Does that make sense?
Getting an answer is only half the job. The other half is asking: Does this make sense? Checking for reasonableness catches mistakes before they cause trouble.
Four checks for every answer
| Check | Ask |
|---|---|
| 1. Estimate | Is my answer close to a quick estimate? |
| 2. Inverse operation | If I undo my calculation, do I get back to the start? |
| 3. Context | Does the answer fit the real situation? |
| 4. Units | Did I use the right units, and is the size sensible? |
Check 1: Estimate
Problem: 389 + 412
Estimate: 400 + 400 = 800. If you got 701 or 8,001, you know something went wrong.
Check 2: Inverse operation
- Addition ↔ subtraction: 536 − 278 = 258 → check 258 + 278 = 536 ✓
- Multiplication ↔ division: 156 ÷ 12 = 13 → check 13 × 12 = 156 ✓
Check 3: Context
The real situation tells you a lot:
- Can you have half a person? No. If 47 students ride in buses of 20, you need 3 buses, not 2.35.
- Can a price be negative? Not normally.
- Should the answer be bigger or smaller than the numbers you started with? If you share things out, each share is smaller than the total.
Check 4: Units and size
- A Grade 5 student who is 140 m tall? The unit must be cm.
- A pencil costing $400? Probably a decimal slip: $4.00.
- A car trip of 3 hours at highway speed covering 30,000 km? Not possible.
Using benchmarks
Benchmarks help with sense checks:
| Benchmark | About |
|---|---|
| Height of a door | 2 m |
| Mass of a large apple | 200 g |
| Walking speed | 5 km per hour |
| One school year | about 190 school days |
Worked examples
Example 1: Jack says 6 × 48 = 2,880. Is it reasonable?
Estimate: 6 × 50 = 300. 2,880 is about 10 times too big. Not reasonable: the answer is 288.
Example 2: A recipe for 4 needs 300 g of pasta. Lena says a recipe for 8 needs 150 g. Reasonable?
More people should need more pasta. Not reasonable; it should be 600 g.
Example 3: 145 people need tables of 8. Max says 18.125 tables. Reasonable?
You can’t have part of a table. Round up to 19 tables.
Common mistakes
- Trusting a calculator without a quick estimate.
- Ignoring context, giving answers like 3.5 buses.
- Skipping the check because you’re in a hurry.
Try it yourself
- Is 512 − 289 = 323 reasonable? Check with addition.
- A class of 28 shares 7 pizzas equally. Sara says each student gets 4 pizzas. Reasonable?
- Is a mass of 50 kg reasonable for a Grade 4 backpack?
- Estimate to check: 49 × 21 = 1,029.
Answers: 1) No: 323 + 289 = 612. The answer is 223. 2) No: each gets 1/4 of a pizza. 3) No; about 5 kg is more reasonable. 4) 50 × 20 = 1,000, so yes.
Quick recap
- Check every answer for reasonableness.
- Estimate, use the inverse operation, think about context and units.
- If something seems off, go back and find the mistake.