Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Ratio modelling in practical contexts

Ratio modelling in practical contexts

Formulate, solve and interpret practical ratio models using one common multiplicative scale factor.

Updated 2026-07-24 - 6 min read

Formulate, solve and interpret practical ratio models using one common multiplicative scale factor. 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. Build and test a ratio model

A ratio model names two quantities in order and preserves their relationship by multiplying or dividing both terms by the same non-zero factor. A prediction also needs an assumption about what remains unchanged.

Decision check: Apply this lesson's rule to the worked example: Name both quantities, apply one common scale factor and state the assumption behind the prediction. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: Which ratio statement models this situation: There are 3 red counters for every 5 blue counters.

  1. Keep the order of the quantities the same in the words and the ratio.
  2. The matching model is red:blue = 3:5.

Answer: red:blue = 3:5

Check: Name both quantities and preserve their order.

Worked example 2

Question: A model uses the ratio blue:red = 2:3. If the blue quantity is 4, what is the matching red quantity?

  1. The first ratio term is multiplied by 2.
  2. Apply the same multiplier to the second term: 3 × 2 = 6.

Answer: 6

Check: Equivalent ratios multiply or divide both terms by the same factor.

Worked example 3

Question: A student changes the ratio 2:3 to 8:12. Which evaluation is correct?

  1. Compare the multiplicative scale factor applied to each term.
  2. valid; both terms were multiplied by 4

Answer: valid; both terms were multiplied by 4

Check: Equivalent ratios require the same non-zero multiplier for both terms.

Method map for this topic

  1. Build and test a ratio model: Name both quantities, apply one common scale factor and state the assumption behind the prediction.

Common mistakes and how to correct them

  • ratio model table: Not yet. Equivalent ratios multiply or divide both terms by the same factor. Recheck the ratio model table step, then try again.
  • ratio context choice: Not yet. Name both quantities and preserve their order. Recheck the ratio context choice step, then try again.
  • ratio scale factor: Not yet. A valid ratio model applies one common multiplier to both quantities. Recheck the ratio scale factor step, then try again.
  • ratio model check: Not yet. Equivalent ratios require the same non-zero multiplier for both terms. Recheck the ratio model check step, then try again.
  • ratio assumption: Not yet. State what must remain unchanged when the ratio is scaled. Recheck the ratio assumption step, then try again.
  • ratio interpretation: Not yet. A justification must name the common multiplicative change. Recheck the ratio interpretation step, then try again.

Practice

  1. Which ratio statement models this situation: There are 3 red counters for every 5 blue counters.
  2. Which ratio statement models this situation: A cordial mix uses 2 cups of concentrate for every 7 cups of water.
  3. A model uses the ratio blue:red = 2:3. If the blue quantity is 4, what is the matching red quantity?
  4. A model uses the ratio flour:cocoa = 5:2. If the flour quantity is 15, what is the matching cocoa quantity?
  5. A student changes the ratio 2:3 to 8:12. Which evaluation is correct?
  6. A student changes the ratio 5:7 to 15:21. Which evaluation is correct?

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

  1. red:blue = 3:5 — Keep the order of the quantities the same in the words and the ratio. The matching model is red:blue = 3:5.
  2. concentrate:water = 2:7 — Keep the order of the quantities the same in the words and the ratio. The matching model is concentrate:water = 2:7.
  3. 6 — The first ratio term is multiplied by 2. Apply the same multiplier to the second term: 3 × 2 = 6.
  4. 6 — The first ratio term is multiplied by 3. Apply the same multiplier to the second term: 2 × 3 = 6.
  5. valid; both terms were multiplied by 4 — Compare the multiplicative scale factor applied to each term. valid; both terms were multiplied by 4
  6. valid; both terms were multiplied by 3 — Compare the multiplicative scale factor applied to each term. valid; both terms were multiplied by 3

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | represent ratio model | Represent a practical constraint with an ordered ratio and equivalent-ratio table. | | solve ratio model | Solve a practical ratio model by applying one multiplicative scale factor to both quantities. | | interpret justify ratio model | Interpret a ratio-model result, state an assumption and justify whether the relationship was preserved. |

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 ratio modelling in practical contexts 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 ratio modelling in practical contexts 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