Patterns and Sequences

Students learn how to recognise and describe a number and picture sequence using a term-to-term and position-to-term rule.  As learning progresses they find the nth term of a sequence and begin to plot sequences on a grid.

This unit takes place in Term 4 of Year 7 and is followed by Functions, Graphs and Equations.

Patterns and Sequences Lessons
Prerequisite Knowledge
  • Use simple formulae
  • Generate and describe linear number sequences
  • Express missing number problems algebraically
  • Find pairs of numbers that satisfy an equation with two unknowns
Key Concepts
  • A sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
  • A term is a number or diagram in a sequence.
  • A sequence can be described on a term-to-term basis or position to term.
  • A formula can be used to calculate the term of a sequence when given its position number.  n is often used to represent the position number for any term of the sequence.
  • Linear sequences will appear as straight lines when drawn as a graph.
Working mathematically

Develop fluency

  • Select and use appropriate calculation strategies to solve increasingly complex problems
  • Develop algebraic and graphical fluency, including understanding linear functions

Reason mathematically

  • Identify variables and express relations between variables algebraically and graphically

Solve problems

  • Begin to model situations mathematically and express the results using a range of formal mathematical representations
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
Subject Content


  • Substitute numerical values into formulae and expressions, including scientific formulae
  • Understand and use standard mathematical formulae
  • Recognise, sketch and produce graphs of linear functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
  • Generate terms of a sequence from either a term-to-term or a position-to-term rule
  • Recognise arithmetic sequences and find the nth term
  • Recognise geometric sequences and appreciate other sequences that arise.

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