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Ten Mental Maths Tricks That Make Number Games Easier
By the Nerdania team · · 3 min read
Number games such as Math Dash Challenge, Quick Count Quest and Number Detective reward speed, but speed in maths does not come from frantic calculating. It comes from knowing a few shortcuts so well that you barely have to think. Here are ten mental maths tricks that children and adults can learn in an afternoon, with examples you can practise right away.
1. Make tens
Ten is the friendliest number in arithmetic. When adding a list, look for pairs that make ten: 1+9, 2+8, 3+7, 4+6, 5+5. To add 7 + 6 + 3 + 4, pair 7+3 and 6+4 to get 10 + 10 = 20. Children who know their "ten pairs" by heart add far faster than those who count on their fingers.
2. Add a little more, then take it back
Adding 9 is awkward; adding 10 is easy. So add 10 and subtract 1. For 46 + 9, think 46 + 10 = 56, minus 1 = 55. The same works for 19, 29 and 99: 135 + 99 = 135 + 100 − 1 = 234.
3. Split numbers into tens and ones
For 47 + 35, add the tens (40 + 30 = 70) and the ones (7 + 5 = 12), then combine: 70 + 12 = 82. This works for subtraction too: 83 − 27 is 83 − 20 = 63, then 63 − 7 = 56.
4. Count up to subtract
Many people find subtraction easier as "how far from here to there?" For 62 − 38, count up from 38: two gets you to 40, twenty more to 60, two more to 62. That is 2 + 20 + 2 = 24. Shopkeepers used to give change exactly this way.
5. Doubles and near doubles
Most children learn doubles early: 6+6, 7+7, 8+8. Use them for nearby sums. 7 + 8 is "double 7, plus 1" = 15. 25 + 26 is "double 25, plus 1" = 51.
6. Multiply by 5 using 10
Multiplying by 10 is just adding a zero. Five is half of ten, so to multiply by 5, multiply by 10 and halve it. 5 × 18 = 180 ÷ 2 = 90. 5 × 46 = 460 ÷ 2 = 230.
7. The nines trick
For 9 × a single digit, the answer's digits add up to 9, and the tens digit is one less than the number you multiplied by. 9 × 7: the tens digit is 6, and 6 + 3 = 9, so the answer is 63. Many children also learn the finger version: hold up ten fingers, fold down the seventh, and read 6 fingers on the left and 3 on the right.
8. Double and halve
If one number in a multiplication is even, you can halve it and double the other without changing the answer. 16 × 25 becomes 8 × 50, then 4 × 100 = 400. 14 × 15 becomes 7 × 30 = 210.
9. Count in groups, not ones
In Quick Count Quest you must count scattered objects before the timer runs out. Counting one by one is slow and easy to lose track of. Instead, let your eyes find small groups – pairs, triangles of three, squares of four – and add the groups. Most people can recognise up to four objects instantly without counting; this ability is called subitising. Use it: "four, four, three, two: that's thirteen."
10. Look for the rule, not the number
Number Detective shows a sequence and asks for the next number. Instead of guessing, write down (or think about) the difference between each pair of numbers.
- 3, 7, 11, 15 … each step adds 4, so next is 19.
- 2, 6, 18, 54 … each step multiplies by 3, so next is 162.
- 1, 4, 9, 16 … these are square numbers (1×1, 2×2, 3×3, 4×4), so next is 25.
- 5, 8, 6, 9, 7 … two rules take turns: +3, −2, +3, −2, so next is 10.
If the differences themselves change, look at the differences of the differences. In 1, 2, 4, 7, 11 the gaps are 1, 2, 3, 4, so the next gap is 5 and the next number is 16.
How to practise without it feeling like homework
- Learn one trick at a time. Spend a few days on "make tens" before moving to the nines trick.
- Say it out loud. Explaining the trick to someone else is the fastest way to remember it.
- Use real life. Add up the prices in a shopping basket, work out how many minutes until dinner, or count cars in groups on a car journey.
- Play short rounds. A few levels of Math Dash Challenge each day is more effective than one long session a week.
- Accuracy before speed. A correct answer slowly is better than a fast wrong one. Speed follows naturally as the tricks become automatic.
For younger children
Children aged 3 to 6 are still learning what numbers mean. Before tricks, they need lots of counting real objects. Games such as Counting Cove, Number Train, Happy Addition and Picnic Portions have no timer and work well with an adult counting alongside. Touching each object as you count it, and saying the last number loudly ("…five! Five shells!"), helps children understand that the last number tells you how many.
Mental maths is a set of habits, and habits grow with gentle, regular practice. Pick one trick from this list, try it in a few rounds of the numbers and maths games, and notice how much faster the answers come.