Does the answer make sense?
Calculators and careful work still produce mistakes: a slipped digit, a missed decimal, a wrong button. Estimation gives you a quick target, so you can tell if an exact answer is reasonable.
Estimate before, check after
- Before calculating, estimate the answer.
- Calculate the exact answer.
- Compare. Are they close? If not, look for an error.
Example: 412 × 9
- Estimate: 400 × 10 = 4,000.
- Calculation gives 3,708.
- Close to 4,000 ✓. (If you’d written 37,080 or 370, you’d know to recheck.)
Estimation strategies
| Strategy | Example |
|---|---|
| Rounding | 489 + 312 ≈ 500 + 300 = 800 |
| Front-end | 6,281 − 2,947 ≈ 6,000 − 2,000 = 4,000 |
| Compatible numbers | 418 ÷ 7 ≈ 420 ÷ 7 = 60 |
| Benchmarks | 0.48 of something is about half of it |
Over or under?
Know which way your estimate leans:
- Rounding both numbers up when adding gives an overestimate.
- Rounding both down gives an underestimate.
Example: 47 + 38 rounded up → 50 + 40 = 90, an overestimate. The exact answer (85) should be below 90.
Reasonableness questions
Ask these about every answer:
- Size: Is it about the right size?
- Units: Is it in the right units (cm, $, people)?
- Sense: Does it fit the situation? You can’t have 3.5 buses or −4 children.
- Direction: If you added, did the answer get bigger? If you divided by a number greater than 1, did it get smaller?
Real-world sense checks
| Answer | Reasonable? |
|---|---|
| A Grade 4 student is 135 cm tall | Yes |
| A dog weighs 3,000 kg | No (that’s a small car!) |
| A walk to school takes 15 minutes | Yes |
| A pencil costs $45 | Very unlikely |
Worked examples
Example 1: Kai says 298 + 506 = 1,804. Is that reasonable?
Estimate: 300 + 500 = 800. 1,804 is far off. Not reasonable. (Correct: 804.)
Example 2: 72 × 48 = 3,456. Reasonable?
Estimate: 70 × 50 = 3,500. Yes.
Example 3: A recipe needs 3 cups of flour per batch. Zoe says 7 batches need 2.1 cups. Reasonable?
More batches need more flour. 7 × 3 = 21. Not reasonable: she put the decimal in the wrong place.
Common mistakes
- Skipping the estimate and trusting the calculator blindly.
- Estimating too roughly to be useful.
- Ignoring units and context.
Try it yourself
- Estimate 596 + 203.
- Is 81 × 19 = 1,539 reasonable?
- Is 5,200 ÷ 4 = 130 reasonable?
- Will 312 + 489 rounded to the nearest hundred give an over- or underestimate?
Answers: 1) about 800 2) yes (80 × 20 = 1,600) 3) no; it should be about 1,300 4) An underestimate: 300 + 500 = 800, just below the exact sum of 801.
Quick recap
- Use estimation to predict and check answers.
- Judge reasonableness by size, units and context.
- Know whether your estimate is an overestimate or underestimate.