Mathematics Standard • Year 11 • Module 3 • Lesson 3
Commission, Piecework and Leave Loading
Build fluency in commission (flat, retainer-based, tiered), piecework and leave loading calculations.
1. Quick recall
Answer each question in the space provided. 1 mark each
Q1.1 Convert each percentage rate to a decimal:
2.5% = ____________ 4% = ____________ 17.5% = ____________
Q1.2 Write the piecework formula: Piecework pay = ______________ × ______________.
Q1.3 Complete the leave loading formula on a weekly wage W:
Leave loading = ____ × (W × ____)
2. Worked example — retainer + commission
Follow each line. Every step has a reason on the right.
Problem. Daniela earns a weekly retainer of $620 and 2.8% commission on all sales. This week she sold $84,000 of cars. Calculate her total weekly earnings.
Step 1 — Convert the percentage to a decimal.
2.8% = 2.8 ÷ 100 = 0.028
Reason: percent → decimal by dividing by 100.
Step 2 — Calculate the commission.
Commission = $84,000 × 0.028 = $2,352.00
Step 3 — Add the retainer.
Total = $620.00 + $2,352.00 = $2,972.00
Conclusion. Weekly earnings = $2,972.00.
3. Faded example — tiered commission
James earns commission on a tiered structure: 3% on the first $15,000 of monthly sales, 4.5% on sales from $15,001 to $40,000, and 6% on sales above $40,000. In March he achieves $55,000 in sales. Fill the blanks. 4 marks
Step 1 — Tier 1 (first $15,000):
Tier 1 = $15,000 × 0.03 = $ ____________
Step 2 — Tier 2 (the $25,000 from $15,001 to $40,000):
Tier 2 = $ __________ × 0.045 = $ ____________
Step 3 — Tier 3 (sales above $40,000):
Tier 3 amount = $55,000 − $40,000 = $ __________
Tier 3 = $ __________ × 0.06 = $ ____________
Step 4 — Sum the three tiers:
Total commission = $ __________ + $ __________ + $ __________ = $ ____________
4. Graduated practice — commission, piecework, leave loading
Show your working in the space below each part. Keep dollar amounts to 2 decimal places.
Foundation — single-formula application (4 questions)
| Q | Problem | Answer |
|---|---|---|
| 4.1 1 | Total sales $45,000 at a flat 3.5% commission. Find the commission. | |
| 4.2 1 | A worker is paid $1.80 per item. They make 245 items. Find their pay. | |
| 4.3 1 | An employee earns $980 per week. Find the leave loading on 4 weeks of leave (17.5%). | |
| 4.4 1 | What decimal should be used for a commission rate of 4.5%? |
Standard — typical HSC difficulty (6 questions)
Show at least one line of substitution and clearly label your final answer with units.
4.5 A salesperson receives a retainer of $540 plus 3.2% commission on sales. This week she made $48,000 in sales. Calculate her total earnings. 2 marks
4.6 A worker is paid $2.45 per box packed. They pack 172 boxes in a day. Calculate the day's pay. 2 marks
4.7 An employee earns $1,120 per week. Calculate the annual leave loading paid on 4 weeks of leave. 2 marks
4.8 A farm worker is paid $2.35 per crate of strawberries. In one shift they pick 186 crates. Calculate the shift pay. 2 marks
4.9 A real-estate agent earns a $1,200 monthly retainer plus 1.8% commission on the value of houses sold. In March they sell two houses worth $720,000 and $885,000. Calculate the monthly earnings. 2 marks
4.10 A worker earns $1,240 per week. Calculate the total amount paid (leave pay + leave loading) for 4 weeks of annual leave. 2 marks
Extension — tiered commission + threshold (2 questions)
4.11 A worker's tiered commission is 4% on the first $20,000 and 7% on sales above $20,000. They achieve $35,000 in sales. Calculate the total commission. 3 marks
4.12 A car salesperson earns a fortnightly retainer of $800 plus 3.5% commission on sales above a threshold of $6,000 per fortnight. This fortnight sales are $34,000. Calculate the total fortnightly earnings. 3 marks
5. Self-check the easy 3
Tick the first three once you've checked your method works.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1 — Percentage to decimal
2.5% = 0.025. 4% = 0.04. 17.5% = 0.175.
Q1.2 — Piecework formula
Piecework pay = number of items (n) × rate per item (rp).
Q1.3 — Leave loading formula
Leave loading = 0.175 × (W × 4).
Q3 — Faded example (tiered commission)
Step 1: Tier 1 = $15,000 × 0.03 = $450.00.
Step 2: Tier 2 = $25,000 × 0.045 = $1,125.00.
Step 3: Tier 3 amount = $55,000 − $40,000 = $15,000. Tier 3 = $15,000 × 0.06 = $900.00.
Step 4: Total = $450 + $1,125 + $900 = $2,475.00.
Q4.1 — Flat commission
Commission = $45,000 × 0.035 = $1,575.00.
Q4.2 — Piecework
Pay = 245 × $1.80 = $441.00.
Q4.3 — Leave loading on $980/week
4 weeks' pay = $980 × 4 = $3,920. Loading = $3,920 × 0.175 = $686.00.
Q4.4 — 4.5% as a decimal
4.5% = 0.045.
Q4.5 — Retainer + commission
Commission = $48,000 × 0.032 = $1,536.00.
Total = $540 + $1,536 = $2,076.00.
Q4.6 — 172 boxes at $2.45
Pay = 172 × $2.45 = $421.40.
Q4.7 — Leave loading on $1,120/week
4 weeks' pay = $1,120 × 4 = $4,480. Loading = $4,480 × 0.175 = $784.00.
Q4.8 — Farm worker, 186 crates
Pay = 186 × $2.35 = $437.10.
Q4.9 — Real-estate March earnings
Total sales = $720,000 + $885,000 = $1,605,000.
Commission = $1,605,000 × 0.018 = $28,890.00.
Total monthly earnings = $1,200 + $28,890 = $30,090.00.
Q4.10 — Total leave payment
Leave pay = $1,240 × 4 = $4,960.00.
Leave loading = $4,960 × 0.175 = $868.00.
Total = $4,960 + $868 = $5,828.00.
Q4.11 — Tiered: 4% then 7%
Tier 1: $20,000 × 0.04 = $800.00.
Tier 2: ($35,000 − $20,000) × 0.07 = $15,000 × 0.07 = $1,050.00.
Total commission = $800 + $1,050 = $1,850.00. (Applying 7% to the full $35,000 = $2,450 is a common error.)
Q4.12 — Retainer + commission above threshold
Commission-eligible sales = $34,000 − $6,000 = $28,000.
Commission = $28,000 × 0.035 = $980.00.
Fortnightly earnings = $800 + $980 = $1,780.00. (Applying 3.5% to the full $34,000 gives $1,190 — wrong.)