How to check your maths homework properly

There is a particular kind of dread that comes from handing in homework and having no idea whether it is right. The good news is that you do not need the answer sheet to find out. Maths is one of the few subjects where you can usually prove your own answer correct, and the habit of doing so is worth more than any single mark.

1. Estimate first, then compare

Before you work anything out, round the numbers and make a rough guess. To check 19 × 21, think 20 × 20 = 400. If your final answer is 399, lovely. If it is 3,990 or 40, something has gone wrong with a place value or a key press. Estimating takes ten seconds and catches the most embarrassing slips.

2. Work backwards

Every operation has an opposite. If you worked out 84 ÷ 7 = 12, multiply back: 12 × 7 = 84. If you subtracted, add the answer back to the number you took away. For equations, put your solution into the original and see if both sides match. If 2x + 5 = 17 and you found x = 6, then 2 × 6 + 5 = 17, which confirms it.

3. Solve it a second way

If you factorised a quadratic, try the formula as well. If you added fractions with the lowest common denominator, try a bigger common denominator and simplify at the end. Two different routes reaching the same answer is very strong evidence.

4. Read the question again, slowly

A surprising number of lost marks come from answering a slightly different question. Did it ask for the area or the perimeter? A percentage or a decimal? To the nearest whole number? Underline the instruction word and the units, then check your answer ticks both boxes.

5. Use a calculator as the last step, not the first

Working the problem on paper first and then confirming with a calculator turns the calculator into a checker rather than a crutch. If the two answers match, you are done. If they differ, compare your written steps with the calculator's working. Our calculators show each step for exactly this reason.

Method	Takes	Best for
Estimation	10 seconds	Arithmetic and decimals
Reverse working	30 seconds	Division, subtraction, equations
Second method	2 minutes	Algebra and fractions
Re-reading the question	20 seconds	Word problems
Calculator check	1 minute	Final confirmation

What to do when your answer is wrong

Do not rub it out. Draw a line under the working, go back one line at a time and ask "is this step definitely true?" The mistake is almost always a sign error, a dropped bracket or a copied number that changed on the way down the page. Finding it yourself is the single best way to stop making it again.

Checking is not a sign you doubt yourself. It is what people who are good at maths do.