Mental Maths Strategies
Mental maths is the ability to perform calculations in your head, without paper or a calculator. It is one of the most practical skills in everyday life and a genuine indicator of number sense.
People have been calculating without written aids for thousands of years. The abacus, one of the oldest calculating tools, has been used across Mesopotamia, China, and Rome for over 2,500 years to support rapid mental arithmetic. More recently, techniques from Vedic mathematics — a set of ancient Indian calculation methods compiled and popularised by the Indian scholar Bharati Krishna Tirthaji in the 20th century — showcase many of the same shortcuts taught here, such as breaking numbers apart and working from known facts.
Why Mental Maths Matters
Strong mental maths lets you estimate quickly, spot errors in calculations, handle money, and solve problems in real time. It also deepens your understanding of how numbers work together.
Addition Strategies
| Strategy | How it works | Example |
|---|---|---|
| Make a ten | Adjust numbers to reach a multiple of 10 | 7 + 8 = 7 + 3 + 5 = 15 |
| Split and add | Break a number into tens and ones | 46 + 37 = 40 + 30 + 6 + 7 = 83 |
| Near-doubles | Use a known double and adjust | 6 + 7 = 6 + 6 + 1 = 13 |
| Add to hundreds | Round to nearest hundred, then correct | 199 + 56 = 200 + 56 − 1 = 255 |
Subtraction Strategies
| Strategy | How it works | Example |
|---|---|---|
| Count up | Count from smaller to larger number | 83 − 47: count from 47 to 83 = 36 |
| Compensation | Round, subtract, adjust | 74 − 29 = 74 − 30 + 1 = 45 |
| Breaking apart | Split the subtrahend | 85 − 37 = 85 − 30 − 7 = 48 |
Multiplication Strategies
- Double and halve: 14 × 5 = 7 × 10 = 70
- Multiply by 9: Multiply by 10 then subtract: 7 × 9 = 70 − 7 = 63
- Use known facts: 6 × 8 = 6 × 4 × 2 = 24 × 2 = 48
- Multiply by powers of 10: 43 × 100 = 4300
Division Strategies
- Use multiplication facts: 56 ÷ 7: think "7 × ? = 56" → 8
- Halving: 96 ÷ 4 = (96 ÷ 2) ÷ 2 = 48 ÷ 2 = 24
- Divide by powers of 10: 3600 ÷ 100 = 36
Key Takeaways
- Making tens, near-doubles and splitting are powerful addition strategies.
- Compensation (round then adjust) works well for both addition and subtraction.
- Double-and-halve and using known facts speed up multiplication.
- Relating division to multiplication tables is the fastest mental division approach.
Practice: Mental Maths Challenge
A calculation using one of the four strategies above appears below. Solve it in your head. If you get it wrong (or leave it blank), we'll show you the strategy step by step.