Foundation Mathematics requires students to select and use the most appropriate calculation method for a given situation. No single method is always best — context determines whether to calculate mentally, on paper, or with technology.
KEY TAKEAWAY: Choosing the right method is a skill. A simple calculation may not need a calculator; a complex multi-step problem often does.
Best for: simple operations, quick estimates, checking answers.
Techniques:
- Partitioning: \$46 + 37 = (40 + 30) + (6 + 7) = 70 + 13 = 83$
- Compensation: \$99 + 46 = 100 + 46 - 1 = 145$
- Multiplication facts: Know times tables to \$12 \times 12$
- Fraction-percentage links: $\frac{1}{4} = 0.25 = 25\%$
Best for: showing working in exams, multi-digit arithmetic, problems without a calculator.
Long Multiplication Example:
$\$347 \times 23$$
$$= 347 \times 20 + 347 \times 3$$
$$= 6940 + 1041 = 7981$$
Long Division Example:
$\$756 \div 12$$
$\$12 \times 60 = 720, \quad 756 - 720 = 36$$
$\$12 \times 3 = 36$$
$$\therefore 756 \div 12 = 63$$
Best for: complex multi-step problems, large numbers, checking written work.
Calculator use tips:
- Always enter the full number, not a rounded version, when using a calculator
- Use memory keys (M+, MR) for multi-step calculations
- Use brackets to handle order of operations correctly
- For percentages: $15\%$ of $\$240$ → enter \$240 \times 0.15 = 36$
| Tool | Best Use Case | Limitation |
|---|---|---|
| Mental arithmetic | Quick single-step | Unreliable for large numbers |
| Written algorithm | Showing steps, exam work | Slow for complex problems |
| Calculator | Multi-step, checking | Can’t catch input errors |
| Spreadsheet | Repeated calculations | Requires data entry setup |
EXAM TIP: In VCAA exams, always show your method — even if you use a calculator, write down the expression you entered and the result.
When multiple operations appear, follow this order:
$$\text{Brackets} \to \text{Orders (powers/roots)} \to \text{Division/Multiplication} \to \text{Addition/Subtraction}$$
Example:
$\$3 + 4 \times (6 - 2)^2$$
$$= 3 + 4 \times 4^2$$
$$= 3 + 4 \times 16$$
$$= 3 + 64 = 67$$
COMMON MISTAKE: Students often add before multiplying. Remember: multiplication and division come before addition and subtraction.
A council fence is $3.6\text{ m}$ high and $47.5\text{ m}$ long. Paint covers $8\text{ m}^2$ per litre and costs $\$12.50$ per litre. Find the total paint cost.
Step 1 (Mental estimate): Area $\approx 4 \times 48 = 192\text{ m}^2$; litres $\approx 192 \div 8 = 24$; cost $\approx 24 \times \$12 = \$288$
Step 2 (Calculator/written):
$$\text{Area} = 3.6 \times 47.5 = 171\text{ m}^2$$
$$\text{Litres} = 171 \div 8 = 21.375 \to 22\text{ L (round up)}$$
$$\text{Cost} = 22 \times 12.50 = \$275$$
Step 3 (Check): $\$275$ is close to the estimate $\$288$ → reasonable.
VCAA FOCUS: VCAA tasks test whether you can select appropriate methods and show your reasoning. Don’t just write the final answer.
