \

c.33____ ____= ______

5/ \

d.92____ ____= ______

6/ \

e.75____ ____= ______

7/ \

f. 63____ ____= ______

7/ \

g.35____ ____= ______

5/ \

h.74____ ____= ______

2. First subtract the balls that are not in the ten-groups.a.51 7 = _______51 5 = _______51 3 = _______51 6 = _______

b.42 4 = _______42 5 = _______42 3 = _______42 6 = _______

Strategy 2: Use known subtraction facts

Since 14 6 = 8, we know that the answer to 74 6 will end in 8,but it will be in the sixties sixty-something. So it is 68.Since 15 8 = 7, we know that the answer to 55 8 will end in 7,but it will be in the forties forty-something. So it is 47.

3.Subtract. The first problem in each box is a helping problem for the others.a.14 9 = _______ 24 9 = _______ 44 9 = _______b.17 8 = _______ 27 8 = _______ 37 8 = _______c.12 9 = _______ 52 9 = _______ 32 9 = _______

d.15 9 = _______ 65 9 = _______ 45 9 = _______e.13 8 = _______ 33 8 = _______ 93 8 = _______f.16 8 = _______ 86 8 = _______ 36 8 = _______

4.a.Amy has $32. She bought a comic book for $7. How much does she have now?b.Peter had $29. A toy train he wants costs $39. Mom paid him $5 for working. How much more does Peter now need to buy the train?c.A flower shop has 55 roses. Eight of them are white, and the rest are red. How many are red?

Strategy 3:Subtract in parts: tens and ones

Break the number being subtracted into its tens and ones. Subtract in parts.

75 21

=75 201

= 551= 54

First subtract 20, then 1.

87 46

=87 406

= 476= 41

First subtract 40, then 6.

5.Subtract in parts: Break the second number into its tens and ones.a.89 26

89 206

= __________b.56 35

56

= __________c.75 51

75

= __________

d.69 19

e.67 36

f.64 33

Strategy 4: Add.

You can add backwards. This works well if the two numbers are close to each other.Instead of subtracting, think how much you need to add to the number being subtracted (the subtrahend) in order to get the number you are subtracting from (the minuend).

71 67 = ??Think: 67 +____= 71558 556 = ??Think: 556 +____= 558

6. Subtract.a.78 75 = _______ 61 58 = _______b.112 108 = _______ 692 688 = _______c.505 499 = _______ 1000 994 = _______

7. You had $50. You purchased two bouquets of roses for $13 each. How much do you have left after the purchase?8. What if you boughtthreebouquets of roses for $13 each with your $50? How much would you have left after the purchase?9. Fifteen children were playing on the playground. Seven of them left. Then, ten more children came. How many are playing on the playground now?10. A lion chased an antelope for 400 feet, then another 200 feet, and lastly 200 feet more. Then the lion pounced on the antelope. What was the total number of feet that the lion chased the antelope?

Strategy 5: Add up to find the difference.

To find the difference, start at the smaller number, andadd upuntil youget to the bigger number. You can first complete the next ten, then add whole tens, then add ones again.84 37 = ?37 +3=40

40 +40=80

80 +4= 84

I added 3, 40, and 4 or a total of 47.84 37 = 47.92 35 = ?35 +5=40

40 +50=90

90 +2= 92

I added a total of 57.92 35 = 57.

11.Add up to find the differences, or use some other strategy such as subtracting in parts.a.65 26= _____+

+

+

26306065

b.83 35= _____+

+

+

35408083

c.56 28 = _______55 24 = _______d.72 18 = _______82 46 = _______e.54 37 = _______91 57 = _______f.74 55 = _______63 34 = _______