Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Substitution and formulas

Substitution and formulas

Represent everyday formulas algebraically, substitute known values and determine unknown values.

Updated 2026-07-24 - 5 min read

Represent everyday formulas algebraically, substitute known values and determine unknown values. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Define each variable before operating. Every symbol, table entry and graph coordinate should retain one consistent meaning and unit.

1. Use and vary everyday formulas

A formula states a relationship that works for a family of values. Units and variable definitions are part of its meaning.

Decision check: Apply this lesson's rule to the worked example: Substitute known values first; then use inverse operations and interpret the unit. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: In the formula P = 2l + 2w, which symbol represents perimeter?

  1. Read the definitions supplied by the context.
  2. P represents perimeter.

Answer: P

Check: A variable’s meaning comes from the context, not from its alphabet position.

Worked example 2

Question: Use C = 3n + 2. Find the left-hand variable when n = 5.

  1. Substitute the given value or values into C = 3n + 2.
  2. Follow operation order to obtain 17.

Answer: 17

Check: Write the substituted formula before calculating.

Worked example 3

Question: Using T = 4n + 1, the input changes from 2 to 5. By how much does the output change?

  1. The first output is 9.
  2. The second output is 21.
  3. Change = 21 - 9 = 12.

Answer: 12

Check: Calculate both outputs before comparing them.

Method map for this topic

  1. Use and vary everyday formulas: Substitute known values first; then use inverse operations and interpret the unit.

Common mistakes and how to correct them

  • formula substitution: Not yet. Write the substituted formula before calculating. Recheck the formula substitution step, then try again.
  • variable meaning: Not yet. A variable’s meaning comes from the context, not from its alphabet position. Recheck the variable meaning step, then try again.
  • systematic variation: Not yet. Calculate both outputs before comparing them. Recheck the systematic variation step, then try again.
  • unknown in formula: Not yet. Substitute first, then undo operations in reverse order. Recheck the unknown in formula step, then try again.
  • formula context: Not yet. Check which quantity is fixed and which changes. Recheck the formula context step, then try again.
  • formula structure: Not yet. Brackets and division bars apply to the grouped quantities shown. Recheck the formula structure step, then try again.

Practice

  1. In the formula P = 2l + 2w, which symbol represents perimeter?
  2. In the formula C = 5 + 2n, which symbol represents number of items?
  3. Use C = 3n + 2. Find the left-hand variable when n = 5.
  4. Use P = 2l + 2w. Find the left-hand variable when l = 7 and w = 4.
  5. Using T = 4n + 1, the input changes from 2 to 5. By how much does the output change?
  6. Using y = 3x - 2, the input changes from 4 to 7. By how much does the output change?

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

  1. P — Read the definitions supplied by the context. P represents perimeter.
  2. n — Read the definitions supplied by the context. n represents number of items.
  3. 17 — Substitute the given value or values into C = 3n + 2. Follow operation order to obtain 17.
  4. 22 — Substitute the given value or values into P = 2l + 2w. Follow operation order to obtain 22.
  5. 12 — The first output is 9. The second output is 21. Change = 21 - 9 = 12.
  6. 9 — The first output is 10. The second output is 19. Change = 19 - 10 = 9.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | identify variables everyday formulas | Identify variables and their units in everyday formulas. | | substitute determine formula unknown | Substitute known values into formulas to determine an unknown. | | describe systematic formula variation | Describe how an output changes when formula inputs vary systematically. |

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 substitution and formulas 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

Model a changing school or household quantity using substitution and formulas. Define every variable and unit, test at least two inputs, and explain what the outputs mean.

Sources