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# 4. Sequences and graphs

Created on 25 July 2019 by ncetm_administrator
Updated on 03 September 2019 by ncetm_administrator

## 4. Sequences and graphs

Theme 4 is Sequences and graphs. It comprises two interconnected core concepts, each of which covers a set of ‘knowledge, skills and understanding’ statements.

For each core concept, we have produced a detailed guidance document underpinned by a clear set of pedagogical principles and practices to support planning. Each document offers an overview of the content within the statements of knowledge, skills and understanding, and breaks them down further into focused key ideas.

At the end of the documents, some of the key ideas are exemplified, to demonstrate what planning for secure and deep understanding of mathematics at Key Stage 3 might involve. Other key ideas are left for individual departments and teachers to work on, alongside existing material and schemes.

There is also a guidance document that offers an overview of the theme as a whole.

• 4 Sequences and graphs
Theme 4 explores arithmetic and other sequences, coordinates, equations and graphs, and the modelling of situations graphically

• 4.1 Sequences
This core concept covers sequences through exploration of the mathematical structure. It also introduces the idea of the nth term of a linear sequence

• 4.2 Graphical representations
This core concept introduces the idea of x- and y-coordinates as the input and output of a function. Linear and quadratic functions are explored, as well as how linear graphs are used to solve simultaneous equations

Easy-download: Theme 4 (All guidance documents and the overview document for this theme in one easy-to-download zip file.)

## Acknowledgements

The NCETM and Maths Hubs would like to thank the following for their contribution to the materials:

• Secondary mathematics specialists: Debbie Barker; Frances Carr; Clare Dawson; Pete Griffin; Alison Hopper; Carol Knights; Steve Lomax; Richard Perring; Pete Sides; Maths Hubs Secondary Mastery Specialists

• Educational consultant: Dr Alf Coles, University of Bristol

• Editorial and production: Natasha Chippendale; Charlotte Christensen; Bronwyn Enright; Jackie Mace; David Mantovani; Andrew Young

• Illustrations: Steve Evans

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02 March 2020 11:41
Thank you, John for spotting this. There is indeed an error on this diagram.

For this to represent an arithmetic sequence, the final coordinate should be (4,16) and not (4,14).
28 February 2020 22:34
There may be an error in the plottjng of one of the coordinates in the LHS diagram in 4.2 Overview.