How to stop losing marks to silly mistakes in Maths

There is a particular frustration in getting a Maths question wrong when you understood it perfectly. A sign dropped, a digit copied incorrectly, the right answer to a slightly different question.

Students tend to shrug these off as carelessness and promise to concentrate harder next time. That never works, because concentration is not a tap you can turn up. What works is changing the mechanics of how you write.

Name the mistake before you fix it

"Silly mistake" is too vague to act on. Almost all of them fall into a handful of types:

• Transcription. You copied 37 from the question as 73, or dropped a term moving from one line to the next.
• Sign errors. A minus that vanished or multiplied wrongly.
• Misread question. You found x when it asked for 2x, or gave the area when it wanted the perimeter.
• Premature rounding. You rounded halfway through and the final answer drifted.
• Units. Right number, wrong unit, or a mix of centimetres and metres.

Go back through your last three tests and tally which of these you actually make. Nearly everyone finds that one type accounts for most of their losses — and it is rarely the one they assumed.

Fixes, by type

Transcription: Write the question's numbers at the top of your working, once, and use your copy. Most transcription errors happen between line four and line five, not from the question.

Sign errors: Put brackets around anything negative, always, even when it is unnecessary. Substituting minus three into an expression should be written with the brackets showing, every time, and half of this error class disappears.

Misreading: Underline what the question asks for before you start, and circle it in your final answer. If the last line of your working does not match the thing you underlined, you have caught it.

Rounding: Carry full precision through the calculation and round once, at the end.

Units: Convert everything to one unit before you begin, and write the unit on every line rather than only the answer.

Leave a gap between finishing and checking

Checking a question the instant you finish it does not work well. Your brain replays the same reasoning and sees what it expects to see.

Better: finish the whole section, then go back. By then you have lost the memory of your own working and you actually read what is on the page.

Check by a different route

Re-reading your working finds almost nothing. Instead:

• Substitute the answer back into the original equation.
• Estimate. If the answer should be roughly 50 and you have 4.7, something is wrong regardless of where.
• Ask whether it is sensible. A negative length, a probability above one, a speed of 4000 km/h — these announce themselves if you look.

Count them, deliberately

For the next two weeks, every time you lose a mark to a non-knowledge error, write down which of the five types it was.

Two weeks of tallying tells you more about where your marks are going than another month of revision would. And unlike learning a new chapter, fixing one mechanical habit takes days and keeps paying out for the rest of your exams.