Year 7 Mathematics · AC9M7A02

Formulating Algebraic Expressions

We are learning to formulate algebraic expressions using constants, variables, operations and brackets

Ready to project and teach

Learning goalsSay it simply

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.

Success criteria

  • I can translate mathematical language into an algebraic expression.
  • I can use coefficients and brackets to preserve operation order.
  • I can verify an expression by substitution.
Key conceptTeach from the board

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

Translate words precisely

  1. Read the full phrase “3 less than twice n”.
  2. Let n represent the number and translate “twice n” as 2n.
  3. Translate “3 less than twice n” by subtracting 3 from 2n.
  4. Write the expression 2n−3 without an equals sign.

Final answer: 2n−3

Check: For n=5, both “3 less than twice n” and 2(5)−3 give 7.

Example 2

Model a perimeter

  1. Let the length be x+2 and width be x.
  2. Use P=2l+2w.
  3. Substitute P=2(x+2)+2x.
  4. Expand and collect like terms.

Final answer: P=4x+4

Check: For x=3, a 5 by 3 rectangle and 4(3)+4 both give 16.

Example 3

Application problem 1

Problem: A rectangle has length 3x+2 and width x−1. Write an expression for its perimeter, simplify it, and explain why brackets matter.

  1. Plan: Represent the information first, then calculate, interpret and independently check the result.
  2. Work: P = 2(3x+2)+2(x−1) = 8x+2. Brackets ensure both terms in each side length are doubled.
  3. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

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

Application problem 2

Problem: Write and simplify the sum of three consecutive integers beginning with n.

  1. Plan: Write all three integers before simplifying.
  2. Work: 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.
  3. Interpret: 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.

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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M7A02 - Formulating Algebraic Expressions
Example 1

Example 1 Translate words precisely Read the full phrase “3 less than twice n”. Let n represent the number and translate “twice n” as 2n. Translate “3 less than twice n” by subtracting 3 from 2n. Write the expression 2n−3 without an equals sign. Final answer: 2n−3 Check: For n=5, both “3 less than twice n” and 2(5)−3 give 7.

Example 2

Example 2 Model a perimeter Let the length be x+2 and width be x. Use P=2l+2w. Substitute P=2(x+2)+2x. Expand and collect like terms. Final answer: P=4x+4 Check: For x=3, a 5 by 3 rectangle and 4(3)+4 both give 16.

Example 3

Example 3 Application problem 1 Problem: A rectangle has length 3x+2 and width x−1. Write an expression for its perimeter, simplify it, and explain why brackets matter. Plan: Represent the information first, then calculate, interpret and independently check the result. Work: P = 2(3x+2)+2(x−1) = 8x+2. Brackets ensure both terms in each side length are doubled. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills. 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

Example 4 Application problem 2 Problem: Write and simplify the sum of three consecutive integers beginning with n. Plan: Write all three integers before simplifying. Work: 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. Interpret: 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. 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.

Curriculum examplesCopied content

Content description: formulate algebraic expressions using constants, variables, operations and brackets.

Questions and answersWith answers

Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.

  1. 1. Write “7 more than x”.

    Check answer

    Answer: x+7

    Hint: Start with x, then add 7.

    Why: Using the method “Start with x, then add 7.” gives x+7.

  2. 2. Write “four times y”.

    Check answer

    Answer: 4y

    Hint: Put the coefficient directly before y.

    Why: Using the method “Put the coefficient directly before y.” gives 4y.

  3. 3. Write “the sum of n and 6, doubled”.

    Check answer

    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. 4. Write “5 less than 3p”.

    Check answer

    Answer: 3p−5

    Hint: Write 3p first, then subtract 5.

    Why: Using the method “Write 3p first, then subtract 5.” gives 3p−5.

  5. 5. Four bags each hold m marbles and there are 3 loose marbles. Write an expression.

    Check answer

    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. 6. Write and simplify the perimeter of a rectangle with sides a and a+5.

    Check answer

    Answer: 4a+10

    Hint: Start with 2a+2(a+5).

    Why: Using the method “Start with 2a+2(a+5).” gives 4a+10.

  7. 7. Are 3(x+2) and 3x+2 equivalent? Explain.

    Check answer

    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. 8. A cinema charges $12 per ticket and one $5 booking fee. Give the cost for t tickets and for t=4.

    Check answer

    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. 9. Write and simplify the sum of three consecutive integers beginning with n.

    Check answer

    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. 10. A rectangle has length 3x+2 and width x−1. Write an expression for its perimeter, simplify it, and explain why brackets matter.

    Check answer

    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.

Practice and reviewReady for practice

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.

Curriculum alignmentStart here

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.

Success criteria

  • I can translate mathematical language into an algebraic expression.
  • I can use coefficients and brackets to preserve operation order.
  • I can verify an expression by substitution.
Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.