A key skill in Foundation Mathematics is being able to check whether a calculated answer is reasonable. This means using estimation and mental strategies — not just accepting whatever a calculator displays.
KEY TAKEAWAY: A calculator can give a wrong answer if you enter the wrong numbers. Always estimate first to catch errors.
Round numbers to 1 significant figure, then calculate mentally:
$\$268 \div 4 \approx 300 \div 4 = 75 \quad \text{(exact: } 67\text{)}$$
The estimate $75$ is close enough to confirm the exact answer $67$ is reasonable.
Ask: should the answer be in the tens, hundreds, thousands?
Example: A school buys $32$ chairs at $\$47$ each.
$\$32 \times 47 \approx 30 \times 50 = 1500$$
If someone calculates $\$150.40$, it’s clearly wrong — it’s off by a factor of 10.
If $x = 156 \div 12$, check by multiplying back:
$\$12 \times 13 = 156 \checkmark$$
Check that units make sense:
- A person’s height of $1750\text{ mm}$ = $1.75\text{ m}$ ✓
- A room area of $24000\text{ cm}^2$ = $2.4\text{ m}^2$ ✓ (for a small storage space)
EXAM TIP: If asked “Is this answer reasonable?”, always write a brief justification: state your estimate, compare it to the given answer, and conclude yes/no.
| Strategy | When to Use | Example |
|---|---|---|
| Round to nearest 10/100 | Multi-step arithmetic | \$384 + 219 \approx 380 + 220 = 600$ |
| Halving and doubling | Multiplication | \$15 \times 24 = 30 \times 12 = 360$ |
| Factoring | Larger multiplications | \$35 \times 12 = 35 \times 4 \times 3 = 140 \times 3 = 420$ |
| Benchmark fractions | Percentage estimates | $\frac{1}{4} = 25\%$, $\frac{1}{3} \approx 33\%$, $\frac{3}{4} = 75\%$ |
| Break-and-bridge | Addition | \$67 + 48 = 67 + 3 + 45 = 70 + 45 = 115$ |
A recipe needs $2.75\text{ kg}$ of flour. Flour costs $\$1.80$ per kg. Estimate the total cost.
Step 1 (Estimate): $3\text{ kg} \times \$2 = \$6$
Step 2 (Calculate): \$2.75 \times 1.80 = \$4.95$
Step 3 (Check): $\$4.95$ is less than $\$6$ — reasonable, since we rounded up for the estimate.
REMEMBER: Your estimate doesn’t need to match exactly — it just needs to be close enough to confirm no major error occurred.
APPLICATION: In everyday life, estimation is used constantly — checking change, comparing prices, budgeting. These VCAA tasks are drawn directly from such real-world situations.
