Estimation and checking
OCR J560 awards marks for estimation on every paper — both Foundation and Higher. The skill is rounding numbers to 1 significant figure (1 s.f.), computing mentally, and reporting a sensible estimate.
The standard method
- Round every number to 1 s.f.
- Carry out the simplified calculation.
- Show the rounded numbers and the result clearly.
✦Worked example— Worked examples
Estimate 312 × 48.7 / 9.6: Round: 300 × 50 / 10 = 15000 / 10 = 1500. Actual answer is around 1583 — the estimate is close enough to confirm a calculator answer.
Estimate √(48.7 × 102): Round: √(50 × 100) = √5000 ≈ 70 (since 70² = 4900). Actual ≈ 70.5.
Estimate (4.97 + 3.12)² / 0.21: Round: (5 + 3)² / 0.2 = 64 / 0.2 = 320.
Decimals less than 1
Watch for "0.196" — round to 0.2, not to 0. Otherwise division blows up.
When estimates differ from the calculator
Use the estimate as a sanity check. If you computed 312 × 48.7 / 9.6 = 158.3 on the calculator but the estimate is 1500, you have probably mis-keyed (forgotten a digit). Re-do the calculation.
Bounds (related skill)
Lower and upper bounds give a precise envelope rather than an estimate. For 4.7 m measured to the nearest 0.1 m: lower bound 4.65 m, upper bound 4.75 m. Bounds are tested at Higher tier.
OCR mark scheme conventions
- M1 for rounding all values to 1 s.f. correctly.
- A1 for the final estimate.
- "Estimate" means "to 1 s.f. by default" unless the question states otherwise.
- Showing the rounded values is essential — answer alone is not enough on "estimate" questions.
⚠Common mistakes
- Rounding mid-calculation rather than at the start.
- Rounding 0.197 to 0 instead of 0.2.
- Reporting the calculator answer instead of an estimated value.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves