AC9M7A02 • Year 7 Maths • Algebra • Learn
formulate algebraic expressions using constants, variables, operations and brackets.
We are learning to formulate algebraic expressions using constants, variables, operations and brackets.
An algebraic expression records a calculation using constants, variables, operations and brackets; unlike an equation, it does not assert that two quantities are equal.
Translate the quantities first, then preserve operation order: “three less than twice n” is 2n−3, while “three times the sum of n and 4” requires 3(n+4).
Expressions model perimeter, grouped costs and number patterns. Verify a translation by substituting a simple value into both the words and the expression and comparing the results.
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 1
Final answer: 2n−3
Check: For n=5, both “3 less than twice n” and 2(5)−3 give 7.
Example 2
Final answer: P=4x+4
Check: For x=3, a 5 by 3 rectangle and 4(3)+4 both give 16.
Example 3
Problem: A rectangle has length 3x+2 and width x−1. Write an expression for its perimeter, simplify it, and explain why brackets matter.
Final answer: P = 2(3x+2)+2(x−1) = 8x+2. Brackets ensure both terms in each side length are doubled.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: Write and simplify the sum of three consecutive integers beginning with n.
Final answer: The integers are n, n+1 and n+2, so their sum is n+(n+1)+(n+2)=3n+3; substituting n=4 checks 4+5+6=15 and 3(4)+3=15.
Check: The complete model for “Write and simplify the sum of three consecutive integers beginning with n.” shows The integers are n, n+1 and n+2, so their sum is n+(n+1)+(n+2)=3n+3; substituting n=4 checks 4+5+6=15 and 3(4)+3=15.
Common mistake: Expression and equation confused.
Correction: An equation includes an equals sign and a statement of equality.
Common mistake: Word order reversed in subtraction.
Correction: Analyse ‘less than’ and ‘subtracted from’ carefully.
Common mistake: Brackets omitted.
Correction: 3(n+4) differs from 3n+4.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Write “7 more than x”.
Answer: x+7
Hint: Start with x, then add 7.
Why: Using the method “Start with x, then add 7.” gives x+7.
2. Write “four times y”.
Answer: 4y
Hint: Put the coefficient directly before y.
Why: Using the method “Put the coefficient directly before y.” gives 4y.
3. Write “the sum of n and 6, doubled”.
Answer: 2(n+6)
Hint: Use brackets around the whole sum.
Why: Using the method “Use brackets around the whole sum.” gives 2(n+6).
4. Write “5 less than 3p”.
Answer: 3p−5
Hint: Write 3p first, then subtract 5.
Why: Using the method “Write 3p first, then subtract 5.” gives 3p−5.
5. Four bags each hold m marbles and there are 3 loose marbles. Write an expression.
Answer: 4m+3
Hint: Represent the equal groups before the loose amount.
Why: Using the method “Represent the equal groups before the loose amount.” gives 4m+3.
6. Write and simplify the perimeter of a rectangle with sides a and a+5.
Answer: 4a+10
Hint: Start with 2a+2(a+5).
Why: Using the method “Start with 2a+2(a+5).” gives 4a+10.
7. Are 3(x+2) and 3x+2 equivalent? Explain.
Answer: No. Distributing 3 to both terms gives 3(x+2)=3x+6, which differs from 3x+2; for x=1 the values are 9 and 5.
Hint: Distribute 3 to both bracketed terms.
Why: The reasoning for “Are 3(x+2) and 3x+2 equivalent? Explain.” is complete because No. Distributing 3 to both terms gives 3(x+2)=3x+6, which differs from 3x+2; for x=1 the values are 9 and 5.
8. A cinema charges $12 per ticket and one $5 booking fee. Give the cost for t tickets and for t=4.
Answer: The model is C=12t+5 because $12 is charged for each ticket and $5 is added once; for t=4, C=12(4)+5=$53.
Hint: Separate the variable and fixed costs.
Why: The complete model for “A cinema charges $12 per ticket and one $5 booking fee. Give the cost for t tickets and for t=4.” shows The model is C=12t+5 because $12 is charged for each ticket and $5 is added once; for t=4, C=12(4)+5=$53.
9. Write and simplify the sum of three consecutive integers beginning with n.
Answer: The integers are n, n+1 and n+2, so their sum is n+(n+1)+(n+2)=3n+3; substituting n=4 checks 4+5+6=15 and 3(4)+3=15.
Hint: Write all three integers before simplifying.
Why: The complete model for “Write and simplify the sum of three consecutive integers beginning with n.” shows The integers are n, n+1 and n+2, so their sum is n+(n+1)+(n+2)=3n+3; substituting n=4 checks 4+5+6=15 and 3(4)+3=15.
10. A rectangle has length 3x+2 and width x−1. Write an expression for its perimeter, simplify it, and explain why brackets matter.
Answer: P = 2(3x+2)+2(x−1) = 8x+2. Brackets ensure both terms in each side length are doubled.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Content description: formulate algebraic expressions using constants, variables, operations and brackets.
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
Math Antics — Understand how letters represent quantities and how expressions describe calculations.
As you watch: How is a variable different from a fixed number?
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Try it: Write C = 4n for the cost of n items at $4 each; identify the variable and constant, then calculate C when n = 6.
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Mapped skill: formulate algebraic expressions using constants, variables, operations and brackets
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7A02 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7A02 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-ALG-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M7A02 — Formulating Algebraic Expressions
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