Same Math › Grades 3–5 › Estimating with compatible numbers
What are compatible numbers?
Compatible numbers are nearby numbers that are easy to work with together. To estimate 247 ÷ 6, swap 247 for 240, because 240 ÷ 6 is easy: about 40.
- Find a friendly number nearby: 240 is a multiple of 6.
- Do the easy problem: 240 ÷ 6 = 40.
- So 247 ÷ 6 is about 40
Why schools teach it
Estimating catches mistakes
Third and fourth graders are expected to check whether answers are reasonable using mental math and estimation (3.OA.D.8, 4.OA.A.3). A quick estimate catches answers like 412 for 247 ÷ 6 before they're handed in.
Compatible numbers are often better than plain rounding. Rounding 247 ÷ 6 gives 250 ÷ 6, which is awkward. Picking 240 gives a clean answer.
At the kitchen table
What to say, and what to skip
Say this
What number close to 247 is easy to divide by 6?
Is your real answer close to your estimate?
If not, something went wrong.Would rounding work here, or is there a friendlier number?
Is the real answer a bit more or a bit less?
247 is a bit more than 240, so a bit more than 40.
Skip this
- Insisting on one right estimate.250 + 300 and 240 + 310 are both reasonable estimates.
Just work it out exactly.
The point of estimating is a quick check, not a second calculation.- Rounding every number the same way.Compatible numbers are chosen to work together, not by a fixed rule.
See it in action
Estimating 38 × 7
Pick a friendly number near 38
40Do the easy multiplication
40 × 7 = 280Compare with the real answer
38 × 7 = 266, close to 280
The estimate is a bit high because 40 is more than 38.
Free practice sheet
Make a compatible numbers sheet
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Parents also ask
How is this different from rounding?
Rounding follows a rule. Compatible numbers are chosen to make the math easy, which may mean rounding a different way.
Is there one right answer?
No. Any estimate that's close and easy to work out is fine.
When should kids estimate?
Before or after solving, as a check that the answer makes sense.
Does this work with fractions?
Yes. Benchmark fractions like ½ are compatible numbers for fractions.