Number Sense



Mental Math Strategies

Adding or Subtracting in Parts using the Distributive Property

Ex. 346 + 128 = 346 + 100 = 446 + 20 = 466 + 8= 474

456 – 174 = 456 – 100 = 356 – 70 – 286 – 4 = 282

Compatible Numbers or Make Ten (Twenty, One-hundred, etc.)

Ex. 6 +8 +4 + 4 +2 = (6 + 4) + (8 + 2) + 4

or

Ex. 45 + 45 + 37 + 23 + 55 = (45 + 55) + (37 + 23) + 45

Multiplying in Parts using the Distributive Property

Ex. 67 ? 7 = (60 ? 7) + (7 ? 7)

Up over the tens

Ex. 344 + 79 = 344 + 6 = 350 + 73

Taking and Giving

Ex. 45 + 98 = 50 + 93 45 + 5 = 50 and 98 – 5 = 93

Giving and Taking Back

Ex. 63 – 28 = 68 – 28 = 40 - 5 63 + 5 = 68

58 ? 7 = (60 ? 7) – (2 ? 7)

Doubling

Ex. 56 ? 4 = 56 ? 2 = 112 ? 2 = 224

Doubling and Halving

Ex. 67 ? 5 = 67 ? 10 = 670 / 2 = 33

Mental Math Practice

Strategy 1: Adding or Subtracting in Parts using the Distributive Property

Ex. a) 346 + 128 = 346 + 100 = 446 + 20 = 466 + 8 = 474

b) 456 – 174 = 456 – 100 = 356 – 70 – 286 – 4 = 282

1. 74 + 38 = 74 + ____ = ____ + ____ = _____

2. 95 + 29 = 95 + ____ = ____ + ____ = _____

3. 88 + 36 = 88 + ____ = ____ + ____ = _____

4. 56 + 49 = 56 + ____ = ____ + ____ = _____

5. 58 – 35 = 58 - ____ = ____ - ____ = ____

6. 87 – 49 = 87 - ____ = ____ - ____ = ____

7. 345 – 74 = 345 - ____ = ____ - ____ = _____

8. 782 – 265 =

782 - ____ = ____ - ____ = ____ - ____ = _____

9. 623 – 392 =

623 - ____ = ____ - ____ = ____ - ____ = _____

10. 372 + 118 =

372 + ____ = ____ + ____ = ____ + ____ = _____

Strategy 2: Compatible Numbers or Making Tens (or twenties, fifties, hundreds using the Commutative Property and Associative Property

Ex. 4 + 8 + 7 + 12 + 3 + 9 + 6 = (4 + 6) + (8 + 12) + (7 + 3) + 9 = 49

1. 5 + 4 + 18 + 7 + 16 + 3 + 15 + 12

= (___+___) + (___+___) + (___+___) (___+___) = ___

2. 32 + 6 + 23 + 8 + 25 + 4 + 17

= (___+___) + (___+___) + (___+___) + ___ = ____

3. 19 + 34 + 5 + 16 + 3 + 21 + 2

= (___+___) + (___+___) + (___+___+____) = ____

4. 43 + 28 + 18 + 7 + 32 + 22 + 12

= (___+___) + (___+___) + (___+___) + ____ = ____

5. 75 + 12 + 25 + 17 + 13 + 3 + 15

= (___+___) + (___+___) + (___+___) + ___ = ____

Strategy 3: Multiplying in Parts using the Distributive Property

Ex. 45 x 8 = (40 x 8) + (5 x 8) = 320 + 40 = 360

1. 67 x 9 = (____ x ____) + (____ x ____)

= _____ + _____ = ______

2. 48 x 8 = (____ x ____) + (____ x ____)

= _____ + _____ = ______

3. 9 x 67 = (____ x ____) + (____ x ____)

= _____ + _____ = ______

4. 89 x 5 = (____ x ____) + (____ x ____)

= _____ + _____ = ______

Strategy 4: Up over the tens – build to the nearest ten first!

Ex. 344 + 79 = 344 + 6 = 350 + 73

1. 456 + 78 = 456 + ____ = 460 + ____ = _____

2. 76 + 89 = 76 + ____ = 80 + ____ = _____

3. 238 + 75 = 238 + ____ = _____ + ____ = _____

4. 872 + 58 = 872 + ____ = _____ + ____ = _____

5. 743 + 76 = 743 + ____ = _____ + ____ = _____

Strategy 5: Taking and Giving – take from the second number to make the first number easier to work with.

Ex. 45 + 98 = 50 + 93 = 143 (45 + 5 = 50 and 98 – 5 = 93)

782 + 25 = 800 + 7 = 807

1. 56 + 78 = ____ + ____ = _____

2. 34 + 28 = ____ + ____ = _____

3. 48 + 55 = ____ + ____ = _____

3. 785 + 29 = ____ + ____ = _____

5. 345 + 56 = ____ + ____ = _____

Strategy 6: Giving and Taking Back (Subtraction)

Ex. 63 – 28 = 35

a) Make it easier: 68 – 28 = 40;

b) Since you added 5 to 63 to get 68, you need to take it back! 40 – 5 – 35

1. 84 – 56 = 86 – 56 = 30 - _____ = _____

2. 63 – 87 = ____ - ____ = ____ - ____ = _____

3. 81 – 46 = ____ - ____ = ____ - ____ = _____

4. 94 – 29 = ____ - ____ = ____ - ____ = _____

5. 56 – 19 = ____ - ____ = ____ - ____ = _____

Strategy 7: Giving and Taking Back (Multiplication)

Ex. 58 x 7

a) Make it easier: 60 x 7 = 420;

b) Take back the extra (2 x 7); 420 – 14 = 406

1. 45 x 9 = (____ x ____) – (_____ x _____) = _____

2. 78 x 8 = (____ x ____) – (_____ x _____) = _____

3. 27 x 9 = (____ x ____) – (_____ x _____) = _____

4. 51 x 4 = (____ x ____) – (_____ x _____) = _____

5. 69 x 9 (____ x ____) – (_____ x _____) = _____

Strategy 8: Doubling (works great with powers of 2)

Ex. 56 x 4 = 56 x 2 = 112 x 2 = 224

1. 54 x 4 = 54 x 2 = _____ x 2 = ______

2. 128 x 4 = 128 x 2 = ______ x 2 = ______

3. 120 x 8 = 120 x 2 = ____ x 2 = ____ x 2 = ____ x 2 = ____

Strategy 9: Doubling and Halving (multiples of 5)

Ex. 45 x 5 = 45 x 10 = 450/2 = 225

1. 23 x 5 = 23 x 10 = ______/2 = ____

2. 67 x 5 = ____ x 10 = _____/2 = ____

3. 78 x 5 = ____ x 10 = _____/2 = ____

4. 124 x 5 = ____ x 10 = ______/2 = ____

Strategy 10: Doubling and Halving Take 2 and Tripling and Thirding . . .

Ex. 48 x 5 = 24 x 10 (1/2 of 48 = 24 and 2x 5 = 10)

3 x 24 = 9 x 8

1. 16 x 4 = _____ x _____ = _____

2. 28 x 4 = _____ x _____ = _____

3. 27 x 3 = _____ x _____ = _____

4. 18 x 6 = _____ x _____ = _____

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