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.
