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.
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 Questions
- Calculate 38 + 45 mentally by splitting tens and ones.
- Use compensation to find 72 − 39.
- Use double-and-halve to find 16 × 5.
- Use multiplication facts to solve 63 ÷ 9.
- Find 99 + 47 by rounding 99 to 100 and adjusting.