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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.

Click the links below to download the documents.

  • 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.)

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).
By petegriffin
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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.
By JohnTench
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23 January 2020 11:36
Hi DeGenera, we don't provide such links, although you'll find video materials and resources in a number of places on this site. You might want to post your query in one of our communities.
22 January 2020 21:30
please i would like to know if there is a link where i can download or read textbooks or video on mathematics
By DeGeneral
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19 August 2019 11:55
It is a pity that the idea of 'function' as a unifying theme is not explored more creatively. I worry that the approach presented here would lead to a misunderstanding that all functions are well-behaved and algebraic, where in some other high performing countries the approach is more general, with sequences, linear and quadratic being special cases.that we can deal with at this stage.
By Anne_Watson
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