• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• find pairs of numbers that satisfy number sentences involving two unknowns
• enumerate possibilities of combinations of two variables

Pupils should be taught to:

• Use and interpret algebraic notation, including:
  • ab in place of a × b
  • 3y in place of y + y + y and 3 × y
  • a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b
  • ab in place of a ÷ b
  • coefficients written as fractions rather than as decimals
  • brackets
• substitute numerical values into formulae and expressions, including scientific formulae
• understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
• simplify and manipulate algebraic expressions to maintain equivalence by:
  • collecting like terms
  • multiplying a single term over a bracket
  • taking out common factors
  • expanding products of two or more binominals
• understand and use standard mathematical formulae; rearrange formulae to change the subject
• model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
• use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
• work with coordinates in all four quadrants
• recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
• interpret mathematical relationships both algebraically and graphically
• reduce a given linear equation in two variables to the standard form y=mx+c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
• use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
• find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
• generate terms of a sequence from either a term-to-term or position-to-term rule
• recognise arithmetic sequences and find the nth term
• recognise geometric sequences and appreciate other sequences that arise.