Your child has an answer, but the instruction to "check your work" does not tell them what to do next. Repeating the same calculation may help, yet it can also repeat the same mistake. Give checking a specific job: test the size of the answer, test the arithmetic, or test whether it answers the question.
Here are three checks to practise during Math homework. Choose numbers your child already understands and try one check at a time. These are invented examples, not questions from an examination paper.
1. Estimate: is the answer a sensible size?
Six notebooks cost $2.85 each. A student calculates a total of $171.
Before doing the exact multiplication again, round $2.85 to $3. Six notebooks at $3 each would cost $18. Because the actual price is a little lower, the actual total must be a little below $18. A total of $171 cannot fit.
Exact calculation: 6 × $2.85 = $17.10.
Check: $17.10 is below $18 and close to it, as expected.
Ask, "Should the real total be above or below our estimate?" This makes the check more useful than simply saying the answer looks big.
The limit: a rough estimate does not prove an answer is correct. An incorrect answer such as $16.10 could still look plausible beside $18. Use estimation to spot an unreasonable size, then check the exact arithmetic if needed.
2. Reverse: does the result take you back?
A 7.2 m ribbon is cut into three equal pieces. The calculation is 7.2 ÷ 3 = 2.4, so each piece is 2.4 m long.
Reverse the division by multiplying the proposed piece length by the number of pieces:
2.4 m × 3 = 7.2 m.
The three equal pieces add back up to the original ribbon length.
If a student wrote 0.24 m instead, multiplying by three would give 0.72 m. That does not recover the original 7.2 m, so there is something to revisit.
The same idea works with a simple subtraction: if 18 − 7 = 11, then 11 + 7 should return 18. Use the numbers from the question when checking, so a copying error is less likely to travel unnoticed into the check.
The limit: reversing an operation checks that calculation. It does not establish that the operation was the right one for the problem. Multiplying instead of dividing can still be reversed successfully, even when multiplication answers the wrong question.
3. Reread: have you answered what was asked?
Three full bottles each contain 1.5 L of juice. After 0.8 L is poured out altogether, how much juice remains?
A student writes 3 × 1.5 = 4.5 and gives 4.5 L as the final answer. The multiplication is correct. But 4.5 L is the amount at the start, not the amount remaining.
Reread the final question and finish the calculation:
Starting amount: 3 × 1.5 L = 4.5 L.
Amount remaining: 4.5 L − 0.8 L = 3.7 L.
Then check the unit. If the question instead asked for the answer in millilitres, the final answer would be 3700 mL. Writing 3.7 mL would change the amount, not just the label.
Useful prompts are: "What does this number describe?" and "Which words show what we need to find?" Look at the whole situation; a single word such as "more" is not enough to decide an operation.
Choose a check that can catch this kind of mistake
| When you are unsure about… | Try… |
|---|---|
| The size or decimal position | An estimate and a comparison |
| The arithmetic in one step | The inverse operation |
| The quantity or unit requested | A reread of the question |
A sensible-looking answer can still be wrong. A calculation that reverses neatly can still answer the wrong question. These checks complement one another, but your child does not need to perform all three mechanically on every line of working.
A short practice set
For each example, decide what the proposed answer means and choose a useful first check. Try the check before opening the explanation.
- Four pens cost $1.95 each. A student writes a total of $78. What would an estimate tell you?
- A 9.6 m rope is cut into four equal pieces. A student writes 2.4 m per piece. How can you reverse the calculation?
- A jug contains 2 L of water. After 350 mL is poured out, a student answers "350 mL remains". What quantity have they found instead?
Open the worked answers
- Four pens at about $2 each would cost about $8. The actual total should be just under $8, so $78 is unreasonable. The exact total is 4 × $1.95 = $7.80.
- Multiply the proposed length by four: 2.4 m × 4 = 9.6 m. This matches the original rope length.
- 350 mL is the amount poured out. Convert the starting amount to the same unit: 2 L = 2000 mL. The amount remaining is 2000 mL − 350 mL = 1650 mL.
Make checking a small, useful habit
During the next homework session, pick one completed question and ask your child to show a check that suits it. If it reveals a mistake, return to the relevant step together. There is no need to turn a short checking exercise into a second full worksheet.
If your child needs help choosing the first step, our guide to helping with one hint at a time offers prompts that leave the thinking with them. You can also explore Genie's Upper Primary Math classes for support with understanding and explaining their working.
Further reading: OpenStax: Decimal Operations is a reference for decimal arithmetic. The examples and checking routine here are our own practical suggestions, not a prescribed exam method. Always follow the instructions on the work your child has been given.