Mathematics • Year 10 • Unit 1 • Lesson 1
Wages and Salaries — Skill Drill
Build fluency with the two Australian pay structures from Lesson 1: hourly wages (Gross Pay = Hours × Hourly Rate) and annual salaries (÷ 52, ÷ 26 or ÷ 12 for the pay period). One step at a time, from a fully worked example through guided practice to independent problems.
1. I do — fully worked example
Read every step. Each one has a short reason on the right so you can see why, not just what.
Problem. Priya works 38 hours this week at an hourly rate of $32.50. Calculate her gross weekly wage.
Step 1 — Spot the rule.
Hours worked at an hourly rate → use the wage formula.
Reason: Gross Pay = Hours Worked × Hourly Rate (wage formula from the lesson).
Step 2 — Substitute the numbers.
Gross Pay = 38 × 32.50
Reason: hours = 38, hourly rate = $32.50. Order doesn't matter for multiplication.
Step 3 — Evaluate the multiplication.
38 × 32.50 = 1235
Reason: 38 × 32 = 1216, then 38 × 0.50 = 19. Add them: 1216 + 19 = 1235.
Step 4 — Write the answer with units.
Gross Pay = $1,235.00
Reason: money answers must show a dollar sign and two decimal places.
Answer: Priya's gross weekly wage is $1,235.00.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Marcus earns an annual salary of $78,400. Calculate his fortnightly pay before tax.
Step 1 — Spot the rule: an annual salary paid every fortnight means we divide by the number of __________________ in a year.
Step 2 — How many fortnights are in a year?
52 weeks ÷ 2 = ______ fortnights
Step 3 — Substitute into the salary formula:
Fortnightly Pay = 78,400 ÷ ______
Step 4 — Evaluate the division (to the nearest cent):
Fortnightly Pay = $ ______________
Step 5 — Sanity check. Multiply your fortnightly figure by the number of fortnights — it should return to (about) $78,400.
______________ × ______ ≈ $78,400 ✓
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (single-step). The middle two are standard (two-step). The last two are extension (multi-step in syllabus).
Foundation — single step
3.1 Aisha works 20 hours at $28.00 per hour. Calculate her gross pay. 1 mark
3.2 Convert an annual salary of $62,400 to a weekly amount. 1 mark
3.3 Convert an annual salary of $96,000 to a monthly amount. 1 mark
3.4 A pay slip shows gross pay of $1,420 and total deductions of $355. Find the net pay. 1 mark
Standard — two steps
3.5 Chen works 22 hours at $29.80 per hour. Calculate his gross pay, and then his net pay if tax of $146.79 is deducted. 2 marks
3.6 A graduate accepts a job paying $1,920 per fortnight. What is the annual equivalent? 2 marks
Extension — push your thinking
3.7 Sarah earns a salary of $71,500 and Ben works 38 hours per week at $36.00 per hour. Who earns more per year, and by how much? 3 marks
3.8 An office worker earns $5,400 per month. Their friend says "that's $5,400 × 12 = $64,800 per year". A second friend says "no, $5,400 ÷ 4 = $1,350 per week, then × 52 = $70,200 per year". Which calculation is correct, and which one is wrong? Justify your answer in one sentence. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded $78,400 salary)
Step 1: number of fortnights.
Step 2: 52 ÷ 2 = 26 fortnights.
Step 3: Fortnightly Pay = 78,400 ÷ 26.
Step 4: 78,400 ÷ 26 = $3,015.38 (to nearest cent).
Step 5: $3,015.38 × 26 = $78,399.88 ≈ $78,400 ✓.
3.1 — Aisha's gross pay
Gross Pay = 20 × $28.00 = $560.00.
3.2 — $62,400 to weekly
Weekly = 62,400 ÷ 52 = $1,200.00 per week.
3.3 — $96,000 to monthly
Monthly = 96,000 ÷ 12 = $8,000.00 per month.
3.4 — Net pay
Net Pay = Gross − Deductions = $1,420 − $355 = $1,065.00.
3.5 — Chen's gross and net pay
Gross = 22 × $29.80 = $655.60.
Net = $655.60 − $146.79 = $508.81.
Two steps: calculate gross first using the wage formula, then subtract deductions.
3.6 — Fortnightly to annual
Annual = $1,920 × 26 = $49,920.
Multiply by 26 (fortnights in a year) — do not multiply by 24.
3.7 — Sarah vs Ben annual
Sarah's annual salary = $71,500.
Ben's annual wage = 38 × $36.00 × 52 = $1,368 × 52 = $71,136.
Difference = $71,500 − $71,136 = $364. Sarah earns $364 more per year.
The lesson's anchor — "always compare annual equivalents" — is what makes this question fair.
3.8 — Which calculation is correct?
The first friend is correct: $5,400 × 12 = $64,800 per year.
The second friend is wrong because "÷ 4" assumes every month has exactly 4 weeks, but a year has 52 weeks — not 48 — so 4 weeks per month underestimates the year by 4 weeks and overstates the weekly figure.
Trap: months and weeks don't line up neatly. Use 12 for monthly, 26 for fortnightly, 52 for weekly.