Understand the idea.
Check the size first
A reasonable answer has the size the situation suggests. Before calculating the cost of books at dollars each, think of . The exact cost should be near dollars, making dollars suspicious.
An estimate can reject a very large or very small answer, but nearby wrong answers may pass the same check. After checking size, use exact working or a different method to confirm the digits.
Use another method
Inverse operations undo one another. To check , multiply by and look for the starting total . To check a subtraction, add the difference to the amount taken away.
Finish by checking meaning and units. A cost needs a money unit; a count of containers must hold every item when the question asks for enough containers. Correct arithmetic can still answer the wrong question if the result is interpreted carelessly.
See the method in action.
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?
Worked solution
- 1
Estimate the cost of a nearby number of books.
24 books must cost slightly less than 25 books at the same positive price.
- 2
Reject the proposed size.
A cost above 200 dollars is impossible when even 25 books cost only 200 dollars.
- 3
Calculate both parts of 24 books.
Partitioning 24 into 20 and 4 still counts every book.
- 4
Combine the costs.
The correct cost is 192 dollars, which fits the estimate.
No. The correct cost is 192 dollars.
Check a division
Check whether 432 ÷ 6 = 72.
Worked solution
- 1
Multiply the proposed quotient by the divisor.
Multiplication reverses division by a non-zero number.
- 2
Evaluate the multiplication.
The partial products add to the original dividend.
- 3
Confirm the original division.
72 groups of 6 account for the whole 432 with nothing left over.
The answer 72 is correct.
Try it yourself.
Check your understanding
Check 903 − 487 = 416 using addition.
Show answer & reasoning
487 + 416 = 903, so the subtraction is correct.
Add the proposed difference to the subtracted amount: . This reproduces the starting total, so is correct.
Keep practising
6 worksheet questions · 10 marks
Read the questions online
- A student writes . 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 using the inverse operation.1 mark
- Which is reasonable for : 1,029 or 10,290? Explain.2 marks
- Check .1 mark
- Mia estimates 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 . Explain why the answer is unreasonable and find the correct product.2 marks
is only 3,200. Calculate .
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
. A total of 432 is close to 500.
432 pencils; for example, estimate . - Check using the inverse operation.1 mark
.
Correct, because . - Which is reasonable for : 1,029 or 10,290? Explain.2 marks
. Exact calculation is .
1,029 - Check .1 mark
.
Correct, because . - Mia estimates as 700, then says 690 must be the exact answer because it is close. Is that enough? Find the exact answer.2 marks
. 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 ↗