Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Variables and algebraic expressions

Variables and algebraic expressions

Use variables, constants, operations and brackets to represent situations and evaluate expressions.

Updated 2026-07-24 - 6 min read

Use variables, constants, operations and brackets to represent situations and evaluate expressions. 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. Build expressions from situations

A variable represents a quantity that may change. A coefficient multiplies it, while a constant stays fixed.

Decision check: Apply this lesson's rule to the worked example: Define the variable and translate the fixed and changing parts separately. Identify the exact value, label or property that satisfies the rule.

2. Read and evaluate expressions

Brackets group operations. Substitution replaces every occurrence of a variable before the order of operations is applied.

Decision check: Apply this lesson's rule to the worked example: Write the substituted expression on a new line before calculating. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: The pattern 4, 7, 10, 13, ... has rule 3n + 1. Find term 8.

  1. Substitute n = 8 into 3n + 1.
  2. The value is 25.

Answer: 25

Check: The term number is the input n, not the previous term.

Worked example 2

Question: Which description matches 2(a + 3)?

  1. Use brackets and operation order to read the expression.
  2. The matching description is: double the sum of a and 3.

Answer: double the sum of a and 3

Check: Read from the grouped operation outward.

Worked example 3

Question: Which expression represents “5 more than n”?

  1. Identify the operation named in the phrase.
  2. Keep the variable’s role and order: n + 5.

Answer: n + 5

Check: Translate one phrase at a time and pay attention to order for subtraction and division.

Worked example 4

Question: Evaluate 4n + 3 when n = 5.

  1. Substitute 5 for n.
  2. Follow the order of operations to get 23.

Answer: 23

Check: Replace every occurrence of the variable, then calculate.

Method map for this topic

  1. Build expressions from situations: Define the variable and translate the fixed and changing parts separately.
  2. Read and evaluate expressions: Write the substituted expression on a new line before calculating.

Common mistakes and how to correct them

  • phrase to expression: Not yet. Translate one phrase at a time and pay attention to order for subtraction and division. Recheck the phrase to expression step, then try again.
  • context expression: Not yet. A coefficient multiplies the variable; a constant does not change. Recheck the context expression step, then try again.
  • substitution order: Not yet. Replace every occurrence of the variable, then calculate. Recheck the substitution order step, then try again.
  • expression meaning: Not yet. Read from the grouped operation outward. Recheck the expression meaning step, then try again.
  • term number: Not yet. The term number is the input n, not the previous term. Recheck the term number step, then try again.
  • multiple variables: Not yet. Keep each value paired with the correct variable. Recheck the multiple variables step, then try again.
  • expression structure: Not yet. Separate the variable term from the constant term. Recheck the expression structure step, then try again.

Practice

  1. The pattern 4, 7, 10, 13, ... has rule 3n + 1. Find term 8.
  2. The pattern 6, 10, 14, 18, ... has rule 4n + 2. Find term 9.
  3. Which description matches 2(a + 3)?
  4. Which description matches 5m - 4?
  5. Which expression represents “5 more than n”?
  6. Which expression represents “three times x”?
  7. Evaluate 4n + 3 when n = 5.
  8. Evaluate 2x - 7 when x = 9.

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

  1. 25 — Substitute n = 8 into 3n + 1. The value is 25.
  2. 38 — Substitute n = 9 into 4n + 2. The value is 38.
  3. double the sum of a and 3 — Use brackets and operation order to read the expression. The matching description is: double the sum of a and 3.
  4. multiply m by 5, then subtract 4 — Use brackets and operation order to read the expression. The matching description is: multiply m by 5, then subtract 4.
  5. n + 5 — Identify the operation named in the phrase. Keep the variable’s role and order: n + 5.
  6. 3x — Identify the operation named in the phrase. Keep the variable’s role and order: 3x.
  7. 23 — Substitute 5 for n. Follow the order of operations to get 23.
  8. 11 — Substitute 9 for x. Follow the order of operations to get 11.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | create expression pattern evaluate it | Create an expression for a pattern and evaluate it for a given term number. | | interpret variable coefficient constant | Identify the roles of variables, coefficients, constants and operations in expressions. | | formulate algebraic expressions | Formulate algebraic expressions from words, patterns and practical contexts. | | evaluate expressions substitution | Evaluate expressions by substituting values and following operation order. |

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 variables and algebraic expressions 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 variables and algebraic expressions. Define every variable and unit, test at least two inputs, and explain what the outputs mean.

Sources