The idea, step by step
Check the size first
Before accepting an answer, ask roughly how large it should be. If 24 books cost 8 dollars each, their total is close to 25 × 8 = 200 dollars. An answer near 2,000 dollars is much too large.
An estimate catches many errors, but does not prove every digit is correct. Several nearby answers can have the same rounded estimate. Use an exact check when the exact value matters.
Use another method
Multiplication and division undo each other. If 432 ÷ 6 = 72, check 72 × 6 = 432. For subtraction, add the difference back to the amount taken away.
Read the situation too. An answer should have the correct unit and be possible: a required number of buses cannot leave people behind, and a total cost cannot be below every positive item cost.
A common trap
An answer close to my estimate must be exactly right.
Instead: An estimate checks size. Use exact calculation or an inverse operation to check the precise answer.
See the thinking
Catch a factor-of-ten error
Lena writes 24 × 8 = 1,920 for the cost of 24 books at 8 dollars each. Is it reasonable?
- Estimate 25 × 8 = 200, so 1,920 is much too large.
- Calculate 20 × 8 + 4 × 8 = 160 + 32 = 192.
Check a division
Check whether 432 ÷ 6 = 72.
- Multiply the proposed quotient by the divisor: 72 × 6 = 432.
- The product equals the starting dividend, so the division is correct.
Check your understanding
Check 903 − 487 = 416 using addition.
Show answer
487 + 416 = 903, so the subtraction is correct.
Adding the difference back to the amount subtracted reproduces the starting number.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- A student writes 364 × 8 = 29,120. Explain why the answer is unreasonable and find the correct product.2 marks
- There are 18 boxes with 24 pencils each. Find the total and give an estimate to check it.2 marks
- Check 903 − 487 = 416 using the inverse operation.1 mark
- Which is reasonable for 49 × 21: 1,029 or 10,290? Explain.2 marks
- Check 936 ÷ 9 = 104.1 mark
- Mia estimates 298 + 403 as 700, then says 690 must be the exact answer because it is close. Is that enough? Find the exact answer.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A student writes 364 × 8 = 29,120. Explain why the answer is unreasonable and find the correct product.2 marks
400 × 8 is only 3,200. Calculate 2,400 + 480 + 32 = 2,912.
It is about ten times too large; the correct product is 2,912. - There are 18 boxes with 24 pencils each. Find the total and give an estimate to check it.2 marks
18 × 24 = 360 + 72 = 432. A total of 432 is close to 500.
432 pencils; for example, estimate 20 × 25 = 500. - Check 903 − 487 = 416 using the inverse operation.1 mark
487 + 400 + 16 = 903.
Correct, because 487 + 416 = 903. - Which is reasonable for 49 × 21: 1,029 or 10,290? Explain.2 marks
50 × 20 = 1,000. Exact calculation is 49 × 20 + 49 = 1,029.
1,029 - Check 936 ÷ 9 = 104.1 mark
100 × 9 + 4 × 9 = 900 + 36 = 936.
Correct, because 104 × 9 = 936. - Mia estimates 298 + 403 as 700, then says 690 must be the exact answer because it is close. Is that enough? Find the exact answer.2 marks
298 + 400 + 3 = 701. An estimate alone does not confirm an exact value.
No; the exact answer is 701.
Curriculum reference & lesson scope
Australian Curriculum v9; SA Curriculum Mathematics 2026
Whole-number revision; partitioning; rounding/estimating quantities; checking reasonable answers.
Official curriculum source ↗