Year level: Year 7

Strand: Algebra

Lesson length: 60 mins

In this lesson, students are introduced to solving one-variable linear expressions using a variety of concrete materials, which are related to authentic contexts to enhance their understanding.

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

Solving equations with algebra mats Image

Achievement standard

Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data, and substitute values into formulas to determine unknown values. They solve linear equations with natural number solutions. 

Content description

Students solve one-variable linear equations with natural number solutions; verify the solution by substitution. AC9M7A03

General capabilities


Critical and Creative Thinking:

  • Interpret concepts and problems (Level 5)

The following formative assessment items are suggested for this lesson:

  • Students respond to the question ‘In your own words, what does “solving” an equation mean?’
  • Students complete the Tarsia puzzle and submit their completed puzzle.

Use the information provided by students in the exit ticket to inform the beginning discussion in the lesson, ‘Solving equations with algebra tiles’, ensuring any misconceptions about what it means to solve an equation are clarified. Consider students’ confidence levels in engaging with the mild/medium/spicy question sets.

Some students may:

  • think that the ‘=’ sign indicates to record an example, rather than expressing an equivalence relationship
  • think that a particular variable always holds the same value
  • find identifying inverse integer operations counterintuitive, particularly when negative integers are involved
  • forget, or not realise, they need to do the same thing to both sides of the equation
  • have trouble neatly recording each step of their working out when solving equations.

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

  • the concept of variables
  • constructing equations from word problems
  • conventions associated with the order of operations for integers
  • knowledge of algebraic conventions (covered in prior lessons)
  • how ‘=’ indicates an equivalence statement
  • how to substitute values into equations
  • how to model equations and substitute values using cups and counters.

What you need:

  • Lesson plan (Word)

  • Teacher's slides (PowerPoint)

  • Solving equations worksheet (Word)

  • Tarsia puzzle (PDF)

  • Algebra mat template (Word)

  • Cups and counters (per student pair)

    Mini whiteboards/markers (optional)