Money models

Classroom resources

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Students will be able to

• I can work out income tax across brackets.
• I can explain the difference between the marginal and effective rate.
• I can model pay with a rate, hours and overtime, and check the answer makes sense.

Timing

Predict and Run 8 min · Investigate 10 min · Modify 10 min · Practise and Make 12 min

Before class

Do the Run board yourself first. Students need percentage change (previous lesson).

The one idea: each part of the income is taxed at its own bracket's rate, so crossing into a higher bracket never lowers take-home pay. The common mistake is taxing the whole income at the top rate (Jay's mistake).

The board uses a simplified version of Australia's 2026–27 resident rates (0%, 15%, 30%, 37%, 45%, with thresholds $18 200, $45 000, $135 000, $190 000), without the Medicare levy or offsets. Check the ATO's current rates before quoting them as exact; the 15% rate is legislated to fall to 14% from 1 July 2027.

Wider: effective rates across incomes as a graph; superannuation contributions.

Running the lesson

1. Predict: ask what happens to the first $45 000 when income passes it.
2. Run: ask which rate goes up in steps and which rises smoothly.
3. Investigate: ask Jay to split his income into parts.
4. Modify: ask why time and a half is × 1.5.
5. Make: ask what the model leaves out.

The hard part (on purpose)

Taxing parts, not the whole. Ask students to split the income into the bracket parts on paper before they calculate.

When students get stuck

Answers to the checks

1. one more dollar: Your income goes from $45 000 to $45 001, into the 30% bracket. What happens to your tax?
   It goes up 30 cents. Only the part above $45 000 is taxed at 30%; the rest is taxed as before.
2. tax on an income: Set the income to $60 000. Read the tax and the two rates. Was your prediction right?
   
   Tax $8520: the marginal rate is 30%, but the effective rate is 8520 ÷ 60 000 = 14.2%.
3. Tax on $30 000: What is the tax on an income of $30 000, in dollars?
   1770
   30 000 − 18 200 = 11 800, and 15% of 11 800 = $1770.
4. Find the mistake: Jay works out his tax. Click the line where his model goes wrong.
   line 3
   Line 3: only the part above $45 000 is taxed at 30%. Tax = 15% of 26 800 + 30% of 5000 = 4020 + 1500 = $5520.
5. Two rates: Someone earns $60 000. Why is their effective tax rate (14.2%) lower than their marginal rate (30%)?
   Most of their income is taxed at 0% or 15%; only the top part is taxed at 30%
   The lower brackets pull the average down.
6. The 15% bracket: Find the income at the top of the 15% bracket. What is the tax there?
   
   15% of 26 800 = $4020.
7. Over 20%: Find an income whose effective tax rate is more than 20%.
   
   Any income above about $94 800: at $95 000, 19 020 ÷ 95 000 ≈ 20.02%; at $100 000, 20.52%.
8. Pay: A job pays $28.50 an hour. Set the board for 12 hours. What is the pay?
   
   28.50 × 12 = $342.
9. Overtime: Overtime is paid at time and a half. How much is 3 hours of overtime at a rate of $28.50, in dollars?
   128.25
   1.5 × 28.50 = $42.75 an hour, × 3 = $128.25.
10. Tax on $100 000: What is the tax on $100 000, in dollars?
    20520
    4020 + 30% of 55 000 = 4020 + 16 500 = $20 520.
11. Effective rate: What is the effective tax rate on $100 000, as a percentage to 2 decimal places?
    20.52
    20 520 ÷ 100 000 = 20.52%.
12. Improve the model: How could this tax model be improved to match a real tax bill?
    Add the Medicare levy and tax offsets
    The model leaves out the Medicare levy (usually 2%) and offsets, so real tax is a bit different.
13. Review: decrease: Review: decrease $250 by 12%. What is the new amount, in dollars?
    220
    250 × 0.88 = $220.
14. An overdrawn account: A bank account is overdrawn: its balance is −$120. Then $85 is paid in and a $40 fee is taken. What is the balance now, in dollars?
    -75
    −120 + 85 − 40 = −75: still overdrawn, by $75.
15. $50 000 to spend: Find an income (to the nearest $1000) that leaves about $50 000 after tax: between $49 500 and $50 500.
    
    $58 000: tax 4020 + 3900 = $7920, leaving $50 080.

Solutions

One possible solution for each task. Other correct programs are fine.

brackets and pay › The 15% bracket

Open task: any program that does what the step asks.

brackets and pay › Over 20%

Open task: any program that does what the step asks.

brackets and pay › Pay

Open task: any program that does what the step asks.

brackets and pay › Overtime

Open task: any program that does what the step asks.

$50 000 to spend

Open task: any program that does what the step asks.

Stretch and support

Stretch: Plot the effective rate for incomes from $20 000 to $200 000. Why does it rise smoothly when the marginal rate jumps?

Support: A table with one row per bracket: the part of the income, the rate, the tax.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Money models".

The idea: Modelling financial and real-world contexts: I can Students formulate and solve models for financial problems including personal income tax, and interpret and communicate solutions including review of model appropriateness.

What understanding looks like:
- Formulates a model correctly from a financial or real-world context.
- Interprets the solution with appropriate units and contextual meaning.
- Reviews whether the model captures the situation accurately.

Mistakes students often make here:
- A student taxes the whole income at the top rate.
- A student forgets the tax-free part.
- A student mixes up marginal and effective.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- If I seem to be missing the idea that comes before this one (Modelling percentage increase and decrease), check it quickly, then come back.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Money models".

Exit ticket

Tax is 0% on the first $18 200 of income, 15% on the next part up to $45 000, and 30% on the part from $45 000 to $135 000. Find the tax on $50 000.

15% of (45 000 − 18 200) = 15% of 26 800 = $4020, plus 30% of 5000 = $1500: $5520 in all.

What each step is for

• one more dollar: Committing to what happens when income crosses a bracket shows whether they think the whole income is taxed at the higher rate.
• tax on an income: Moving the income across brackets shows each part taxed at its own rate, and the effective rate staying below the marginal rate.
• marginal and effective: Tax is added up part by part (Jay taxes the whole income at the top rate); marginal and effective rates answer different questions.
• brackets and pay: Finding incomes with given taxes and rates, then modelling pay with a rate, hours and overtime.
• money models: Tax, the effective rate and judging the model, mixed; taxing the whole income at the top rate is the planted slip; the percentage review keeps multipliers fresh.
• $50 000 to spend: Searching for an income with a given after-tax amount uses the model in reverse and checks it in context.

Where it leads

This completes AC9M8N05.

Where it leads: financial mathematics in Years 9 and 10 (interest, budgets), and modelling with rates.

Sources

• Tax rates – Australian residents (ATO) (checked 12 October 2026)
• Income tax rates and brackets, including the 14% rate from 1 July 2027 (SuperGuide) (checked 12 October 2026)