what does compensation strategy mean?
if anyone could help, i would greatly appreciate it!
my HW question ask the following;
for which of the addition problems below do you think the compensation strategy would be easier to use? tell why
a)499 b)1297 c) 1234
+154 +48 +343
The compensation strategy in mathematics is a method used to estimate the result of an addition or subtraction problem by adjusting or compensating one number to make the calculation easier. It involves breaking one or both of the numbers in the problem into more friendly or easier-to-work-with values.
To determine which of the addition problems (499 + 154, 1297 + 48, or 1234 + 343) would be easier to solve using the compensation strategy, we need to evaluate each problem individually.
For problem a) 499 + 154:
We can use the compensation strategy here by adjusting the numbers slightly. For example, we can round 499 up to 500 and round 154 down to 150. Now, we have an easier calculation of 500 + 150, which results in 650. This can be used as an estimate.
For problem b) 1297 + 48:
Here, we can use the compensation strategy by adjusting the numbers. We can round 1297 down to 1300 and round 48 up to 50. This gives us an easier calculation of 1300 + 50, which is 1350. Again, this can serve as an estimate.
For problem c) 1234 + 343:
Using the same compensation strategy, we can round 343 down to 340 and round 1234 up to 1230. This gives us an easier calculation of 1230 + 340, resulting in 1570, which can be used as an estimate.
Based on the numbers in each problem, it appears that problem b) (1297 + 48) would be easier to solve using the compensation strategy because the numbers are closer together, making it easier to adjust them. Rounding to the nearest ten or hundred is generally easier than rounding to the nearest hundred or thousand.
Remember, the compensation strategy is a method to help estimate and simplify calculations. It is not the only way to solve an addition problem, but it can be helpful when mental math or estimation is required.