Mathematics Standard • Year 11 • Module 3 • Lesson 1
Wages, Salaries and Pay Periods
Apply pay-period conversions to realistic Australian workplace scenarios — choose, convert, conclude.
Problem 1 — Apprentice budget plan
Liam is starting an apprenticeship paying $24.60 per hour for a 38-hour week. He wants to plan a monthly budget but is paid fortnightly.
Set up: What are we solving for?
(i) Calculate Liam's weekly pay. 1 mark
(ii) Calculate his fortnightly pay (what lands in his account each pay). 1 mark
(iii) Calculate his equivalent monthly pay (to the nearest cent), then state in one sentence why this monthly figure is NOT simply weekly × 4. 3 marks
Stuck? Revisit lesson § Pay Period Conversions — convert via annual first.Problem 2 — Choosing between two graduate roles
Mira is comparing two graduate jobs.
Role A: Salary of $72,800 per year, paid fortnightly.
Role B: Hourly rate of $36.40 per hour for a 38-hour week.
Set up: What are we solving for?
(i) Calculate Role A's fortnightly pay. 1 mark
(ii) Calculate Role B's annual income. 2 marks
(iii) State which role pays more annually, and by how much, in a clear conclusion sentence. 2 marks
Stuck? Convert both to the same unit (annual) before comparing.Problem 3 — What's the equivalent hourly rate?
A NSW high-school teacher earns $86,580 per year and works 38 hours per week. A casual relief teacher is offered $44.20 per hour for the same work.
Set up: What are we solving for?
(i) Calculate the salaried teacher's weekly pay. 1 mark
(ii) Calculate the salaried teacher's equivalent hourly rate, to the nearest cent. 2 marks
(iii) Compare the two hourly rates. Which earns more per hour, and by how much per hour? 2 marks
Stuck? Revisit lesson § Worked Example 4 — Annual → Hourly.Problem 4 — Three friends, three pay periods
Three friends compare what they earn.
Ana: $1,210 per week.
Ben: $2,560 per fortnight.
Chen: $5,460 per month.
Set up: What are we solving for?
(i) Convert each friend's pay to an annual figure. 3 marks
(ii) Rank them from highest annual pay to lowest. 1 mark
(iii) By how much per year does the highest-paid friend earn over the lowest-paid friend? 1 mark
Stuck? Convert all three to annual using × 52, × 26 and × 12.Problem 5 — Reverse-engineer the hours
A retail worker is paid $24.80 per hour. Her weekly take-home (before tax) was $942.40 for a particular week. The award allows a standard week of 38 hours, anything above is overtime.
Set up: What are we solving for?
(i) Calculate the standard weekly pay for a 38-hour week at her rate. 1 mark
(ii) Using only her hourly rate, work out how many hours she must have worked this week to receive $942.40. 2 marks
(iii) Did she work any overtime this week? Justify with one sentence. 2 marks
Stuck? Pay ÷ hourly rate = hours. Then compare with 38.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Apprentice budget
Set up. We are finding weekly, fortnightly and monthly pay for the same job, and explaining why the monthly figure is not simply weekly × 4.
(i) Weekly = $24.60 × 38 = $934.80.
(ii) Fortnightly = $934.80 × 2 = $1,869.60.
(iii) Annual = $934.80 × 52 = $48,609.60. Monthly = $48,609.60 ÷ 12 = $4,050.80. This is not weekly × 4 ($934.80 × 4 = $3,739.20) because some months contain 5 weeks of work — using ÷ 12 on the annual figure shares the year out fairly.
Problem 2 — Mira's two roles
Set up. Convert both roles to annual, then compare.
(i) Role A fortnightly = $72,800 ÷ 26 = $2,800.00.
(ii) Role B weekly = $36.40 × 38 = $1,383.20; annual = $1,383.20 × 52 = $71,926.40.
(iii) Difference = $72,800.00 − $71,926.40 = $873.60. Role A pays more by $873.60 per year.
Problem 3 — Teacher hourly rate
Set up. Convert the salaried teacher's annual to weekly to hourly, then compare with the casual hourly rate.
(i) Weekly = $86,580 ÷ 52 = $1,665.00.
(ii) Hourly = $1,665.00 ÷ 38 = $43.815... ≈ $43.82/hr.
(iii) Casual = $44.20/hr; salaried ≈ $43.82/hr. The casual relief teacher earns more per hour, by about $0.38 per hour — though the salaried teacher gets paid leave and other benefits.
Problem 4 — Three friends ranked
Set up. Convert all three to annual, rank, then find the gap.
(i) Ana = $1,210 × 52 = $62,920. Ben = $2,560 × 26 = $66,560. Chen = $5,460 × 12 = $65,520.
(ii) Rank (high to low): Ben ($66,560) > Chen ($65,520) > Ana ($62,920).
(iii) Ben − Ana = $66,560 − $62,920 = $3,640 per year.
Problem 5 — Reverse-calculate hours
Set up. Work backwards from total pay to number of hours, then compare to a standard week.
(i) 38-hour standard week pay = $24.80 × 38 = $942.40.
(ii) Hours worked = $942.40 ÷ $24.80 = 38 hours.
(iii) No overtime. She worked exactly 38 hours, which is the standard week — anything above 38 would have been overtime, but here the total matches the standard week pay exactly.