Year level: 7

Strand: Algebra / Measurement

Lesson length: 60 mins

In this lesson, students use algebra tiles to solve one-variable linear equations involving multiplication and division, applying these skills in real-world contexts to enhance their understanding.

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

Algebra mat with algebra tiles representing equation 3x = 15

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. 

Students use formulas for the areas of triangles and parallelograms and the volumes of rectangular and triangular prisms to solve problems.

Content descriptions

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

Students solve problems involving the area of triangles and parallelograms using established formulas and appropriate units. AC9M7M01

General capabilities


  • Number patterns and algebraic thinking (Level 6)

Critical and Creative Thinking

  • Interpret concepts and problems (Level 5)

The following formative assessment activity is recommended as the conclusion of this lesson.

  • Students complete the Algebra maze individually, which is found in the Solving equations shapes worksheet.
  • Evaluate students’ responses to the formative assessment to determine their conceptual understanding and procedural fluency with the topic.
  • Consider incorrect responses on the maze to determine underlying misconceptions.

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 solve one-variable linear equations involving addition and subtraction
  • how to use formulas to find the area of a triangle, rectangle and parallelogram.

As this lesson will be using two different coloured algebra tiles to denote positive and negative values, it is important that prior to this lesson, students have practised using concrete tools to carry out calculations involving positive and negative numbers.

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, that 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.

What you need:

  • Lesson plan (Word)

  • Teacher's slides (PowerPoint)

  • Solving equations shapes worksheet (Word)

  • Algebra mats and algebra tiles (PDF)