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# Progression maps: Algebra – Equations, formulae and identities

### Page 1 of 18

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.