Download • Front-end Estimation: • Using Compatible Numbers:

The following are mental math strategies that will be used to solve problems in
Unit 3.
•
Front-end Estimation:
Keep whatever number is in the front and make all other digits zero.
For example:
546 + 267 = 813
Front-end Estimate: 500 + 200 = 700
→ Please note that this method is fast and is also inaccurate.
•
Using Compatible Numbers:
Compatible numbers are numbers that are close in value to the actual numbers.
Example:
297 + 348 = 645
Make the numbers compatible and round up to the nearest hundred and the nearest ten. The
equation becomes 300 + 350. The answer is about 650.
Actual sum: 297 + 348 = 645
Using Compatible Numbers: 300 + 350 = 650
Another Example:
Roger has $17 986 in the bank and spends $196 buying new school clothes. In order to
determine about how much money he has left in his account, use the strategy of compatible
numbers.
$17 986 (compatible number $18 000) - $196 (compatible number $200).
So, $18 000 - $200 = $17 800. Roger has about $17 800 left in his account.
• Rounding:
This involves rounding a number to its greatest, or left-most, place value. For example,
round the number 456 to its greatest or left-most place value. The 5, which is to the right of
the 4 (left-most number) is the number that will determine whether the 4 will remain the
same or round up to 5. The rule-of-thumb is if the number to the right of the place value
being rounded is 5 or greater than the number to the left will round up. If the number to the
right of the number being rounded is 4 or lower than the number to the left remains the same.
456 will round up to 500.
436 will round down to 400.
•
Compensation:
Compensation is adjusting an estimate to make it closer to the calculated answer.
For example,
Estimate the sum of: 136.2 + 26.2 + 55.2
By rounding or by using compatible numbers, the equation can be written as
140 + 30 + 60 = 120
This results in a very high estimate because all addends were rounded up. In situations where
all addends are rounded in the same direction, you could choose to round one in the opposite
direction in order to improve the accuracy of the estimate. This is the compensation.
So, for example, to compensate:
136.2 (↑) + 26.2 (↑) + 55.2 (↓)
140 + 30 + 50 = 220
The actual sum of the equation is 217.6
This results in a better estimate.