Year level: 7

Strand: Algebra

Lesson length: 60 mins

In this lesson introduce the concept of variables using physical materials and explore the construction of algebraic expressions in authentic contexts.

This is the first lesson in a series of lessons to develop understandings and proficiency in algebraic thinking. 

Formulating algebraic expressions Image

Achievement standard

Students use algebraic expressions to represent situations.

Content descriptions

Students recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown. AC9M7A01

Students formulate algebraic expressions using constants, variables, operations and brackets. AC9M7A02

General capabilities


  • Number patterns and algebraic thinking (Level 6)

Critical and Creative Thinking:

  • Analysing: interpret concepts and problems (Level 5)

The following formative assessment is suggested for this lesson.

  • Have students complete their Decimats worksheet as homework to be handed in for you to assess and reflect on each student before proceeding to the following lesson, ‘Expressions, formulas and substitution’.
  • Ask students to record on their Decimat worksheet how well they felt they understood the lesson about constructing algebraic expressions (for example, by circling  😀 or 😐 or 😟 on their exit ticket).

Some students may:

  • consider that the ‘=’ sign indicates to record an example, rather than expressing an equivalence relationship
  • think that a variable represents the count for the number of objects (for example, 3a means 3 apples)
  • have difficulties understanding the lack of multiplication signs in algebraic expressions, such as 3 × a = 3a
  • have difficulties with different decimal and fraction representations in algebraic expressions, such as 0.5 a = 1 2 a = a 2
  • think that a particular variable always holds the same value
  • think that the same variable in an expression can hold different values, such as thinking that t could be 2 and 4 in the expression t + t = 6.

Prior to this lesson, it is assumed that students have knowledge of:

  • conventions associated with the order of operations for integers
  • addition, subtraction, multiplication and division facts and strategies.

It is also useful if students have an understanding that ‘=’ indicates an equivalence statement.

What you need:

  • Lesson plan (Word)

  • Teacher's slides (PowerPoint)

  • Working with algebra worksheet (Word)

  • Decimat worksheet (Word)

  • Mini-whiteboards or A3 blank paper