Almost every lesson has the same scene: the student solves the problem correctly, yet the answer comes out wrong. We look into it, and it turns out they solved a different problem from the one on the page. The mistake wasn’t in the calculations — it happened in the first twenty seconds, when the statement was skimmed and filled in from memory: “oh, this is like last week’s.” It isn’t carelessness in the everyday sense; it’s the habit of reading a problem as a familiar template rather than as a set of instructions.

The first habit is to read the statement twice, and differently each time. The first read is for the whole thing, to get the story: what it’s about and what is happening to what. The second read goes sentence by sentence, marking every number and every linking phrase in pencil: “3 more than”, “half as many”, “at least”, “an hour after”. These are exactly the phrases that decide what goes into the equation, and exactly the ones that slip away when you skim. On the second pass it helps to say the text to yourself — the pace instantly drops to where it should be.

The most expensive mistake on the OGE doesn’t cost a mark for arithmetic — it costs the whole problem, and it happens before the student has even picked up a pen.

The second habit is to separate the question from the statement before you start solving. Underline the last sentence and write down separately exactly what you need to find and in what units. The classic lost mark looks like this: everything is solved correctly and the speed of the first pedestrian is found — but the question asked for the difference between the speeds. Or the answer is in metres when kilometres were needed. A written-out question stays in front of your eyes and won’t let you stop one step too early.

The third habit is a quick common-sense check. Once you have an answer, go back to the statement and put the number back into the story: does it fit? A bus doing 400 km/h, a discount after which the price went up, a son older than his father — all of these are caught in fifteen seconds. In mock exams we make this check a required part of the solution, and on average it wins back one or two marks that would otherwise simply be lost.

Together, all three habits take about a minute per problem. In the exam that minute pays for itself: the time goes not into re-solving, but into solving exactly what was asked the first time round.