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:
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.
