Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Percentages, financial contexts and modelling

Percentages, financial contexts and modelling

Model practical percentage and financial problems, calculate efficiently and interpret whether the answer fits the situation.

Updated 2026-07-24 - 6 min read

Model practical percentage and financial problems, calculate efficiently and interpret whether the answer fits the situation. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Track the value represented at every step: an efficient method is valid only when it preserves the number, comparison or required accuracy.

1. Find percentages of quantities

Percent means per hundred. Familiar percentages can be decomposed: 15% is 10% + 5%, and 12.5% is one eighth.

Decision check: Apply this lesson's rule to the worked example: Convert the percentage to a useful decimal or fraction before multiplying. Identify the exact value, label or property that satisfies the rule.

2. Discounts and percentage increases

A discount is subtracted from the original price; an increase is added. The percentage is normally based on the original amount.

Decision check: Apply this lesson's rule to the worked example: Label original, change and final amounts on separate lines. Identify the exact value, label or property that satisfies the rule.

3. Financial calculations with several steps

A fixed fee and a percentage change behave differently. Apply each operation to the quantity named in the situation and in the stated order.

Decision check: Apply this lesson's rule to the worked example: Write a calculation plan before entering numbers. Identify the exact value, label or property that satisfies the rule.

4. Build and interpret a percentage model

Modelling begins by identifying the base amount, the relationship and any constraints. A correct calculation still needs a sentence answering the practical question.

Decision check: Apply this lesson's rule to the worked example: State the percentage base and finish with units and context. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: Find 25% of 80.

  1. Write 25% as 0.25.
  2. 0.25 × 80 = 20.

Answer: 20

Check: Convert the percentage to a decimal before multiplying.

Worked example 2

Question: An item costs $50 and is discounted by 20%. What is the sale price?

  1. Discount = 0.2 × 50 = 10.
  2. Sale price = 50 - 10 = 40.

Answer: 40

Check: Subtract the discount amount from the original price.

Worked example 3

Question: 18 is what percentage of 60?

  1. Form the fraction 18/60.
  2. Multiply by 100: (18 ÷ 60) × 100 = 30%.

Answer: 30

Check: Percentage = part ÷ whole × 100.

Method map for this topic

  1. Find percentages of quantities: Convert the percentage to a useful decimal or fraction before multiplying.
  2. Discounts and percentage increases: Label original, change and final amounts on separate lines.
  3. Financial calculations with several steps: Write a calculation plan before entering numbers.
  4. Build and interpret a percentage model: State the percentage base and finish with units and context.

Common mistakes and how to correct them

  • percentage of: Not yet. Convert the percentage to a decimal before multiplying. Recheck the percentage of step, then try again.
  • discount vs price: Not yet. Subtract the discount amount from the original price. Recheck the discount vs price step, then try again.
  • percentage increase: Not yet. An increase is added to the original value. Recheck the percentage increase step, then try again.
  • percentage base: Not yet. Percentage = part ÷ whole × 100. Recheck the percentage base step, then try again.
  • financial model: Not yet. Check that the remaining amount is smaller than the starting budget. Recheck the financial model step, then try again.
  • multi step finance: Not yet. Apply the percentage to the original price before adding the fixed fee. Recheck the multi step finance step, then try again.

Practice

  1. Find 25% of 80.
  2. Find 15% of 60.
  3. An item costs $50 and is discounted by 20%. What is the sale price?
  4. An item costs $120 and is discounted by 25%. What is the sale price?
  5. 18 is what percentage of 60?
  6. 24 is what percentage of 80?

<details> <summary>Answers and reasoning</summary>

  1. 20 — Write 25% as 0.25. 0.25 × 80 = 20.
  2. 9 — Write 15% as 0.15. 0.15 × 60 = 9.
  3. 40 — Discount = 0.2 × 50 = 10. Sale price = 50 - 10 = 40.
  4. 90 — Discount = 0.25 × 120 = 30. Sale price = 120 - 30 = 90.
  5. 30 — Form the fraction 18/60. Multiply by 100: (18 ÷ 60) × 100 = 30%.
  6. 30 — Form the fraction 24/80. Multiply by 100: (24 ÷ 80) × 100 = 30%.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | calculate percentage amounts | Calculate a percentage of an amount using an efficient representation. | | solve discount increase financial problems | Solve discount, increase, fee and budget problems accurately. | | formulate interpret percentage model | Formulate a percentage model and justify the chosen representation and interpretation. |

Retrieval prompts

  • State the defining relationship for each method above without looking.
  • Give one example where two visually similar representations mean different things.
  • Diagnose one misconception from the list and explain the first corrective step.
  • Name a check that is independent of simply repeating the same calculation.

Teach-back and self-check

Close the worked examples and explain percentages, financial contexts and modelling as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.

Use this four-part check before calling the method secure:

  1. Identify: What information is given, and what must be found or justified?
  2. Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
  3. Reason: Which rule connects the representation to the required answer?
  4. Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?

If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.

Transfer task

Create a percentages, financial contexts and modelling decision from a shopping, recipe, travel or measurement context. State the quantities and required accuracy, solve it, then explain why your representation and rounding are suitable.

Sources