Same Math › Grades 2–4 › Compensation
What is the compensation strategy?
Compensation changes a problem into an easier one, then makes up for the change. For 48 + 27, move 2 from the 27 to the 48: now it's 50 + 25, which is easy.
- Give 2 to the 48 to make a friendly 50.
- Take 2 from the 27 so the total doesn't change.
- 50 + 25 = 75, so 48 + 27 = 75
Why schools teach it
It's how confident adults do mental math
Ask an adult to add 99 + 46 in their head and most will do 100 + 45. That's compensation. Second and third graders are expected to add and subtract fluently using strategies based on place value and properties of operations (2.NBT.B.5, 3.NBT.A.2), and this is one of the most useful.
For subtraction, the move is slightly different: 63 − 29 becomes 63 − 30, then add 1 back because you took away one too many.
At the kitchen table
What to say, and what to skip
Say this
Which number is close to a ten?
If you give it 2, where does the 2 come from?
You took away 30 instead of 29. Did you take too many or too few?
For subtraction, this is the step to talk through.Can you check it another way?
Skip this
- Changing one number and forgetting to adjust.48 + 27 is not 50 + 27. The 2 has to come from somewhere.
- Adjusting subtraction the wrong way.63 − 30 takes away one too many, so add 1 back, not subtract it.
That's not the real way.
It's a real strategy the standards expect, and adults use it all the time.
See it in action
Solving 82 − 39 with compensation
Round 39 up to a friendly 40
82 − 40 = 42You took away 1 too many
40 is 1 more than 39Give the 1 back
42 + 1 = 43
Subtracting 40 is much easier than subtracting 39.
Free practice sheet
Make a compensation sheet
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Parents also ask
Why not just add normally?
For mental math, compensation is often much faster. Kids still learn the standard method too.
How do I know which number to change?
Pick the one closest to a ten or a hundred, like 48, 99 or 198.
Is it the same as rounding?
It starts like rounding, but then adjusts so the answer is exact.
Does it work for bigger numbers?
Yes: 398 + 245 is 400 + 243.