Teaching mental mathematics from level 5: Algebra

These resources can be used to help improve pupils’ mathematical thinking skills in algebra. The teaching approaches cover ‘hard to teach’ aspects of algebra, including algebraic conventions, solving linear equations, sequences, and functions and graphs.

Use these teaching activities to introduce new algebraic concepts and design revision or intervention tasks for pupils who are struggling with aspects of algebraic thinking. These activities can also help you develop pupils’ mental maths images and mathematical talk through paired or group work.

Topics covered

This resource contains teaching approaches that can be used to develop mental maths abilities beyond level 5. These are selected from the Algebra section of the learning objectives on the Framework for secondary mathematics.

This includes some of the aspects of algebra that have been reported as difficult to teach and hard to learn, such as:

  • algebraic conventions
  • solving linear equations
  • sequences
  • functions and graphs.

They also include aspects of algebra that have been reported as having implications for teaching and learning from the Key Stage 3 tests. For example, to help pupils improve their performance, teachers should:

  • give pupils more experience of forming equations and help them to understand the use of inverse operations when solving or rearranging equations
  • help pupils to improve their understanding of the meaning of coefficients and symbols, taking account of common misconceptions
  • provide opportunities to practise transformations of algebraic expressions for pupils at higher levels.

Benefits of using this resource

The suggested activities in this resource will help you to plan sequences of lessons that provide opportunities for pupils to:

  • extend their experiences of forming equations
  • understand the use of inverse operations when solving or rearranging equations
  • improve their understanding of coefficients and symbols
  • expose and discuss common misconceptions
  • practise transformations of algebraic expressions.

Some of the topics have been selected because, although they are fundamental ideas, it can be difficult to map or identify pupils’ acquisition of them. For example, pupils gradually gain thorough understanding of the meaning of symbols through various different experiences. Gaps in their understanding can undermine later stages of pupils’ learning.

The tasks described in this resource aim to address some typical algebraic misconceptions. They are designed to engage pupils with algebra through discussion and collaborative work.

The tasks may easily be adapted to adjust the challenge and keep pupils on the edge of their thinking.