Lesson 1: Ways of Earning Money

Year level: Year 10 (middle ability set)Duration: 60 minutesFocal concept/topic: Earning money: wages, salary, commission, piecework and royalties

Lesson aim:

Introduce the unit with the question "Which job pays the most?", find out what students already know with a diagnostic quiz, and teach the main ways people are paid.

Learning intention:

We are learning to identify the different ways people are paid and to calculate earnings from a wage, commission, piecework and royalties.

Success criteria:

□ I can describe the difference between a wage, a salary, commission, piecework and a royalty
□ I can calculate a wage from an hourly rate and the hours worked
□ I can calculate earnings from commission, piecework and royalties, and work backwards from total pay to find sales

Syllabus outcomes and content:

NSW Education Standards Authority (NESA, 2022)

  • MA5-FIN-C-01: solves financial problems involving simple interest, earning money and spending money
  • MAO-WM-01: develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
  • Content: Calculate earnings from non-wage sources exploring commission, piecework and royalties

Working Mathematically indicators:

  • Decide what information is needed to compare jobs that are paid in different ways (Hook)
  • Choose the right calculation for each way of being paid (Worked examples, You do)
  • Explain why a percentage is changed to a decimal before multiplying (Worked example 1)
  • Work backwards from total pay to find the value of sales (You do Q5)

ICT:

  • Diagnostic quiz in Google Forms (quiz mode, multiple choice), answered on student devices. Each wrong option comes from one misconception, so the item-by-item summary shows straight away which misconception each student holds, not only who got a question wrong.
  • The questions are grouped by topic, two per topic: percentages (Q1–Q2), multiplying and dividing money (Q3–Q4), time and pay periods (Q5–Q6), and the pay rule and timesheets (Q7–Q8). The summary therefore also shows which topic to re-teach now and which to plan for in Lessons 2 and 3.
  • The quiz results are kept and compared with later exit tickets to track progress across the unit.

LIT:

  • Read job-advertisement language ("per hour", "p.a.", "+ commission", "per item") in the opening hook
  • Students make a vocabulary card for each way of being paid: the term, a definition in their own words, and one worked example
  • Exit ticket matching task links each term to its meaning

Prerequisite knowledge:

  • Changing percentages to decimals
  • Finding a percentage of an amount
  • Multiplying and dividing decimals
  • Opening a link and completing an online form on a device

Resources:

Before the lesson:

  • Open the diagnostic quiz on a student device to check the link works.
  • Print the vocabulary cards, worksheet and exit tickets.

Labels used in this plan: WM Working Mathematically LIT Literacy ICT Technology AfL Assessment for learning AoL Assessment of learning

Key teacher question → Expected: suggested student response. Self-designed WM indicators are in italics.


Teaching sequence

Steps & timingTeaching & learning activities
ORIENTATION0–8 minHook: Which job pays the most?LITWM

Teacher

  • Show five job ads and tell the class they are made up for this lesson:
    • A. Café barista: $25 per hour
    • B. Office assistant: $58,500 p.a.
    • C. Phone shop sales: $400 per week + 5% commission on sales
    • D. T-shirt printer: $1.80 per shirt printed
    • E. Children's book author: 10% royalty on every book sold
  • LIT Read the ads aloud together. Ask students to point out the words they have not seen before, such as "p.a.", "commission" and "royalty". Tell them each one is explained today.
  • Students vote with a show of hands for the job they think pays the most.

Key question: Can we actually tell which job pays the most?

Expected: No, it depends. We need to know how many hours the barista works, how much the salesperson sells, how many shirts are printed and how many books are sold.

Key question: What would we need to do to compare the barista with the office assistant?

Expected: Find out the barista's hours, then put both jobs over the same time, for example per week.

  • Show the unit map:
    • Lesson 1: the different ways people are paid
    • Lesson 2: extra pay for overtime, weekends and public holidays
    • Lesson 3: weekly, monthly and yearly pay, tax and take-home pay
    • Lessons 4–6: earning interest on savings
    • Lessons 7–9: spending money and making financial decisions
  • Tell the class that by the end of Lesson 3 they will be able to answer "Which job pays the most?" properly.

Students

  • Read the ads, vote, and suggest what extra information is needed.
ORIENTATION8–18 minDiagnostic quizICTAfL

Teacher

  • ICT Share the quiz link. Students answer on their own, calculators allowed.
  • Watch the live summary as answers come in.
# Question Answer Wrong options and the misconception each one shows
Percentages: needed for commission (today) and leave loading (L3)
1 Write 5% as a decimal. 0.05 0.5: moved the point one place. 5.0: did not divide by 100. 0.005: moved it too far
2 Find 15% of $400. $60 $6: wrote 15% as 0.015. $600: wrote 15% as 1.5. $415: added 15
Multiplying and dividing money: needed for penalty rates and working backwards to an hourly rate (L2)
3 Calculate 1.5 × $24. $36 $25.50: added 1.5 instead of multiplying. $12: found only the half. $48: doubled
4 Calculate $90 ÷ 4. $22.50 $22.20: wrote the remainder 2 as .2. $360: multiplied. $86: subtracted
Time and pay periods: needed for reading timesheets (L2) and converting between pay periods (L3)
5 Write 3 hours 30 minutes as a decimal number of hours. 3.5 hours 3.30: read the clock time as a decimal. 210: gave minutes, not hours
6 For pay calculations, how many weeks are in a year? 52 48: took a month as 4 weeks. 12: mixed up weeks and months. 365: mixed up weeks and days
The pay rule and timesheets: needed for using the pay rule and reading a table of shifts (L2)
7 Pay = rate × hours. Find the pay when the rate is $25 and the hours are 6. $150 $31: added instead of multiplying. $4.17: divided. $1,500: added an extra zero
8 A timesheet shows Monday 4 h, Wednesday 3.5 h and Saturday 5 h. How many hours in total? 12.5 hours 12: left out the half hour. 13: rounded 3.5 up to 4. 70: multiplied the hours
  • AfL When everyone has submitted, show the class summary for 1–2 minutes and go over the question with the lowest score, starting from its most-chosen wrong option.
  • If fewer than about 70% got Q1 or Q2 right, model one percentage example before Worked example 1.
  • Note the low-scoring questions for later. Q3, Q4, Q5, Q7 and Q8 feed the Lesson 2 starter. Q6 feeds Lesson 3.

Try the quiz as students see it. Answers submitted here go to the teacher's results, so delete any test answers before the lesson.

What the teacher sees (example from 12 simulated responses, not real students). The Google Forms summary gives the class score range, then shows for each question how many students chose each option. Here 5 students chose 3.30 for Q5, so they read the clock time as a decimal, and 4 chose 48 for Q6, so they took a month as 4 weeks.

Google Forms Insights: average 5.42 out of 8, median 5, range 4 to 7, with the total points distribution

Question 5 summary: 6 of 12 correct; 3.30 chosen by 5 students, 210 by 1

Question 6 summary: 7 of 12 correct; 48 chosen by 4 students, 365 by 1

Students

  • Complete the quiz on their own.
ENHANCING18–24 minLearning intention, wage and salaryLIT

Teacher

  • Reveal the learning intention and success criteria.
  • Define wage and salary using ads A and B.
  • LIT Students start their vocabulary cards with "wage" and "salary".

Key question: Ella, the barista in ad A, works 20 hours this week at $25 per hour. What is her wage?

Expected: $25 × 20 = $500.

Key question: If the office assistant works 5 extra hours this week, does their pay go up?

Expected: Usually not. A salary is a set amount for the year, paid in equal parts, unless the contract says otherwise.

Students

  • Answer when named, then fill in the wage and salary cards.
ENHANCING24–37 minWorked examples: commission, piecework, royaltiesWMLITAfL

Teacher

  • Model one example of each, writing every step on the board.
  • Call a named student to say each step.
  • LIT After each example, students fill in that vocabulary card.

Worked example 1: commission. Jess sells phones. She is paid a retainer of $400 per week plus 5% commission on her sales. This week she sold $6,000 of phones.

  • Commission = 5% of $6,000 = 0.05 × $6,000 = $300
  • Total pay = $400 + $300 = $700

Key question: Why do we write 5% as 0.05 and not 0.5?

Expected: Per cent means "out of 100", so 5% = 5 ÷ 100 = 0.05. 0.5 would be 50%.

Key question: Is the 5% worked out on the $400 or on the $6,000?

Expected: On the $6,000. Commission is a percentage of what she sells, not of her retainer.

  • Show the retainer–commission diagram. Point to the arrow. The 5% comes from the $6,000 of sales, and the $400 is added afterwards.
  • We do: Jess sells $9,000 of phones next week. Students work out her pay in their books before the answer is shown. (Expected: 0.05 × $9,000 = $450. $400 + $450 = $850.)

Retainer plus commission. The 5% is worked out on the $6,000 of sales, then added to the $400 retainer

Worked example 2: piecework. Tom prints T-shirts and is paid $1.80 for each shirt. On Tuesday he printed 240 shirts.

  • Pay = $1.80 × 240 = $432

Key question: Is Tom paid for his time or for what he produces?

Expected: For what he produces. The more shirts he prints, the more he earns.

Worked example 3: royalty. An author earns a 10% royalty on each book sold. The book sells for $25 and 3,000 copies are sold.

  • Royalty per book = 10% of $25 = 0.10 × $25 = $2.50
  • Total royalty = $2.50 × 3,000 = $7,500

Key question: How is a royalty like commission?

Expected: Both depend on sales. A royalty is paid to the person who created the work each time it is sold or used. It can be a percentage of the price, like this book, or a set amount each time, like a song being streamed (Q4).

Students

  • Copy each example, try the "we do" on their own, and complete the commission, piecework and royalty cards.
ENHANCING37–50 minYou doWMAfL

Teacher

  • Hand out the worksheet.
  • AfL Circulate and check two things: that percentages are changed to decimals correctly, and that commission is worked out on the sales, not on the retainer.
  • Students who need support use their vocabulary cards as worked examples. Students who finish early start the extension.

Students

  • Work on their own.

  • Q1. Leo works 15 hours at $23.50 per hour. What is his wage?

  • Q2. A car salesperson earns 3% commission. She sells a car for $28,000. How much commission does she earn?

  • Q3. A fruit picker is paid $3.20 for each bucket of fruit and picks 85 buckets. How much does she earn?

  • Q4. A musician earns a royalty of $0.004 each time her song is streamed. The song is streamed 250,000 times. How much does she earn?

  • Q5. Jess (from Worked example 1) earned $820 this week, made up of her $400 retainer plus 5% commission. What were her sales?

  • Extension. Many Aboriginal art centres are owned and governed by Aboriginal people. When an artwork sells, most of the money goes to the artist, and a small part goes back to the art centre for its running costs and community programs (Desart, n.d.). An art centre sells a painting for $1,800 and keeps 25% commission. How much does the artist receive?

Teacher note: NESA lists commission on artworks among the Aboriginal and Torres Strait Islander histories and cultures connections for this content (NESA, 2022). Desart is the association of Central Australian Aboriginal art centres. The $1,800 and the 25% are made up.

SYNTHESIZING50–60 minBack to the hook, and exit ticketAfLWM

Teacher

  • Go back to the five job ads. Ask students to say, for each ad, which way of being paid it is.
  • Go back to the success criteria. Students tick the ones they can now do on their exit ticket.

Key question: Which way of being paid would you choose for your first job, and why?

Expected (any reasoned answer): A wage, because the pay is the same each week. Or commission, because good sales can earn more, though the pay changes from week to week. Or piecework, because working faster earns more.

  • Hand out the exit ticket and collect it before students leave.
  • Preview Lesson 2: "Next lesson: what happens to Ella's pay on a Sunday?"

Exit ticket

(a) Match each term to its meaning: wage, salary, commission, piecework, royalty.

  • a payment for each item produced
  • pay worked out as hours worked × hourly rate
  • a payment to a creator each time their work is sold or used
  • a set amount per year
  • a percentage of the value of sales

(b) Noah earns $350 per week plus 4% commission on his sales. This week he sold $5,000 of goods. What is his total pay?

Success criteria: tick the ones you can now do. For any you cannot tick, write the step that is still unclear.

Students

  • Complete the exit ticket on their own.

After the lesson

  • AfL Mark the exit tickets against the success criteria.
  • AfL Read the unticked success criteria alongside the answers. Compare each student's exit ticket with their diagnostic quiz. Students who struggled with both get the three-column table scaffold in Lesson 2.

Worked solutions

Task / question Worked solution
Hook No single answer. It depends on hours worked, sales made, shirts printed and books sold. The jobs also need to be compared over the same length of time.
Diagnostic Q1–Q8 Q1 0.05. Q2 $60. Q3 $36. Q4 $22.50. Q5 3.5 hours. Q6 52. Q7 $150. Q8 4 + 3.5 + 5 = 12.5 hours
Ella's wage $25 × 20 = $500
Worked example 1 0.05 × $6,000 = $300. $400 + $300 = $700
We do (Jess, $9,000) 0.05 × $9,000 = $450. $400 + $450 = $850
Worked example 2 $1.80 × 240 = $432
Worked example 3 0.10 × $25 = $2.50 per book. $2.50 × 3,000 = $7,500
Q1 $23.50 × 15 = $352.50
Q2 0.03 × $28,000 = $840
Q3 $3.20 × 85 = $272
Q4 $0.004 × 250,000 = $1,000
Q5 $820 − $400 = $420 commission. $420 ÷ 0.05 = $8,400 in sales
Extension 0.25 × $1,800 = $450 kept by the centre. $1,800 − $450 = $1,350 to the artist
Exit ticket (a) wage: pay worked out as hours worked × hourly rate. salary: a set amount per year. commission: a percentage of the value of sales. piecework: a payment for each item produced. royalty: a payment to a creator each time their work is sold or used
Exit ticket (b) 0.04 × $5,000 = $200. $350 + $200 = $550

Adjustments and anticipated misconceptions

Misconception Why students think this How this lesson addresses it
5% is written as 0.5 They move the decimal point once instead of dividing by 100. Diagnostic Q1 finds it early. Worked example 1 asks "Why 0.05 and not 0.5?"
Commission is worked out on the retainer, or on the total pay "Commission" is a new word, and the retainer is the first number they see. Key question "Is the 5% worked out on the $400 or the $6,000?". The retainer–commission diagram shows the 5% coming from the sales. The teacher checks this while circulating.
"Commission" and "royalty" mean the same as a wage Both words are new and abstract, and students have mostly seen hourly pay. Each term gets a vocabulary card with a worked example and a photo. The exit ticket matching task checks the difference.
A royalty is always a percentage Worked example 3 uses 10% of the price, so students expect every royalty to work that way. The key question "How is a royalty like commission?" names both kinds. Q4 (a set amount for each stream) checks it.
A salary goes up when you work extra hours In casual jobs, more hours always means more pay. Key question about the office assistant working 5 extra hours.
Students who need… Adjustment
more support Use the completed vocabulary cards as worked examples. Give a partly set-out working line for Q2 and Q5 ("Commission = ___% of $___").
more challenge Q5 (working backwards) and the art-centre extension, where the commission is taken away instead of added.
language and literacy support, including EAL/D The vocabulary cards pair each term with a picture and an example. The job ads are read aloud together.

Vocabulary

Term Definition Image
income Money a person receives, for example from working
wage Pay worked out as hours worked × hourly rate Barista making coffee
hourly rate The amount paid for each hour of work
salary A set amount of pay for a year, paid in equal parts (for example weekly or monthly) Office worker at a desk
per annum (p.a.) Per year
commission Pay that is a percentage of the value of what a person sells House with a SOLD sign
retainer A set amount paid each week on top of commission, whatever the sales Diagram in Worked example 1
piecework Pay for each item produced or each task completed People picking cherries into buckets
royalty A payment to the creator of a book, song or other work each time it is sold or used Bookshop shelves

Image credits:

Sources acknowledged in this lesson