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How to start algebra? How to get the pupils engaged and enthused? How to find out what they know? How to avoid rules, rules and more rules ...

Have you ever asked yourself these questions? Year 7 pupils should see this as a fascinating topic that gives them a real taste for ‘grown up mathematics’, it should intrigue them and captivate them. All too often it does just the opposite; presenting a bewildering array of rules that barely hang together. It is made to seem dull, scary and hard to remember.

With this in mind, the Improve Maths team set out to design a suite of progression units in algebra. We based the approach on rich tasks and problem solving activities that:

- engage pupils in ‘expressing generality’ and finding ‘as many ways as you can’
- encourage pupils to explore their thinking in depth, often in pairs or small groups
- serve varied purposes: precursors, exploration, consolidation and practice, application

In this series of blogs I would like to share with you a flavour for the activities in each of the four themes of progression:

**1:** **Algebraic relationships: generalising from arithmetic -** Through gaining insight into the algebraic relationships that underpin number, pupils understand how to construct and transform algebraic expressions and equations and meet principles and methods that they will use in other themes.

Themes 2, 3 and 4 are ‘algebra with a purpose’, in which pupils come to appreciate the power of algebra to help them generalise, justify and find solutions to problems.

**2: Algebraic reasoning: generalising, justifying and proving** - Under‐represented in many schemes of work, the use of algebra to explain, justify and prove results is approached in an accessible way in this theme.

**3: Constructing and solving equations** - The focus on constructing equations gives a sense of purpose, and insight into algebraic structure. Methods for solving equations are built on the generality of the forms a + b = c and ab = c, explored in theme 1.

**4: Deriving and interpreting expressions and formulae** - This theme relates algebra to practical contexts from mathematics (e.g. measures) other subjects, everyday life and work.