• Understand and use the relationships between the four operations, and the principles (not the names) of the arithmetic laws.
  • Use brackets.
  • Read and plot coordinates in all four quadrants.


  • Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations).
  • Use simple formulae from mathematics and other subjects, substitute positive integers in simple linear expressions and formulae and, in simple cases, derive a formula.
  • Generate sequences from practical contexts and describe the general term in simple cases.
  • Express simple functions (in words, then) using symbols; represent them in mappings.
  • Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise straight-line graphs parallel to the x-axis or y-axis.
  • Begin to plot and interpret the graphs of simple linear functions arising from real-life situations.
  • Suggest extensions to problems by asking ‘What if…?’; begin to generalise and to understand the significance of a counter-example.


  • 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 the same way).
  • Substitute integers into simple formulae, including examples that lead to an equation to solve, and positive integers into expressions involving small powers (e.g. 3x2 + 4 or 2x3).
  • Begin to use linear expressions to describe the nth term of an arithmetic sequence.
  • Generate points in all four quadrants and plot the graphs of linear functions; recognise that equations of the form
    y = mx + c correspond to straight-line graphs.

Key Vocabulary:

  • expression, equation, formula, linear, collect like terms, simplify, multiply out, substitute, solve, inverse, construct.

Suggested Lesson Outcomes:



Teaching & Learning Resources:

BIDMAS Resources
Brackets Resources
Simplifying Resources
Substitution Resources
Equations Resources
Function Machine Resources
Coordinates Resources
Graphs Resources
y=mx c Resources
Counting On Resources
Sequences Resources
Linear Sequences Resources
Mapping Resources
nth Term Resources