Applying Number Skills: Financial and Measurement Contexts

Overview

Foundation Mathematics is built around real-world application. This key knowledge area brings together all number skills — operations, percentages, fractions, ratios, rounding — and applies them to financial and measurement situations encountered in everyday life and work.

KEY TAKEAWAY: Number skills are tools. The skill being assessed in VCAA is whether you can choose the right tool and apply it correctly to a realistic scenario.

Financial Contexts

Wages and Salaries

• Hourly rate: $\text{Pay} = \text{hours worked} \times \text{hourly rate}$
• Overtime: Often paid at $1.5\times$ (time-and-a-half) or $2\times$ (double time)

Example:

Normal rate: $\$24.50$/hr. Work $38$ hrs normal + $4$ hrs overtime at $1.5\times$.
$$\text{Normal pay} = 38 \times 24.50 = \$931$$
$$\text{Overtime pay} = 4 \times (24.50 \times 1.5) = 4 \times 36.75 = \$147$$
$$\text{Total} = \$931 + \$147 = \$1078$$

Discounts and Sales

$$\text{Sale price} = \text{Original price} \times (1 - \text{discount rate})$$

$20\%$ off $\$350$: \$350 \times 0.80 = \$280$

GST (Goods and Services Tax)

Australia’s GST rate is $10\%$.

$$\text{Price incl. GST} = \text{price excl. GST} \times 1.10$$
$$\text{GST component} = \text{price incl. GST} \div 11$$

Simple Interest

$$I = P \times r \times t$$

Where $P$ = principal, $r$ = annual rate (as decimal), $t$ = time in years.

$\$5000$ at $4\%$ p.a. for $3$ years:
$$I = 5000 \times 0.04 \times 3 = \$600$$

Budgeting

$$\text{Balance} = \text{Income} - \text{Expenses}$$

A positive balance = surplus; a negative balance = deficit.

EXAM TIP: Show each step of your financial calculation. In multi-step problems, a clear layout earns method marks even if you make an arithmetic error.

Measurement Contexts

Unit Conversions

Speed, Distance, Time

$$d = s \times t, \quad s = \frac{d}{t}, \quad t = \frac{d}{s}$$

A car travels $240\text{ km}$ in $3$ hours: $s = \frac{240}{3} = 80\text{ km/h}$

Cost per Unit Rate

$$\text{Unit price} = \frac{\text{total cost}}{\text{quantity}}$$

$500\text{ g}$ for $\$3.20$ vs $750\text{ g}$ for $\$4.50$:
- $500\text{ g}$: $\$3.20 \div 500 = \$0.0064$/g
- $750\text{ g}$: $\$4.50 \div 750 = \$0.0060$/g → better value

Multi-Step Problem Strategy

1. Identify what is known and what is being asked
2. Choose the appropriate formula or operation
3. Calculate step by step, showing working
4. Check with an estimate
5. State the answer with correct units and appropriate rounding

VCAA FOCUS: VCAA exam questions are set in realistic contexts — shopping, building, cooking, travel, wages. Practice reading the scenario carefully and extracting the numbers you need.