Learning & thinking · a life skill
Simple Problem Restatement
say it back before you solve it
Most wrong answers aren't bad sums. They're the right sum done on the wrong problem, because you started working before you'd understood what was asked. The fix takes a minute: write the problem again in your own words, in your own order, and solve that version.
- Easy to start
- Medium impact
- Learn it in 1 week
- One problem, said back
Both lanes do easy sums. Only one of them answers the question, and it's the one that put the problem in its own words before touching the numbers.
Tonight, with a pen
Try it now.
One problem you're stuck on, or one you'd normally rush. About ten minutes.
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Underline what it asks for
Find the question first and write it on its own line. That's the thing your answer has to be. Everything else is there to help you get to it.
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List what you're given
One fact per line, in plain words. If a fact describes one thing in terms of another, write both names down.
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Circle the word that could flip it
Less, more, than, each, per, not, except, before, after. These are the words people grab and act on. Circle them so you slow down there.
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Say it back in your own order
Rewrite the problem starting from the thing you want to find. "The shop is 2p less than the market" becomes "the market is 2p more than the shop".
If you can't say it back, you've found the real problem: a part you don't understand yet. -
Sketch it, then solve
A line, two boxes, a timeline. Solve your version, then check the answer against what you wrote in step one.
Not just for maths. An email that asks you to "cut the report because nobody reads it" is asking for a report people read. Said back, shorter might not be the answer.
Your problem tonight
Paste the problem, then write your own card for it.
Words that tend to trip people up are circled as you type. Fill in the card underneath the problem, and the checks will tell you if your version still says the problem's words back, misses what it asks for, or leaves a circled word unexplained.
The circled words appear here.
Your restatement card
- Asked
- Given
- Watch
- Mine
Nothing you type is saved or sent anywhere. It's gone when you leave the page, so copy the card if you want to keep it.
Why say it back
People who got word problems wrong tended to grab the numbers. People who got them right tended to build a picture of the situation.
Mary Hegarty, Richard Mayer and Christopher Monk compared students who were good at arithmetic word problems with students who weren't. Their question wasn't who calculated better. It was who understood the problem better before calculating, and how.
They ran two experiments. In one, they tracked the eye movements of 38 undergraduates as they read the problems. In the other, they tested what 37 undergraduates remembered about problems they had read.
Both pointed the same way. The unsuccessful solvers were more likely to read by direct translation: pick out the numbers and the keywords and turn them straight into a sum. The successful solvers were more likely to build a model of the problem, a picture of what was going on, before deciding what to do.
The honest limits: this study compared people who were already good or poor at word problems. It shows how they read differently, not that teaching someone to restate a problem will make them successful. The steps above are a way of doing on paper what the good solvers seemed to do in their heads.
That's 2p less than at the market.
Numbers and keywords out, straight into a sum: 65 − 2.
Who costs more, by how much, then the sum: 65 + 2.
- Experiment 1, where their eyes went. Undergraduates read word problems while the researchers tracked which words they looked at, and when.
- Experiment 2, what they remembered. Undergraduates read word problems and were then tested on what they could recall of them.
The idea
Why it works.
A problem arrives in the order its writer thought of it, not the order you need to solve it. "Less than" describes the first thing in terms of the second, so the sentence leads you to the wrong subtraction. Rewriting it from the thing you want puts the pieces back in working order.
Saying it back also tests whether you understood it. If the words come out easily, you can solve it. If they don't, you've found the gap before spending ten minutes on the wrong sum.
When it goes wrong
Habits that help.
- Use your words, not the problem's. Copying the sentence out again only feels like restating. Change the order or the subject so you have to think about what it means.
- Name both things in a comparison. "2p less" is half a fact. "The shop is 2p cheaper than the market" is the whole one.
- Check the answer against the question. Your answer should be the thing you underlined. A price for the wrong shop is a correct sum and a wrong answer.
- Use it on the problems you'd rush. Restating feels slow on easy problems, and those are the ones you get wrong without noticing.
Go deeper
Keep going.
- Simple Problem Restatement
- Deliberate Problem Restatement
- Advanced Problem Restatement
Keep this going in the app.
HourLife turns these ideas into a daily system — goals, habits, focus, and reflection in one private place.
