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Sharpen your mental maths

Last updated 25 October 2026

Being quick and sure with numbers in your head is a skill, and like any skill it gets better with practice. This page is for students facing a maths paper without a calculator, for parents helping them, and for adults who’d like their sums a little quicker. It sets out what the exam papers ask for, then gives nine techniques, each with a worked example from a real Tot Up round.

Tot Up isn’t connected with any exam board, Qualifications Scotland or the BBC. It’s a free daily numbers game, made by one person in the UK.

Why mental maths still matters

Calculators are useful, and a 2017 report for schools from the Education Endowment Foundation says that “using a calculator does not generally harm students’ mental or pencil-and-paper calculation skills”. But a quick feel for numbers still helps. It lets you check a bill, spot a calculator answer that can’t be right, and keep going on a paper where you aren’t allowed one. Guidance for schools in England and Scotland stresses regular practice to build fluency with number facts.

What the non-calculator papers ask for

In England, the exams regulator Ofqual’s rules for GCSE maths require between 33 and 50 per cent of the marks to come from questions done without a calculator. GCSE maths is set at two tiers, Foundation and Higher, and both tiers have a non-calculator paper.

The number skills behind these papers are the ones Tot Up uses. The GCSE content in England asks students to “recognise and use relationships between operations, including inverse operations”, to “use conventional notation for priority of operations, including brackets”, and to “estimate answers; check calculations using approximation and estimation”. OCR’s specification asks for “non-calculator methods to calculate the sum, difference, product and quotient of positive and negative whole numbers.”

In Scotland, the National 5 Mathematics specification asks learners to “process numbers without using a calculator”, and adds: “The use of a calculator should complement these skills, not replace them.” The 2026 course report, written after marking, says that in Paper 1 “many candidates miss out on valuable marks because they do not demonstrate the necessary basic number skills.”

This is a summary, checked against the published specifications in October 2026. Your teacher will know which board and tier you’re sitting.

Nine techniques

Each of these works in your head and in Tot Up. In the game you combine six number cards with + − × ÷, one step at a time, to reach a target. There are no fractions or minus numbers. Each technique’s example comes from a real round, and every move in it has been checked against the game’s rules.

Know your number bonds

Pairs that make 10 (1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5) are the building blocks. For 100, the tens make 9 and the units make 10 (unless both numbers end in 0), so 37 + 63 = 100 and 82 + 18 = 100. With a 100 card on the board, you can see at once that 100 − 75 = 25 and 100 − 4 = 96.

Example: a Warm-up round with 10, 10, 9, 6, 6 and 1, and a target of 91. Warm-ups have no 100 card, but 10 × 10 = 100. Then the bond 9 + 91 = 100 tells you that 100 − 9 = 91.

Multiply by 25, 50 and 75

To multiply by 25, multiply by 100 and divide by 4: 25 × 12 is 1200 ÷ 4 = 300. For 50, multiply by 100 and halve, so 50 × 9 = 450. Since 75 is 100 − 25, 75 × 7 is 700 − 175 = 525.

Example: a Classic round with 25, 9, 9, 7, 3 and 1, and a target of 309. Make 12 first: 9 + 3 = 12, 25 × 12 = 300, 300 + 9 = 309.

Double and halve

If you halve one number and double the other, the answer stays the same, so 16 × 25 = 8 × 50 = 4 × 100 = 400. Multiplying by 4 is doubling twice, and dividing by 4 is halving twice: 300 → 150 → 75.

Example: a Warm-up round with 10, 9, 8, 5, 4 and 1, and a target of 77. Multiplying by 8 is doubling three times, so for 9 × 8 go 9 → 18 → 36 → 72. The doubling happens in your head. On the board it’s two moves: 9 × 8 = 72, then 72 + 5 = 77.

Look for factors of the target

Before you start, try dividing the target by the small cards. If one goes in exactly, you may only need to make the other factor.

Example: a Classic round with 25, 7, 5, 5, 4 and 2, and a target of 203. Since 203 = 7 × 29 and 29 = 25 + 4, it takes two steps: 25 + 4 = 29, 29 × 7 = 203. Using all six cards takes five: 5 + 5 = 10, 10 − 7 = 3, 25 × 4 = 100, 100 × 2 = 200, 200 + 3 = 203.

Get close, then adjust

Find an easy product near the target, then add or take away a little. Tot Up keeps your closest number, and 1 to 5 away still scores 70 points, so a near miss is worth having.

Example: a Warm-up round with 10, 10, 6, 3, 2 and 2, and a target of 78. Aim for 80: 10 − 2 = 8, 10 × 8 = 80, 80 − 2 = 78.

Work backwards

Start from the target and undo steps until you reach numbers you have. Then play it forwards. This is what the GCSE content calls inverse operations.

Example: a Brain-burner round with 100, 75, 10, 10, 9 and 3, and a target of 711. Add 9 to get 720, divide by 10 to get 72, and add 3 to get 75, which is on the board. Forwards, that’s 75 − 3 = 72, 72 × 10 = 720, 720 − 9 = 711.

Mind the order of operations

BIDMAS (or BODMAS) says multiplying and dividing come before adding and taking away, unless brackets say otherwise. So 3 + 4 × 5 = 23, but (3 + 4) × 5 = 35. In Tot Up each step is worked out as you tap, so the order you tap does the job of brackets.

Example: a Brain-burner round with 75, 25, 8, 4, 3 and 2, and a target of 296. The route 75 + 25 = 100, 100 × 3 = 300, 300 − 4 = 296 is written in one line as (75 + 25) × 3 − 4. Leave out the brackets and 75 + 25 × 3 is only 150.

Estimate first

A rough answer tells you whether an exact one is sensible. Round to easy numbers, work it out, then ask whether the real answer should be a bit more or a bit less.

Example: in the Classic round above with a target of 203, the last move is 29 × 7. That’s about 30 × 7 = 210. Since 29 is under 30, the answer must be just under 210, so 213 can’t be right. It’s 203, bang on.

Check what divides

To test for 3, add the digits: if the total divides by 3, so does the number, and the same goes for 9. To test for 4, look at the last two digits: if they divide by 4, so does the whole number.

Example: The digits of 711 add to 9, so 711 = 9 × 79. In the Brain-burner round above, that gives another route: 10 ÷ 10 = 1, 75 + 3 = 78, 78 + 1 = 79, 79 × 9 = 711.

Ten minutes a day

Little and often is easier to keep up than a long session now and then. Here’s a routine that takes about ten minutes.

To be clear about what this does: Tot Up is practice for number fluency, meaning quick, accurate work with whole numbers. It doesn’t cover fractions, decimals, percentages, algebra or geometry. For an exam, use it alongside revision and past papers, not instead of them.

For parents

Playing together works best when it feels like a game, not a test. A few things help.

If maths makes your child, or you, anxious, National Numeracy has a page about maths anxiety.

More free help

Tot Up isn’t affiliated with any of these organisations. If you spot a mistake on this page, or the exam details change, email hello@tot-up.com.