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Learn Index · Arithmetic and Operations Grade 3–5

Mental math strategies

Smart ways to calculate in your head, like doubling or adding to make a ten.

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Why mental math?

Mental math means working out answers in your head. It’s handy when shopping, checking a calculator answer, or estimating time. The trick isn’t to be a human calculator; it’s to use smart strategies that turn hard questions into easy ones.

Strategy 1: Partitioning

Partitioning splits numbers by place value.

  • 46 + 37 → (40 + 30) + (6 + 7) = 70 + 13 = 83
  • 7 × 23 → (7 × 20) + (7 × 3) = 140 + 21 = 161

Strategy 2: Compensation

Compensation changes a number to a friendly number, then fixes the answer.

  • 58 + 29 → 58 + 30 = 88, then subtract 1 → 87
  • 143 − 98 → 143 − 100 = 43, then add 2 back → 45
  • 19 × 6 → 20 × 6 = 120, then subtract one 6 → 114

Strategy 3: Bridging through ten

Bridging stops at a ten or hundred on the way.

  • 67 + 8 → 67 + 3 = 70, then + 5 → 75
  • 92 − 7 → 92 − 2 = 90, then − 5 → 85

Strategy 4: Counting up to subtract

When numbers are close, count up from the smaller one.

  • 1,002 − 997 → count up: 997 → 1,000 is 3, then 1,000 → 1,002 is 2. Total 5.
  • 82 − 47 → 47 → 50 (3) → 80 (30) → 82 (2) = 35

Strategy 5: Doubling and halving

Doubling one factor and halving the other keeps the product the same.

  • 16 × 5 → 8 × 10 = 80
  • 25 × 14 → 50 × 7 = 350
  • 4.5 × 8 → 9 × 4 = 36

Strategy 6: Using known facts

  • × 4: double, then double again. 4 × 17 → 34 → 68.
  • × 5: multiply by 10, then halve. 5 × 46 → 460 ÷ 2 = 230.
  • × 9: multiply by 10, then subtract once. 9 × 14 → 140 − 14 = 126.
  • × 11 for two-digit numbers: 11 × 23 → 230 + 23 = 253.

Strategy 7: Reordering

Add numbers in a friendly order:

  • 17 + 26 + 3 + 4 → (17 + 3) + (26 + 4) = 20 + 30 = 50
  • 4 × 7 × 25 → (4 × 25) × 7 = 100 × 7 = 700

Choosing a strategy

Problem looks like Try
A number close to 10, 100, 1,000 Compensation
Two numbers close together (subtracting) Counting up
One factor is 5, 25 or 50 Doubling and halving
Several numbers to add Reordering to make tens

Worked examples

Example 1: 298 + 145

Compensation: 300 + 145 = 445, minus 2 → 443.

Example 2: 35 × 4

Double twice: 70, then 140.

Example 3: 503 − 296

Count up: 296 → 300 (4) → 503 (203). Total 207.

Common mistakes

  • Adjusting the wrong way in compensation. If you added too much, take it away.
  • Losing track of parts when partitioning. Say each step out loud.
  • Forcing one strategy on every problem. Choose the easiest path.

Try it yourself

  1. 49 + 36
  2. 402 − 198
  3. 25 × 16
  4. 8 × 34
  5. 6 + 19 + 14 + 1

Answers: 1) 85 2) 204 3) 400 4) 272 5) 40

Quick recap

  • Mental math uses strategies: partitioning, compensation, bridging, counting up, doubling and halving.
  • Turn hard numbers into friendly numbers, then adjust.
  • Pick the strategy that suits the numbers.