Mental Math Mental Computation Grade 4

Quick Addition  This strategy can be used when no regrouping is needed.  Begin at the front end of the number.  Example:  Think: add the 7 from 71 and the 1 from 12 to get 8, then add the 1 from the 71 and the 2 from the 12 to get 3. The answer is 83.  Then this is applied to sums involving thousands.

Quick Addition

Quick Addition

Front End Addition  Add the highest place values and then add the sums of the next place values.  Example:  Think: 30 and 20 is 50, 7 and 6 is 13, and 50 plus 13 is 63.  Example:  Think: 400 and 300 is 700, 50 and 80 is 130, and 700 plus 130 is 830.

Front End Addition

Front End Addition

Finding Compatibles  Look for pairs of numbers that add easily to make a sum that will be easy to work with. Last year, we looked for numbers that added easily to 100. This year, we need to look for numbers that add easily to  Example:  Think: 400 and 600 is 1000, and 1000 plus 720 is 1720.

Finding Compatibles

Finding Compatibles

Break Up and Bridge  In this strategy, you leave the first number as it is and then add the place values from the next number one at a time.  Example:  Think: 45 and 30 (from the 36) is 75, and 75 plus 6 (the rest of the 36) is 81.  Example:  Think: 537 and 200 is 737, and 737 plus 8 is 745.

Break Up and Bridge

Break Up and Bridge

Compensation  Change one number in a sum to a nearby ten or hundred and then adjust the answer to compensate for the original change.  Example:  Think: 52 plus 40 is 92, but I added one too many to take me to the next 10, so to compensate: I subtract one from my answer, 92 – to get 91.  Example:  Think: is 545, but I added 2 too many, so I subtract 2 from 545 to get 543.

Compensation

Compensation

Make 10s, 100s, or 1000s  This strategy adds to one addend to make 10, 100, or  Example:  Think: (from the 6) is 60 plus 4 (the other part of 6) is 64.  Example:  Think: 350 plus 50 (from the 59) is 400, and 400 plus 9 (the other part of 59) is 409.  Example:  Think: 7400 plus 600 (from the 790) is 8000, and 8000 plus 190 (the other part of 790) is 8190.

Make 10s, 100s, or 1000s

Make 10s, 100s, or 1000s

Subtraction – Quick Subtraction  This strategy should be used when no regrouping is needed.  Begin with the front end number.  Example: 86 – 23  Think: 8 take away 2 is 6 and then 6 take away 3 is 3. The answer is 63.

Quick Subtraction 38 – – – – – – – – –

Quick Subtraction 82 – – – – – – – – –

Back Through the 10/100 Extension  Subtract a part of one of the numbers to get to the nearest tens or hundreds, and then subtract the rest of the number.  This strategy is probably most effective when one of the numbers is not too great.  Example: 74 – 6  Think: 74 subtract 4 (one part of the 6) is 70 and 70 subtract 2 (the other part of the 6) is 68.  Example: 530 – 70  Think: 530 subtract 30 (one part of the 70) is 500 and 500 subtract 40 (the other part of the 70) is 460.

Back Through the 10/ – 6 13 – 4 13 – 6 74 – – – – – –

Back Through the 10/ – 7 61 – 5 15 – 7 97 – 8 34 – – – – –

Up Through 10/100  This strategy is an extension of the “counting up through 10” strategy 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 of the distance to the greater number.  This strategy is most effective when the two numbers in the question are close together.  Example: 84 – 77  Think: It is 3 from 77 to 80 and 4 from 80 to 84; therefore, the difference is 3 plus 4, or 7.  Example: 613 – 594  Think: It is to 600 and 13 from 600 to 613; therefore, the difference is 6 plus 13, or 19.

Up Through 10/ – – – – – – – – –

Up Through 10/ – – – – – – – – –

Compensation  Change one of the numbers to the nearest ten or hundred, carrying out the subtraction, and the adjust the answer to compensate for the original change.  Example: 56 – 18  Think: 56 – 20 = 36, but I subtracted 2 too many; so, I add 2 to the answer to get 38.  Example: 145 – 99  Think: 145 – 100 is 45, but I subtracted 1 too many; so, I add 1 to 45 to get 46.

Compensation 74 – – – – 9 15 – – – – –

Compensation 83 – – – – – – – – –

Balancing for a Constant Difference  This is a new strategy for Grade 4.  Both numbers change to make subtraction easier by adding or subtracting.  Example: 87 – 19  Think: Add 1 to both numbers to get 88 – 20; so, 68 is the answer.  Example: 345 – 198  Think: Add 2 to both numbers to get 347 – 200; so, the answer is 147.

Balancing for a Constant Difference 85 – – – – – – – – –

Balancing for a Constant Difference 67 – – – – – – – – –

Break Up and Bridge  Begin with the first number (minuend) and subtract the second number (subtrahend) beginning with the highest place value.  Example: 92 – 26  Think: 92 subtract 20 (from the 26) is 72 and 72 subtract 6 is 66.  Example: 745 – 203  Think: 745 subtract 200 (from the 203) is 545 and 545 minus 3 is 542.

Break Up and Bridge 73 – – – – – – – – –

Break Up and Bridge 74 – – – – – – – – –

Multiplication - Doubles  Connect the two times tables with doubling. 2 x 2 4 x 2 2 x 5 10 x 2 2 x 3

Multiplication – the fives  Think of the clock. Each number is 5 minutes. 5 x 3 5 x 6 5 x 2 1 x 5 7 x 5

Multiplication – the ones  NO CHANGE! When multiplying by one, make no change to the other number. When multiplying by one, make no change to the other number. 5 x 1 = 5 5 x 1 = 5 3 x 1 2 x 1 1 x 9 1 x 8 6 x 1

Multiplication – The tricky zeros  When a number, such as 2, is multiplied by zero, say to yourself – two groups of nothing is still nothing. 4 x 0 8 x 0 3 x 0 0 x 5 0 x 7

Multiplication – The Threes  Double the number plus one more.  Example: 3 x 2  Think: double two is four plus one more two is six. 3 x 4 5 x 3 3 x 6 7 x 3 9 x 3

Multiplication – Four Facts  The double – double strategy  Example: 4 x 4  Think: 4 x 2 = 8, 8 x 2 = 16 4 x 2 4 x 6 5 x 4 7 x 4 4 x 3

Multiplication – Sixes  Multiply by 5 and add one more  Or double your threes. Example: 6 x 2 Think: 5 x 2 = 10 plus one more 2 = 12 Or think: 3 x 2 = 6 plus 3 x 2 = 6 adds up to x 1 6 x 3 4 x 6 7 x 6 8 x 6

Multiplication - Sevens  Multiply by 5 and add two more groups.  Example: 7 x 2  Think: 5 x 2 = 10 and then add 2 x 2 = 4 for 14 7 x 4 3 x 7 7 x 5 1 x 7 6 x 7

Multiplication - eights  Double three times.  Example: 8 x 8  Think: 8 x 2 = 16, then 16 x 2 = 32, and then 32 plus 32 = x 3 8 x 5 7 x 8 9 x 8 4 x 8

Multiplication – Nifty nines  Multiply by ten and then subtract one group.  Example: 9 x 2  Think: 10 x 2 = 20 subtract two equals x 1 3 x 9 5 x 9 9 x 6 8 x 9