Mathematics • Year 10 • Unit 1 • Lesson 2
Overtime, Penalties & Commissions, Skill Drill
Build fluency with multiplier-based pay from Lesson 2: time-and-a-half (× 1.5), double time (× 2), double time and a half (× 2.5), penalty loadings, straight commission (% × sales), and base wage + commission. One step at a time, fully worked example, guided practice, then independent problems.
1. I do, fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Liam works 38 regular hours at $28.00/hour and 6 overtime hours on Saturday at time-and-a-half. Calculate Liam's gross pay for the week.
Step 1, Spot the structure.
Standard hours at the normal rate + overtime hours at a multiplier rate. Two parts.
Reason: penalty and overtime pay is calculated separately and then added, never lumped in with normal pay.
Step 2, Calculate normal pay.
Normal pay = 38 × $28.00 = $1,064.00
Reason: Gross Pay = Hours × Hourly Rate (Lesson 1 wage formula).
Step 3, Calculate the time-and-a-half overtime rate.
Overtime rate = 1.5 × $28.00 = $42.00/hour
Reason: "time-and-a-half" means 1.5 × the normal hourly rate.
Step 4, Calculate the overtime pay.
Overtime pay = 6 × $42.00 = $252.00
Reason: number of overtime hours × the new (higher) hourly rate.
Step 5, Add the parts together.
Total gross = $1,064.00 + $252.00 = $1,316.00
Reason: total earnings = normal pay + extra pay.
Answer: Liam's gross pay is $1,316.00.
2. We do, fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. A car salesperson earns a base wage of $850 per week plus 2.5% commission on all sales. This week they sold $48,000 worth of vehicles.
Step 1, Spot the structure: a fixed weekly amount, plus a percentage of total sales. This is the __________________ + commission formula.
Step 2, Calculate the commission portion. Convert 2.5% to a decimal:
2.5% = ______ ÷ 100 = ______
Step 3, Commission = decimal rate × total sales:
Commission = ______ × $48,000 = $ __________
Step 4, Add the base wage:
Total = $850 + $ __________ = $ __________
Step 5, State the final amount with units:
Weekly earnings = $ __________
3. You do, independent practice
Show your working in the space under each problem. The first four are foundation (single rule). The middle two are standard (combine 2 ideas). The last two are extension (combine 3+ ideas).
Foundation, single rule
3.1 A worker's normal rate is $30.00/hour. Find their time-and-a-half rate. 1 mark
3.2 A nurse normally earns $35.00/hour. Find her double-time-and-a-half rate (public holidays). 1 mark
3.3 A sales rep earns 4% straight commission on sales of $25,000. Find their earnings. 1 mark
3.4 A fruit picker is paid $2.50 per bin. They pick 78 bins. Calculate their piecework pay. 1 mark
Standard, combine two ideas
3.5 Zoe works 38 hours at $32.00/hour and 3 hours overtime at double time. Calculate her gross weekly pay. 2 marks
3.6 A real estate agent has a base wage of $1,100 per week plus 0.8% commission. This week they sold a $920,000 house. Calculate their total earnings. 2 marks
Extension, push your thinking
3.7 A retail worker is paid $24.50/hour. They work 38 normal hours, plus 4 hours at time-and-a-half (Saturday) and 5 hours at double time (Sunday). Calculate gross weekly pay. 3 marks
3.8 A used-car salesperson earns a base wage of $600 per week, plus 3% commission on the first $30,000 of weekly sales, plus 5% on anything above that. They sold $52,000 this week. Calculate total earnings. 3 marks
Section 2, We do (faded commission)
Step 1: base wage + commission.
Step 2: 2.5% = 2.5 ÷ 100 = 0.025.
Step 3: Commission = 0.025 × $48,000 = $1,200.
Step 4: Total = $850 + $1,200 = $2,050.
Step 5: Weekly earnings = $2,050.00.
3.1, Time-and-a-half rate
1.5 × $30.00 = $45.00 per hour.
3.2, Double-time-and-a-half
2.5 × $35.00 = $87.50 per hour.
3.3, Straight commission
0.04 × $25,000 = $1,000.
3.4, Piecework pay
78 × $2.50 = $195.00.
3.5, Zoe with overtime
Normal pay = 38 × $32.00 = $1,216.00.
Double-time rate = 2 × $32.00 = $64.00/hour.
Overtime pay = 3 × $64.00 = $192.00.
Total = $1,216.00 + $192.00 = $1,408.00.
3.6, Real estate agent
Commission = 0.008 × $920,000 = $7,360.
Total = $1,100 + $7,360 = $8,460.
Common slip: writing 8% instead of 0.8%. 0.8% = 0.008 as a decimal.
3.7, Retail weekend penalties
Normal pay = 38 × $24.50 = $931.00.
Sat (time-and-a-half) rate = 1.5 × $24.50 = $36.75. Sat pay = 4 × $36.75 = $147.00.
Sun (double time) rate = 2 × $24.50 = $49.00. Sun pay = 5 × $49.00 = $245.00.
Total = $931.00 + $147.00 + $245.00 = $1,323.00.
3.8, Tiered commission
Band 1: 0.03 × $30,000 = $900.
Band 2: 0.05 × ($52,000 − $30,000) = 0.05 × $22,000 = $1,100.
Total commission = $900 + $1,100 = $2,000.
Total earnings = $600 base + $2,000 = $2,600.
Tiered (or "stepped") commission is common in car sales and recruitment, split sales by band, apply each rate separately, then add.