mental math mental computation grade 4. quick addition this strategy can be used when no regrouping...

Mental MathMental Math

Mental ComputationMental Computation

Grade 4Grade 4

Quick AdditionQuick Addition This strategy can be used when no regrouping is This strategy can be used when no regrouping is

needed.needed. Begin at the front end of the number.Begin at the front end of the number.

Example: 71 + 12Example: 71 + 12 Think: Think: add the 7 from 71 and the 1 from add the 7 from 71 and the 1 from

12 to get 8, then add the 1 from the 71 12 to get 8, then add the 1 from the 71 and the 2 from the 12 to get 3. The and the 2 from the 12 to get 3. The answer is 83.answer is 83.

Then this is applied to sums involving Then this is applied to sums involving thousands.thousands.

Quick AdditionQuick Addition

73 + 2673 + 2632 + 5432 + 5461 + 3561 + 35

723 + 134723 + 134406 + 202406 + 202

72 + 1372 + 1364 + 3264 + 32

292 + 702292 + 702534 + 435534 + 435342 + 232342 + 232

Quick AdditionQuick Addition

6621 + 21006621 + 21001452 + 82001452 + 82004423 + 12004423 + 1200300 + 2078300 + 2078

7600 + 20647600 + 20646334 + 22006334 + 22005200 + 37005200 + 37006245 + 17126245 + 17124678 + 32114678 + 32116621 + 21006621 + 2100

Front End AdditionFront End Addition Add the highest place values and then add the Add the highest place values and then add the

sums of the next place values.sums of the next place values.

Example: 37 + 26Example: 37 + 26 Think: Think: 30 and 20 is 50, 7 and 6 is 13, and 30 and 20 is 50, 7 and 6 is 13, and

50 plus 13 is 63.50 plus 13 is 63.

Example: 450 + 380Example: 450 + 380 Think: Think: 400 and 300 is 700, 50 and 80 is 400 and 300 is 700, 50 and 80 is

130, and 700 plus 130 is 830.130, and 700 plus 130 is 830.

Front End AdditionFront End Addition

34 + 1834 + 1815 + 6615 + 6653 + 2953 + 2974 + 1974 + 19

190 + 430190 + 430340 + 220340 + 220470 + 360470 + 360607 + 304607 + 304

4200 + 53004200 + 53007700 + 11007700 + 1100

Front End AdditionFront End Addition

67 + 2267 + 2242 + 4542 + 45

561 + 220561 + 2206300 + 18006300 + 18006100 + 28006100 + 28005200 + 34005200 + 34007800 + 21007800 + 21003200 + 45003200 + 45004700 + 24004700 + 2400

10 300 + 440010 300 + 4400

Finding CompatiblesFinding Compatibles

Look for pairs of numbers that add easily Look for pairs of numbers that add easily to make a sum that will be easy to work to make a sum that will be easy to work with. Last year, we looked for numbers with. Last year, we looked for numbers that added easily to 100. This year, we that added easily to 100. This year, we need to look for numbers that add easily to need to look for numbers that add easily to 1000.1000.

Example: 400 + 720 + 600Example: 400 + 720 + 600 Think: Think: 400 and 600 is 1000, and 1000 400 and 600 is 1000, and 1000

plus 720 is 1720.plus 720 is 1720.


60 + 30 + 4060 + 30 + 4075 + 95 + 2575 + 95 + 25

300 + 437 + 700300 + 437 + 700800 + 740 + 200800 + 740 + 200900 + 100 + 485900 + 100 + 485310 + 700 + 300310 + 700 + 300750 + 250 + 330750 + 250 + 330200 + 225 + 800200 + 225 + 800342 + 500 + 500342 + 500 + 500600 + 400 + 230600 + 400 + 230


25 + 47 + 7525 + 47 + 7575 + 98 + 2575 + 98 + 2555 + 50 + 5055 + 50 + 50

300 + 445 + 700300 + 445 + 700800 + 200 + 789800 + 200 + 789400 + 983 + 600400 + 983 + 600989 + 900 + 100989 + 900 + 100878 + 500 + 500878 + 500 + 500100 + 234 + 900100 + 234 + 900

353 + 700 + 3000353 + 700 + 3000

Break Up and BridgeBreak Up and Bridge In this strategy, you leave the first number as it is In this strategy, you leave the first number as it is

and then add the place values from the next and then add the place values from the next number one at a time.number one at a time.

Example: 45 + 36Example: 45 + 36 Think: Think: 45 and 30 (from the 36) is 75, and 75 45 and 30 (from the 36) is 75, and 75

plus 6 (the rest of the 36) is 81.plus 6 (the rest of the 36) is 81.

Example: 537 + 208Example: 537 + 208 Think: Think: 537 and 200 is 737, and 737 plus 8 is 537 and 200 is 737, and 737 plus 8 is

745.745.

Break Up and BridgeBreak Up and Bridge

37 + 4537 + 4538 + 4338 + 4372 + 2872 + 28

325 + 220325 + 220439 + 250439 + 250142 + 202142 + 202301 + 435301 + 435506 + 270506 + 270370 + 327370 + 327747 + 150747 + 150


71 + 2871 + 2836 + 4236 + 4248 + 5148 + 51

106 + 31106 + 31412 + 26412 + 26

703 + 140703 + 140335 + 431335 + 431214 + 72214 + 72

526 + 331526 + 331605 + 224605 + 224

CompensationCompensation Change one number in a sum to a nearby ten or hundred Change one number in a sum to a nearby ten or hundred

and then adjust the answer to compensate for the original and then adjust the answer to compensate for the original change.change.

Example: 52 + 39Example: 52 + 39 Think: Think: 52 plus 40 is 92, but I added one too many 52 plus 40 is 92, but I added one too many

to take me to the next 10, so to compensate: I to take me to the next 10, so to compensate: I subtract one from my answer, 92 – to get 91.subtract one from my answer, 92 – to get 91.

Example: 345 + 198Example: 345 + 198 Think: Think: 345 + 200 is 545, but I added 2 too many, 345 + 200 is 545, but I added 2 too many,

so I subtract 2 from 545 to get 543.so I subtract 2 from 545 to get 543.

CompensationCompensation

43 + 943 + 945 + 845 + 8

44 + 2744 + 2756 + 856 + 8

225 + 49225 + 49504 + 199504 + 199826 + 99826 + 99371 + 18371 + 18

326 + 298326 + 298304 + 399304 + 399


56 + 856 + 865 + 2965 + 29

125 + 49125 + 49412 + 499412 + 499526 + 799526 + 799621 + 103621 + 103534 + 104534 + 104461 + 101461 + 101342 + 102342 + 102710 + 105710 + 105

Make 10s, 100s, or 1000sMake 10s, 100s, or 1000s This strategy adds to one addend to make 10, 100, or 1000.This strategy adds to one addend to make 10, 100, or 1000.

Example: 58 + 6Example: 58 + 6 Think: Think: 58 + 2 (from the 6) is 60 plus 4 (the other 58 + 2 (from the 6) is 60 plus 4 (the other

part of 6) is 64.part of 6) is 64.

Example: 350 + 59Example: 350 + 59 Think: Think: 350 plus 50 (from the 59) is 400, and 400 350 plus 50 (from the 59) is 400, and 400

plus 9 (the other part of 59) is 409.plus 9 (the other part of 59) is 409.

Example: 7400 + 790Example: 7400 + 790 Think: Think: 7400 plus 600 (from the 790) is 8000, and 7400 plus 600 (from the 790) is 8000, and

8000 plus 190 (the other part of 790) is 8190.8000 plus 190 (the other part of 790) is 8190.

Make 10s, 100s, or 1000sMake 10s, 100s, or 1000s

680 + 78680 + 78570 + 41570 + 41560 + 89560 + 89490 + 18490 + 18450 + 62450 + 62

2800 + 4602800 + 4608900 + 2308900 + 2303600 + 5223600 + 5225900 + 6605900 + 6603500 + 5903500 + 590

Make 10s, 100s, or 1000sMake 10s, 100s, or 1000s

870 + 57870 + 57170 + 40170 + 40630 + 73630 + 73780 + 67780 + 67

4700 + 4704700 + 4701700 + 8701700 + 8702200 + 9102200 + 9106300 + 8556300 + 8554800 + 4504800 + 4501800 + 7701800 + 770

Subtraction – Quick SubtractionSubtraction – Quick Subtraction

This strategy should be used when no This strategy should be used when no regrouping is needed.regrouping is needed.

Begin with the front end number.Begin with the front end number.

Example: 86 – 23Example: 86 – 23 Think: Think: 8 take away 2 is 6 and then 6 8 take away 2 is 6 and then 6

take away 3 is 3. The answer is 63.take away 3 is 3. The answer is 63.

Quick SubtractionQuick Subtraction

38 – 2538 – 2527 – 1527 – 1597 – 3597 – 3578 – 4678 – 46

745 – 23745 – 23947 – 35947 – 35

357 – 135357 – 135845 – 542845 – 542452 – 311452 – 311624 - 112624 - 112

Quick SubtractionQuick Subtraction

82 – 1182 – 1176 – 3476 – 3485 – 3185 – 3148 – 2348 – 23

846 – 324846 – 324537 – 101537 – 101704 – 502704 – 502809 – 408809 – 408639 – 628639 – 6288605 - 3048605 - 304

Back Through the 10/100 Back Through the 10/100 ExtensionExtension

Subtract a part of one of the numbers to get to the nearest Subtract a part of one of the numbers to get to the nearest tens or hundreds, and then subtract the rest of the number.tens or hundreds, and then subtract the rest of the number.

This strategy is probably most effective when one of the This strategy is probably most effective when one of the numbers is not too great.numbers is not too great.

Example: 74 – 6Example: 74 – 6 Think: Think: 74 subtract 4 (one part of the 6) is 70 and 74 subtract 4 (one part of the 6) is 70 and

70 subtract 2 (the other part of the 6) is 68.70 subtract 2 (the other part of the 6) is 68.

Example: 530 – 70Example: 530 – 70 Think: Think: 530 subtract 30 (one part of the 70) is 500 530 subtract 30 (one part of the 70) is 500

and 500 subtract 40 (the other part of the 70) is and 500 subtract 40 (the other part of the 70) is 460.460.

Back Through the 10/100Back Through the 10/100

15 – 615 – 613 – 413 – 413 – 613 – 674 – 774 – 7

850 – 70850 – 70420 – 60420 – 60760 – 70760 – 70970 – 80970 – 80340 – 70340 – 70320 - 50320 - 50

Back Through the 10/100Back Through the 10/100

42 – 742 – 761 – 561 – 515 – 715 – 797 – 897 – 834 – 734 – 7

810 – 50810 – 50630 – 60630 – 60462 – 70462 – 70852 – 70852 – 70424 - 60424 - 60

Up Through 10/100Up Through 10/100 This strategy is an extension of the “counting up through 10” strategy This strategy is an extension of the “counting up through 10” strategy

that you learned in Grade 3. Count the difference between the two that you learned in Grade 3. Count the difference between the two numbers by starting with the smaller and adding to this amount the rest numbers by starting with the smaller and adding to this amount the rest of the distance to the greater number.of the distance to the greater number.

This strategy is most effective when the two numbers in the question are This strategy is most effective when the two numbers in the question are close together.close together.

Example: 84 – 77Example: 84 – 77 Think: Think: It is 3 from 77 to 80 and 4 from 80 to 84; therefore, It is 3 from 77 to 80 and 4 from 80 to 84; therefore,

the difference is 3 plus 4, or 7.the difference is 3 plus 4, or 7.

Example: 613 – 594Example: 613 – 594 Think: Think: It is 6 594 to 600 and 13 from 600 to 613; therefore, It is 6 594 to 600 and 13 from 600 to 613; therefore,

the difference is 6 plus 13, or 19.the difference is 6 plus 13, or 19.

Up Through 10/100Up Through 10/100

95 – 8695 – 8658 – 4958 – 4988 – 7988 – 7967 – 5967 – 5934 – 2734 – 27

715 – 698715 – 698411 – 398411 – 398727 – 698727 – 698612 – 596612 – 596916 - 897916 - 897

Up Through 10/100Up Through 10/100

62 – 5562 – 5546 – 3846 – 3871 – 6371 – 6342 – 3642 – 3661 – 5661 – 56

846 – 799846 – 799817 – 798817 – 798513 – 498513 – 498631 – 597631 – 597716 - 699716 - 699

CompensationCompensation Change one of the numbers to the nearest ten or Change one of the numbers to the nearest ten or

hundred, carrying out the subtraction, and the hundred, carrying out the subtraction, and the adjust the answer to compensate for the original adjust the answer to compensate for the original change.change.

Example: 56 – 18Example: 56 – 18 Think: Think: 56 – 20 = 36, but I subtracted 2 too 56 – 20 = 36, but I subtracted 2 too

many; so, I add 2 to the answer to get 38.many; so, I add 2 to the answer to get 38.

Example: 145 – 99Example: 145 – 99 Think: Think: 145 – 100 is 45, but I subtracted 1 145 – 100 is 45, but I subtracted 1

too many; so, I add 1 to 45 to get 46.too many; so, I add 1 to 45 to get 46.


74 – 1974 – 1965 – 2965 – 2984 – 1784 – 1787 – 987 – 915 – 815 – 8

673 – 99673 – 99775 – 198775 – 198641 – 197641 – 197765 – 99765 – 99854 - 399854 - 399


83 – 2883 – 2892 – 3992 – 3973 – 1773 – 1718 – 918 – 9

534 – 398534 – 398802 – 397802 – 397721 – 497721 – 497953 – 499953 – 499647 – 198647 – 198444 - 97444 - 97

Balancing for a Constant DifferenceBalancing for a Constant Difference

This is a new strategy for Grade 4.This is a new strategy for Grade 4. Both numbers change to make subtraction easier Both numbers change to make subtraction easier

by adding or subtracting.by adding or subtracting.

Example: 87 – 19Example: 87 – 19 Think: Think: Add 1 to both numbers to get 88 – Add 1 to both numbers to get 88 –

20; so, 68 is the answer.20; so, 68 is the answer.

Example: 345 – 198Example: 345 – 198 Think: Think: Add 2 to both numbers to get 347 – Add 2 to both numbers to get 347 –

200; so, the answer is 147.200; so, the answer is 147.


85 – 1885 – 1878 – 1978 – 1988 – 4888 – 4883 – 2183 – 2195 – 4295 – 42

649 – 299649 – 299912 – 797912 – 797631 – 499631 – 499971 – 696971 – 696659 - 204659 - 204


67 – 3267 – 3242 – 1742 – 1767 – 1867 – 1894 – 1794 – 1775 – 1275 – 12

736 – 402736 – 402948 – 301948 – 301563 – 397563 – 397737 – 398737 – 398811 - 597811 - 597

Break Up and BridgeBreak Up and Bridge Begin with the first number (minuend) and Begin with the first number (minuend) and

subtract the second number (subtrahend) subtract the second number (subtrahend) beginning with the highest place value.beginning with the highest place value.

Example: 92 – 26Example: 92 – 26 Think: Think: 92 subtract 20 (from the 26) is 72 92 subtract 20 (from the 26) is 72

and 72 subtract 6 is 66.and 72 subtract 6 is 66.

Example: 745 – 203Example: 745 – 203 Think: Think: 745 subtract 200 (from the 203) is 745 subtract 200 (from the 203) is

545 and 545 minus 3 is 542.545 and 545 minus 3 is 542.


73 – 3773 – 3777 – 4277 – 4295 – 2795 – 2752 – 3352 – 3393 – 7493 – 74

736 – 301736 – 301632 – 208632 – 208928 – 210928 – 210647 – 120647 – 120848 - 220848 - 220


74 – 1574 – 1585 – 4685 – 4686 – 5486 – 5498 – 2298 – 2277 – 1577 – 15

741 – 306741 – 306847 – 402847 – 402

3580 – 1303580 – 130927 – 605927 – 605758 - 240758 - 240

Multiplication - DoublesMultiplication - Doubles

Connect the two times tables with Connect the two times tables with doubling.doubling.

2 x 22 x 2

4 x 24 x 2

2 x 52 x 5

10 x 210 x 2

2 x 32 x 3

Multiplication – the fivesMultiplication – the fives

Think of the clock. Each number is 5 Think of the clock. Each number is 5 minutes. minutes.

5 x 35 x 3

5 x 6 5 x 6

5 x 25 x 2

1 x 51 x 5

7 x 57 x 5

Multiplication – the onesMultiplication – the ones

NO CHANGE!NO CHANGE! When multiplying by one, make no change to When multiplying by one, make no change to

the other number.the other number. 5 x 1 = 55 x 1 = 5

3 x 13 x 12 x 12 x 11 x 9 1 x 9 1 x 81 x 86 x 16 x 1

Multiplication – The tricky zerosMultiplication – The tricky zeros

When a number, such as 2, is multiplied When a number, such as 2, is multiplied by zero, say to yourself – two groups of by zero, say to yourself – two groups of nothing is still nothing.nothing is still nothing.

4 x 0 4 x 0 8 x 0 8 x 0 3 x 0 3 x 0 0 x 50 x 50 x 70 x 7

Multiplication – The ThreesMultiplication – The Threes

Double the number plus one more.Double the number plus one more. Example: 3 x 2 Example: 3 x 2 Think: Think: double two is four plus one more double two is four plus one more

two is six.two is six.3 x 43 x 45 x 35 x 33 x 63 x 67 x 37 x 39 x 39 x 3

Multiplication – Four FactsMultiplication – Four Facts

The double – double strategyThe double – double strategy Example: 4 x 4Example: 4 x 4 Think: 4 x 2 = 8, 8 x 2 = 16Think: 4 x 2 = 8, 8 x 2 = 16

4 x 24 x 24 x 64 x 65 x 45 x 47 x 47 x 44 x 34 x 3

Multiplication – Sixes Multiplication – Sixes

Multiply by 5 and add one moreMultiply by 5 and add one more Or double your threes.Or double your threes.

Example: 6 x 2Example: 6 x 2Think: 5 x 2 = 10 plus one more 2 = 12Think: 5 x 2 = 10 plus one more 2 = 12Or think: 3 x 2 = 6 plus 3 x 2 = 6 adds up to 12.Or think: 3 x 2 = 6 plus 3 x 2 = 6 adds up to 12.

6 x 16 x 16 x 36 x 34 x 64 x 67 x 67 x 68 x 68 x 6

Multiplication - SevensMultiplication - Sevens

Multiply by 5 and add two more groups.Multiply by 5 and add two more groups. Example: 7 x 2Example: 7 x 2 Think: 5 x 2 = 10 and then add 2 x 2 = 4 for 14Think: 5 x 2 = 10 and then add 2 x 2 = 4 for 14

7 x 47 x 4

3 x 73 x 7

7 x 57 x 5

1 x 71 x 7

6 x 76 x 7

Multiplication - eightsMultiplication - eights

Double three times.Double three times. Example: 8 x 8Example: 8 x 8 Think: 8 x 2 = 16, then 16 x 2 = 32, and then 32 Think: 8 x 2 = 16, then 16 x 2 = 32, and then 32

plus 32 = 64.plus 32 = 64.

8 x 38 x 38 x 58 x 57 x 87 x 89 x 89 x 84 x 84 x 8

Multiplication – Nifty ninesMultiplication – Nifty nines

Multiply by ten and then subtract one group.Multiply by ten and then subtract one group. Example: 9 x 2Example: 9 x 2 Think: 10 x 2 = 20 subtract two equals 18.Think: 10 x 2 = 20 subtract two equals 18.

9 x 19 x 1

3 x 93 x 9

5 x 95 x 9

9 x 69 x 6

8 x 98 x 9

mental math mental computation grade 4. quick addition this strategy can be used when no regrouping...

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