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.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Literacy in Mathematics – Creating Problem Solvers

Last year my school had a OFSTED trial inspection. Whilst the maths team recieved favourable feedback the inspectors noted a need for a focus on whole school literacy. Because of this I was asked to demonstrate how we develop student’s literacy in mathematics. Literacy in Mathematics By developing student’s literacy in mathematics we aim to […]

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]