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Mental maths strategies that really work
Mental maths isn't about being a human calculator. It's about knowing a handful of reliable tricks, so you can turn a hard-looking sum into two or three easy ones. These are the strategies teachers use, and they work just as well for adults.
1. Bridging through 10
To add 8 + 5, split the 5 into 2 and 3: 8 + 2 makes 10, then 10 + 3 = 13. Making a ten first is the single most useful habit for addition, and it relies on knowing your number bonds.
2. Partitioning
Split numbers into tens and ones. 46 + 37 becomes 40 + 30 = 70 and 6 + 7 = 13, so 70 + 13 = 83. It's easiest to start with the tens, working left to right, the same way you read the number.
3. Near doubles
Doubles are easy to remember. Use them for numbers that are close: 7 + 8 is double 7 plus 1, which is 15. And 25 + 26 is double 25 plus 1, which is 51.
4. Round and adjust (compensation)
Adding 9 is adding 10 then taking 1 away: 47 + 9 = 57 − 1 = 56. The same works for 19, 29, 99: 365 + 99 = 465 − 1 = 464. For subtraction, take away 10 and give 1 back: 52 − 9 = 42 + 1 = 43.
5. Count up to subtract
For 62 − 38, count up from 38 instead: 2 more makes 40, then 22 more makes 62. So the difference is 2 + 22 = 24. This is how most people give change.
6. Doubling and halving
To multiply by 4, double twice: 17 × 4 is double 34, which is 68. To multiply by 5, multiply by 10 and halve: 46 × 5 = 460 ÷ 2 = 230. You can also halve one number and double the other: 16 × 25 = 8 × 50 = 4 × 100 = 400.
7. Use 10s for 9s and 11s
9 × 7 is 10 × 7 minus 7, which is 63. And 11 × 14 is 140 + 14, which is 154.
8. Check with odd, even and last digits
Two odd numbers always add up to an even number, and an odd number plus an even number is always odd. The last digit of a sum only depends on the last digits you added. These checks won't tell you the answer, but they quickly tell you when an answer is wrong.
Putting them together
Beequation puzzles use all of these at once. One number in the honeycomb is the sum of two others, and to find it quickly you'll check last digits, use odd and even, and bridge through tens without thinking about it. Try this one:
Show answer
75, because 46 + 29 = 75.Last digits help: 75 ends in 5, so you need two numbers whose last digits add to 5 or 15. Only 6 and 9 do it, so 46 + 29 is the pair.
Try a Beequation puzzle
Every honeycomb hides one number made from two others. It's free in your browser, with levels for children aged 5 to 12 and for adults.