Maths shortcuts

Counting, recognising and writing 1 to 20.

• Counting to 10 on fingersTen fingers, ten numbers — the first calculator anyone ever owns.
• Before and afterNumbers stand in a queue — every one has someone in front and behind.
• Which is bigger?The number you say later when counting is always the bigger one.
• Skip counting in 2s, 5s and 10sJump instead of stepping — the beginning of the times tables.

Adding and subtracting with things you can hold.

• Adding with things you can holdPut them together in one pile and count the pile.
• Taking awayTake some out of the pile and count what is left behind.
• DoublesSame number twice — worth learning by heart, because they unlock everything else.

Circles, squares, and spotting what comes next.

• Shapes you can see at homeEvery shape has a job — find it in the room before naming it.
• What comes next?Say the pattern out loud and your mouth finds the answer before your head does.

Multiply big numbers without writing a single line of working.

• Multiply by 11Split the digits apart and drop their sum in the middle.
• Multiply by 5Halve the number, then add a zero.
• The 9 times table on your fingersFold one finger and read the answer off both hands.
• Multiply by 25Divide by 4 and add two zeros.
• Multiply two numbers near 100Work out how far each is below 100 and let those gaps do the work.
• Same tens digit, units adding to 10When 43 × 47 shows up, the answer takes five seconds.

Any percentage of any number, in your head.

• Any percentage, starting from 10%Find 10% by moving the decimal, then build everything else from it.
• Swap the percentage round18% of 50 is hard. 50% of 18 is easy. They are the same answer.
• Fractions to percentages on sightLearn eight fractions and you can convert almost anything.

Know instantly whether a number divides cleanly.

• Divisible by 3 or 9?Add up the digits — the answer is hiding in the total.
• Divisible by 4 or 8?Ignore the whole number — only the last digits matter.
• Divisible by 11?Add alternate digits, subtract the two groups, look for 0 or 11.

Round, adjust, done — no borrowing.

• Subtract from 100 or 1000All from 9, and the last from 10 — no borrowing at all.
• Add by rounding, then adjustRound the awkward number up, add easily, then give back the difference.

Square numbers instantly when they follow a pattern.

• Square any number ending in 5Multiply the front by the next number, then stick 25 on the end.

Interest, profit and loss the way exams ask for them.

• Averages without adding everythingPick a middle number and only average the small differences.
• Simple interest in one linePrincipal times rate times time, all over a hundred.
• Profit and loss percentageAlways divide by the cost price — never by the selling price.