Recognising equivalent algebraic expressions

Recognise when expressions are equivalent and justify the decision by collecting like terms, expanding, or using substitution.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Alpha textbook: Forming expressions, Ex 11.01, pg 174
  • Alpha textbook: Extras, PSE11A, pgs 174 & 175

Terminology

  • equivalent
  • expression
  • like terms
  • collect
  • simplify
  • expand
  • bracket
  • variable
  • coefficient
  • term
  • unlike terms
  • multiply out

Task goals

  • Identify whether two expressions are equivalent by collecting like terms or using substitution to check their values.
  • Explain why $2x+3x$ and $5x$ are equivalent, and why $4a+4$ and $8a$ are not.
  • Verify equivalence by expanding brackets and collecting like terms, such as showing $2(x+5)$ equals $2x+10$ but not $2x+5$.
  • Use algebraic properties such as commutativity and associativity to justify that $3(a+1)$ and $3a+3$ are equivalent expressions.

Key skills

  • Equivalent expressions
  • Simplify expressions
  • Properties of operations

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included