Progression maps: Algebra – Equations, formulae and identities
 Step 1

 Objective: Understand division and recognise that division is the inverse of multiplication.
 Step 2


Objective 1: Use symbols correctly including less than (<), greater than (>) and equals (=).

Objective 2: Understand the principles of the commutative, associative and distributive laws as they apply to multiplication.
 Step 3


Objective 1: Make general statements about odd and even numbers.

Objective 2: Explain a generalised relationship (formula) in words.
 Step 4


Objective: Understand and use the relationships between the four operations, and principles of the arithmetic laws. Use brackets.
 Step 5

 Objective 1: Use letter symbols to represent unknown numbers or variables.
 Objective 2: Know and use the order of operations and understand that algebraic operations follow the same conventions and order as arithmetical operations.
 Objective 3: Construct and solve equations with positive integer coefficients (unknown on one side only) using appropriate methods.
 Step 6


Objective 1: Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way).
 Objective 2: Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.
 Objective 3: Substitute integers into simple formulae.
 Step 7

 Objective: Construct and solve linear equations with integer coefficients (with and without brackets, with negative signs anywhere in the equation, and with a positive or negative solution) using an appropriate method.
 Step 8

 Objective 1: Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x³ + x = 20.
 Objective 2: Transform algebraic expressions by factorising to produce a single term multiplied by terms in a bracket.
 Step 9


Objective: Square a linear expression, expand the product of two linear expressions of the form x ± n and simplify the corresponding quadratic expression.
 Step 10

 Objective: Solve a pair of simultaneous linear equations by eliminating one variable; link a graphical representation of an equation or pair of equations to the algebraic solution.