# Mental Math Strategies

The curriculum guide requires 10 minutes per day for increasing speed of recall.

These are the strategies implicit for the report card line stated as “Applies Mental Math Strategies”

These grade five outcomes are year-long. The curriculum guide states that masterey is to be by the end of June.  These grade five strategies are named:

• division facts up to and including facts to 81.
• front-end multiplying
• compensation in multiplying
• multiplying by 10, 100 and 1000
• dividing by 10, 100 and 1000
• multiplying by 0.1, 0.01, and 0.001
• balance for a constant difference.

## Strategies Explained

1. Division Facts to 81

In leaving grade four, students were to have mastered the multiplication facts to 81 with a rapid recall to be considered at-grade level.

In grade five, students are to have mastered division facts to 81 with a rapid recall.

2. Front-end multiplication

This strategy involves expanding the larger factor into its place values and multiplying each place value separately to the smaller factor. Then, add all the products together.

As an example, 4 x 352 is the same as 4 x 300 (1200) and 4 x 50 (200) and 4 x 2 (8). One has only to add the three products to find the original product of 4 x 352, which is 1200 + 200 + 8 or 1408.

3. Compensation in multiplying

This strategy involved round the larger factor to the closest multiply of 10, 100 or 1000.  One then multiplies the two factors, followed by subtracting the number that was added on in the rounding-up by the smaller factor in the original equation.

As an example, 3 x 298 is compensated to 3 x 300, which is 900. Since 2 was added (when 298 was rounded up to 300), one must subtract 3 x 2, or 6, from 900 to get back to the original equation. So, 3 x 298 is 894, or 900 -6 ( the product of the 3 x 2 step).

4. Multiplying by 10, 100 and 1000

This strategy involves increasing each place value by one, two or three places.

When multiplying 657 by 10, each place value increases by 10 or one move to the left. The 6 hundreds becomes 6 thousands, the 5 tens becomes 5 hundreds and the 7 ones becomes 7 tens.  For a simpler method, simply add one zero on to the end of the original factor.

657 x 10 = 6 570          45  801 x 10 = 458 010          65.5 x 10 = 655.0 or 655 (note that when multiplying a decimal by 10, it’s not as straight forward as simply adding on a ten.)

Similarly, when multiplying by 100 (or 1000), each place value increase by 100 ( or 1000) or two moves to the left ( three moves to the left).

When multiplying 657 x 100, the 6 hundreds becomes 6 ten thousands (two place value moves to the left), the 5 tens becomes 5 thousands (two place value moves to the left), and the 7 ones becomes 7 hundred (three place value moves to the left.) For a simpler method, simply add two zeroes to the end of the original factor.

657 x 100 = 65 700         45 801 x 100 = 4 580 100       65.5 x 100 = 6550.0 or 6550

5. Dividing by 10, 100 and 1000

This strategy involved decreasing each place value by 10, 100 or 1000.

When dividing 657 by 10, the 6 hundreds becomes 6 tens, the 5 tens becomes 5 ones and the 7 ones become 7 tenths.  For a simple method, move the decimal one place to the left.

(Please note that the blog site does not offer a division symbol.)

657 divided by 10 = 65.7            45 801 divided by 10 = 4 581.0 or 4581

65.5 divided by 10 = 6.55

When dividing by 100 (or 1000), each place value decreased by 100 (or 1000). Each digit moves 2 (or 3) places to the right.

657 divided by 100 = 6.57

657 divided by 1000 = 0.657

6. Multiplying by 0.1, 0.01, and 0.001

This strategy is the same as dividing by 10, 100 and 1000. Each place value decreases by one, two or three places. As with dividing by 10, 100 and 1000, a simpler method is to move the decimal the required number of place value places to the left.

7. Balance for a Constant Difference.

This is a subtracting strategy for when the greater number has less value in the ones place.  When subtracting 399 from 502, consider rounding the 399 up to 400 since subtracting with zeroes is easier. However, in order for the difference to be constant, one must also add the same amount to both numbers.

With 502- 399, add 1 to the 399 to make it 400. To keep a constant difference, add 1 also to the 502.  What started as 502 – 399 is now 503 – 400, which is the original 502 + 1 and the original 399 +1.

So, for 502, think 502  + 1 or 503

for 406, think 406 + 3 or 409