Year level: 7

Strand: Algebra

Lesson length: 60 mins

In this lesson, students build on their understanding of algebraic expressions.  Explore substituting values into formulas to determine unknowns using a variety of contexts to reinforce the importance of algebra in real life. 

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

Line graph showing rabbit population growth over time on Gadigal land

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.

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:

Use the following formative assessment to gauge where students are at.

Exit ticket questions:

  • If x = 2, find the value of 2x–9
  • Label the parts of this expression: 3x–2
  • In your own words, what is the difference between an expression and an equation?

Some students may:

  • think that the '=' sign indicates 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 x a = 3a
  • have difficulties with different decimal and fraction representations in algebraic expressions, such as 0.5a 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:

  • the concept of variables
  • constructing algebraic expressions from word problems
  • conventions associated with the order of operations for integers
  • knowledge of algebraic conventions (covered in prior lesson)
  • how ‘=’ indicates an equivalence statement
  • what is meant by an expression (from prior lesson)
  • how to measure length accurately using rulers (to the mm)
  • how to use formulas to find the area of a triangle and rectangle
  • decimal notation and rounding decimals
  • using calculators to carry simple calculations
  • how to measure mass in grams.

What you need:

  • Lesson plan (Word)

  • Teacher's slides (PowerPoint)

  • Warm up with algebraic expressions worksheet (Word)

  • Workstation instructions (Word)

  • Stacking cups and two different coloured counters, kitchen scale, rulers and calculators