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.