Transcript Document 7127134

Mental Math
Strand B
Grade Five
Quick Addition – no regrouping
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Begin at the front end of the numbers and add.
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Example: 56 + 23
Think: Add 50 and 20 for 70, then add 6 and 3 for 9– answer 79
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Example: 2341 + 3400
Think: Add 2000 and 3000 for 5000, then add 300 and 400 for
700, and then finally add 41. The answer is 5741.
Example: 0.34 + 0.25
Think: Add .30 and .20 for .50 and then add .04 and .05 for .09
– the answer is 0.59.
Quick Addition – no regrouping
71 + 12
44 + 53
291 + 703
507 + 201
5200 + 3700
4423 + 1200
0.3 + 0.6
0.7 + 0.1
2.45 + 3.33
0.5 + 0.1
Quick Addition – no regrouping
37 + 51
66 + 23
234 + 52
534 + 435
4067 + 4900
6621 + 2100
6200 + 1700
6334 + 2200
0.2 + 0.5
0.45 + 0.33
Front End Addition
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Add the highest place value first and the
add the sums of the next place value.
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Example: 450 + 380
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Think: 400 + 300 is 700, and 50 and 80 is
130 and 700 plus 130 is 830.
Front End Addition
340 + 220
470 + 360
3500 + 2300
2900 + 6000
8800 + 1100
5400 + 3400
4.9 + 3.2
3.6 + 2.9
0.62 + 0.23
5.4 + 3.7
Front End Addition
607 + 304
3700 + 3200
2700 + 7200
6800 + 2100
7500 + 2400
6300 + 4400
6.6 + 2.5
0.75 + 0.05
1.4 + 2.5
o.36 + 0.43
Finding Compatibles
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Look for pairs of numbers that add to powers
of 10 (10, 100, and 1000).
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Example: 400 + 720 + 600
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Think: 400 and 600 is 1000,
so the sum is 1720.
Finding Compatibles
800 + 740 + 200
4400 + 1600 + 3000
3250 + 3000 + 1750
3000 + 300 + 700 + 2000
290 + 510
0.6 + 0.9 + 0.4 + 0.1
0.7 + 0.1 + 0.9 + 0.3
0.4 + 0.4 + 0.6 + 0.2 + 0.5
0.80 + 0.26
0.2 + 0.4 + 0.8 + 0.6
Finding Compatibles
300 + 437 + 700
900 + 100 + 485
9000 + 3300 + 1000
2200 + 2800 + 600
3400 + 5600
02. + 0.4 + 0.3 + 0.8 +0.6
0.25 + 0.50 + 0.75
.45 + 0.63
475 + 25
125 + 25
Break Up and Bridge
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Begin with the first number and add the values
in the place values starting with the largest of
the second numbers.
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Example: 5300 + 2400
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Think: 5300 and 2000 (from the 2400) is
7300 and 7300 plus 400 (from the rest
of 2400) is 7700.
Break Up and Bridge
7700 + 1200
7300 + 1400
5090 + 2600
4100 + 3600
2800 + 6100
4.2 + 3.5
6.1 + 2.8
4.15 + 3.22
15.46 + 1.23
6.3 + 1.6
Break Up and Bridge
17 400 + 1300
5700 + 2200
3300 + 3400
15 500 + 1200
2200 + 3200
0.32 + 0.56
5.43 + 2.26
43.30 + 8.49
4.2 + 3.7
2.08 + 3.2
Compensation
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Change one number to a ten or hundred, carry
out the addition, and then adjust the answer to
compensate for the original change.
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Example: 4500 + 1900
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Think: 4500 + 2000 is 6500 but I added
100 too many; so, I subtract 100 from
6500 to get 6400.
Compensation
1300 + 800
3450 + 4800
4621 + 3800
5400 + 2900
2330 + 5900
0.71 + 0.09
0.44 + 0.29
4.52 + 0.98
0.56 + 0.08
0.17 + 0.59
Compensation
2111 + 4900
6421 + 1900
15 200 + 2900
2050 + 6800
3344 + 5500
1.17 + 0.39
0.32 + 0.19
2.31 + 0.99
25. 34 + 0.58
44.23 + 0.23
Quick Subtraction
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Use this strategy if no regrouping is needed.
Begin at the front end and subtract.
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Example: 3700 – 2400
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Think: 3-2 = 1, 7-4= 3, and add two
zeros. The answer is: 1300.
Quick Subtraction
9800 – 7200
8520 – 7200
5600 – 4100
56 000 – 23 000
0.38 – 0.21
0.96 – 0.85
0.66 – 0.42
3.86 – 0.45
0.78 – 0.50
17.36 – 0.24
Quick Subtraction
4850 – 2220
78 000 – 47 000
460 000 – 130 000
500 000 – 120 000
0.33 – 0.23
0.98 – 0.86
0.66 – 0.41
3.85 – 0.43
0.64 – 0.32
0.76 – 0.42
Back Through 10/100
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Subtract part of the first number to get to the nearest
one, ten, hundred, or thousand and then subtract the
rest of the next number.
Use this strategy when the numbers are far apart.
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Example: 530 – 70
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Think: 530 subtract 30 (one part of the 70) is
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500 and 500 subtract 40 (the other part of
the 70) is 460.
Back Through 10/100
420 – 60
540 – 70
340 – 70
760 – 70
9200 – 500
7500 – 700
9500 – 600
4700 – 800
800 – 600
3400 - 700
Back Through 10/100
630 – 60
320 – 50
6100 – 300
4200 – 800
2300 – 600
9100 – 600
7600 – 600
9400 – 500
4500 – 600
700 - 500
Counting on to Subtract
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Count the difference between the two numbers by
starting with the smaller, keeping track of the distance
to the nearest one, ten, hundred, or thousand; and add
to this amount the rest of the distance to the greater
number.
Note: this strategy is most effective when two
numbers involved are quite close together.
Example: 2310 – 1800
Think: It is 200 from 1800 to 2000 and 310
from 2000 to 2310; therefore, the difference
is 200 plus 310, or 510.
Counting on to Subtract
5170 – 4800
9130 – 8950
7050 – 6750
3210 – 2900
2400 – 1800
15.3 – 14.9
45.6 – 44.9
34.4 – 33.9
27.2 – 26.8
23.5 – 22.8
Counting on to Subtract
1280 – 900
8220 – 7800
4195 – 3900
8330 – 7700
52.8 – 51.8
19.1 – 18.8
50.1 – 49.8
70.3 – 69.7
3.25 – 2.99
24.12 – 23.99
Compensation
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Change one number to a ten, hundred or
thousand, carry out the subtraction, and then
adjust the answer to compensate for the
original change.
Example: 5760 – 997
Think: 5760 – 1000 is 4760; but I
subtracted 3 too many; so, I add 3 to
4760 to compensate to get 4763.
Compensation
8620 – 998
9850 – 498
4222 – 998
4100 – 994
3720 – 996
7310 – 194
5700 – 397
2900 – 595
8425 - 990
75 316 - 9900
Compensation
854 – 399
953 – 499
647 – 198
523 – 198
805 – 398
642 – 198
763 – 98
534 – 488
512 – 297
7214 - 197
Balancing For a Constant Difference
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Add or subtract the same amount from both the
first number and the second number so that
each number is easier to work with.
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Example: 345 – 198
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Think: Add 2 to both numbers to get 347
– 200; so the answer is 147.
Balancing for a Constant Difference
649 – 299
912 – 797
631 -499
971 – 696
563 – 397
6.4 – 3.9
4.3 – 1.2
6.3 – 2.2
15. 3 – 5.7
7.6 – 1.98
Balancing for a Constant Difference
486 – 201
382 – 202
564 – 303
437 – 103
829 – 503
8.63 – 2.99
6.92 – 4.98
7.45 – 1.98
27.84 – 6.99
5.40 – 3.97
Break Up and Bridge
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Begin with the first number and subtract the
values in the place values, beginning with the
highest of the second number.
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Example: 8369 – 204
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Think: 8369 subtract 200 (from the 204)
is 8169 and 816 minus 4 (the rest of the
204) is 8165.
Break Up and Bridge
736 – 301
848 – 207
927 – 605
622 – 208
928 – 210
9275 – 8100
10 270 – 8100
3477 – 1060
6350 – 4200
15 100 - 3003
Break Up and Bridge
647 – 102
741 – 306
847 – 412
3586 – 302
758 – 205
38 500 – 10 400
8461 – 4050
4129 – 2005
137 400 – 6100
9371 - 8100
Multiplication and Division
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When you need to divide, think of the question as a
multiplication question.
Example: 12 ÷ 2
Think: 2 x ____ = 12 -- the answer is 6.
40 ÷ 5
45 ÷ 9
56 ÷ 7
54 ÷ 6
36 ÷ 4
Division as Multiplication
240 ÷ 12
880 ÷ 40
1470 ÷ 70
3600 ÷ 12
1260 ÷ 60
6000 ÷ 12
660 ÷ 30
690 ÷ 30
650 ÷ 50
920 ÷ 40
Division as Multiplication
480 ÷ 12
880 ÷ 11
880 ÷ 20
490 ÷ 70
4800 ÷ 12
2400 ÷ 60
6000 ÷ 50
660 ÷ 11
5400 ÷ 6
1200 ÷ 30
Using Mulitplication Facts for Tens,
Hundreds and Thousands
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Multiply the 1-digit number by the one non-zero digit in
the number.
Example: 4 x 6000
Think: 4 x 6 and then add the three zeros for an answer
of 24 000.
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If you have two non-zero digits in the question, you
could mulitply them and then add the appropriate
number of zeros.
Example: 30 x 80
Think: 3 x 8 = 24 and then add two zeros for an answer
of 2400.
Using Multiplication Facts for Tens,
Hundreds and Thousands
30 x 4
20 x 300
6 x 50
6 x 200
90 x 60
10 x 400
8 x 40
70 x 7
8 x 600
4 x 5000
Using Multiplication Facts for Tens,
Hundreds, and Thousands
6 x 900
3 x 70
9 x 30
90 x 40
300 x 4
800 x 7
9 x 800
5 x 900
3 x 2000
6 x 6000
Multiplying by 10, 100, and 1000

Multiplying by 10 increases all the place values of a
number by one place.
Example: 10 x 67
Think: the 6 tens will increase to 6 hundreds and the 7
ones will increase to 7 tens; therefore, the answer is
670.
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Multiplying by 100 increases all the place values of
anumber by two places, and multiplying by 1000
increases all the place values of a number by three
places.
Multiplying by 10, 100, and 1000
10 x 53
100 x 7
100 x 74
$73 x 1000
10 x 3.3
100 x 2.2
100 x 0.12
1000 x 5.66
1000 x 14
100 x 8.3
Multiplying by 10, 100, and 1000
8.36 x 10
100 x 0.41
1000 x 2.2
8.02 x 1000
100 x 15
16 x $1000
0.7 x 10
100 x 9.9
100 x 0.07
1000 x 43.8
Dividing by 0.1, 0.01, and 0.001
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Dividing by 0.1, 0.01, and 0.001 is like multiplying by 10,
100, and 1000. Dividing by tenths increases all the lace values
of a number by one place, by hundredths by two places, and by
thousandths by three places.
Example: 0.4 ÷ 0.1
Think: the 4 tenths will increase to 4 ones, therefore the
answer is 4.
Example: 3 ÷ 0.001
Think: The 3 ones will increase to 3 thousands, therefore the
answer is 3000.
Dividing by 0.1, 0.01, and 0.001
5 ÷ 0.1
46 ÷ 0.1
0.5 ÷ 0.1
0.02 ÷ 0.1
14.5 ÷ 0.1
4 ÷ 0.01
1 ÷ 0.01
0.2 ÷ 0.01
0.8 ÷ 0.01
8.2 ÷ 0.01
Dividing by 0.1, 0.01, and 0.001
7 ÷ 0.01
9 ÷ 0.01
0.3 ÷ 0.01
5.2 ÷ 0.01
5 ÷ 0.001
0.2 ÷ 0.001
7 ÷ 0.001
3.4 ÷ 0.001
1 ÷ 0.001
0.1 ÷ 0.001
Multiplying by 0.1, 0.01, and 0.001
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Multiplying by 0.1 decreases all the place values of a number
by one place.
Multiplying by 0.01 decreases all the place values of a number
by two places.
Multiplying by 0.001 decreases all the place values of a
number by three places.
Example: 5 x 0.01
Think: the 5 ones will decreases to 5 hundredths, therefore the
answer is 0.05.
Example: 0.4 x 0.01
Think: the 4 tenths will decrease to 4 thousandths, therefore the
answer is 0.004.
Multiplying by 0.1, 0.01, and 0.001
6 x 0.01
9 x 0.1
72 x 0.1
0.7 x 0.1
1.6 x 0.1
6 x 0.01
0.5 x 0.01
2.3 x 0.01
100 x 0.01
8 x 0.01
Multiplying by 0.1, 0.01, and 0.001
3 x 0.001
21 x 0.001
62 x 0.001
7 x 0.001
45 x 0.001
9 x 0.001
0.4 x 0.001
3.9 x 0.001
330 x 0.01
1.2 x 0.01
Dividing by 10, 100, and 1000
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Dividing by 10 decreases all the place values of a
number by one place.
Dividing by 100 decreases all the place values of a
number by two places.
Dividing by 1000 decreases all the place values of a
number by three places.
Example: 7500 ÷ 100
Think: the 7 thousands will decreases to 7 tens and the 5
hundreds will decreases to 5 ones; therefore, the
answer is 75.
Dividing by 10, 100, and 1000
70 ÷ 10
200 ÷ 10
90 ÷ 10
800 ÷ 10
40 ÷ 10
100 ÷ 10
400 ÷ 100
4200 ÷ 100
9700 ÷ 100
900 ÷ 100
Dividing by 10, 100, and 1000
7600 ÷ 100
4400 ÷ 100
6000 ÷ 100
8500 ÷ 100
10 000 ÷ 100
82 000 ÷ 1000
66 000 ÷ 1000
430 000 ÷ 1000
98 000 ÷ 1000
70 000 ÷ 1000
Front End Multiplication or the
Distributive Principle
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Find the product of the single-digit factor and
the digit in the highest place value of the
second factor, and adding to this product a
second sub-product.
Example: 3 x 62
Think: 3 times 6 is 18 tens or 180, and 3 times
2 is 6; so, 180 plus 6 is 186.
Front End Multiplication or the
Distributive Principle
53 x 3
29 x 2
62 x 4
32 x 4
83 x 3
3 x 503
606 x 6
309 x 7
410 x 5
209 x 9
Front End Multiplication or the
Distributive Principle
3 x 4200
5 x 5100
2 x 4300
4 x 2100
2 x 4300
4.6 x 2
8.3 x 5
7.9 x 6
3.7 x 4
8.9 x 5
Compensation
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This strategy can be used when one of the factors is
near ten, hundred or thousand.
Change one of the factors to a ten, hundred or
thousand, carry out the multiplication, and then adjust
the answer to compensate for the change that was
made.
Example: 7 x 198
Think: 7 times 200 is 1400, but this is 14 more than it
should be because there were 2 extra in each of the 7
groups; therefore, 1400 subtract 14 is 1368.
Compensation
6 x 39
2 x 79
4 x 49
8 x 29
6 x 89
5 x 399
9 x 198
3 x 199
8 x 698
4 x 198
Compensation
7 x 598
9 x 69
5 x 49
7 x 59
29 x 50
49 x 90
39 x 40
79 x 30
89 x 20
59 x 60
Finding Compatible Factors
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Look for pairs of factors whose product is a
power of ten and then re-associate the factors
to make the overall calculation easier.
Example: 25 x 63 x 4
Think: 4 times 25 is 100, and 100 times 63 is
6300.
Finding Compatible Factors
2 x 78 x 500
5 x 450 x 2
5 x 19 x 2
500 x 86 x 2
2 x 43 x 50
250 x 56 x 4
4 x 38 x 25
40 x 25 x 33
2 x 50 x 300
400 x 5 x 40
Finding Compatible Factors
2 x 69 x 500
5 x 400 x 2
5 x 25 x 2
500 x 87 x 2
2 x 45 x 50
250 x 65 x 4
4 x 83 x 25
40 x 25 x 44
2 x 50 x 600
400 x 5 x 20
Open Frames
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Open frames in addition – think subtraction.
Open frames in subtraction – think addition.
Open frames in multiplication – think division.
Open frames in division – think multiplication.
Example: 25 + = 85
Think: 85 – 25 = 
Open Frames
0.4 + 
= 0.9
29 000 + 
= 30 000
163 + 
= 363
.032 + 0. 
6 = 0.88
5
000 + 30 000= 87 000
36 - 
= 29
487 - 
35 = 252
3567 - 
222 = 1345
46 -2
= 23
7 – 35 = 22

Open Frames
2.24 - 
= 2.00
25 x 
= 50
30 x 
= 60
5
x = 168
9x
= 81
10 ÷ 
=5
120 ÷ 
= 12
6.3 ÷ =63

÷3=8
3
÷5=6
Estimation in Addition, Subtraction,
Multiplication, and DivisionRounding

Round each number to the highest or the
highest two places values.
Example: 348 + 230
Think: 348 rounds to 300 and 230 rounds to
200, so 300 plus 200 is 500.
Estimation in Addition, Subtraction,
Multiplication, and DivisionRounding
28 + 57
303 + 49
490 + 770
8879 + 4238
6110 + 3950
427 – 198
594 – 301
834 – 587
4768 – 3068
4807 - 1203
Estimation in Addition, Subtraction,
Multiplication, and DivisionRounding
4 x 59
9 x 43
889 x 3
7 x 821
7 x 22
370 ÷ 9
458 ÷ 5
638 ÷ 7
409 ÷ 6
732 ÷ 8
Front End Estimation
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Find a “ball-park” answer by working with
only the values in the highest place value.
Example: 4276 = 3237
Think: 4000 plus 3000 is 7000
Front End Estimation
71 + 14
647 + 312
423 + 443
4275 + 2105
1296 + 6388
823 – 240
743 – 519
718 – 338
823 – 240
743 - 519
Front End Estimation
6.7 + 1.2
0.2 + 4.9
5.32 + 0.97
0.86 + 0.93
4.8 + 4.1
6.1 – 2.2
4.1 – 0.9
1.9 – 0.2
5.9 – 3.1
12.3 10.1
Front End Estimation
467 x 4
63 x 8
44 x 7
613 x 6
481 x 9
121 ÷ 6
141 ÷ 7
102 ÷ 5
357 ÷ 5
75 ÷ 3
Adjusted Front End Estimation
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Begin by getting a Front End estimate and then
adjust the estimate to get a closer estimate by
considering the second highest place values.
Example: 437 + 541
Think: 400 plus 500 is 900, but 37 and 41
would account for about another 100;
therefore, the adjusted estimate is 900 + 100 or
1000.
Adjusted Front End Estimation
251 + 445
642 + 264
5695 + 2450
5240 + 3790
589 + 210
645 – 290
935 – 494
9145 – 4968
6210 – 2987
6148 - 3920
Adjusted Front End Estimation
2220 + 5120
4087 + 2120
6060 + 3140
4140 + 5050
7 x 341.25
3 x 943.19
6 x 280.53
2 x 722.56
8 x 776.43
9 x 371.05