The algebra study units focus on three main teaching principles. You can find out about these principles, the main advantages they offer, and how applying them consistently can strengthen teaching and learning of algebra.
The teaching principles
 Providing opportunities for pupils to express generality

Generality lies at the heart of mathematics. Learning to make algebraic generalisations begins with analysis of numerical examples and moves on to the use of letters to stand for unknown numbers or variables.
The first principle is to get pupils to generalise for themselves from examples that they have generated, rather than having generalisations presented to them.
The main advantages are that pupils:
 relate what they are doing in algebra to what they already know in arithmetic
 begin to appreciate the purpose of algebra
 are better able to understand algebraic expressions, equations and formulae, and also sequences, functions and graphs, if they have generated some for themselves.
 Asking pupils to 'find as many ways as you can'

This principle requires that pupils are regularly asked to write algebraic expressions in different ways, for example, to construct expressions, equations or formulae and to transform them, or to represent an algebraic relationship in as many different ways as possible.
The many advantages are that pupils:
 appreciate that the same relationship can be expressed or represented in more than one way
 gain confidence in manipulating and transforming expressions, equations and formulae into different equivalent forms
 have opportunities to choose ways of representing such relationships, using their knowledge of equivalent forms (for example, tables, functions and graphs), so that the context can be analysed and the solution communicated
 have opportunities to discuss which transformations are the most efficient to use in a particular context, for example, when they solve an equation
 learn how expressions are built up and the related process of ‘undoing’, which they need when they simplify expressions or solve equations.
 Creating connections between mathematical topics

Pupils may feel that mathematical learning is compartmentalised. Closely related ideas, notation, or forms of representation stay unconnected in their minds.
By linking activities, you can help to draw out connections across mathematical topics.
The main advantages are that pupils:
 make connections between arithmetic operations and equivalent algebraic forms when they transform expressions and equations
 make connections between sequences, functions and graphs when they explore the effects of varying values
 find it easier to transfer what they learn to similar situations.
Benefits of consistent use
When the three teaching principles are applied consistently, pupils learn to:
 construct and manipulate algebraic expressions, equations and formulae
 represent algebraic relationships based on their understanding.
This provides a far stronger foundation for their learning than when they are given sets of rules to apply. As a result, when the steps in a procedure are not obvious, pupils are far more able to resolve difficulties for themselves.