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Using mathematical representations at Key Stage 3

Created on 16 August 2019 by ncetm_administrator
Updated on 11 November 2019 by ncetm_administrator

Using mathematical representations at Key Stage 3

Although manipulatives and representations are commonly used in primary mathematics or have been historically considered the reserve of lower prior attainers, they can be equally valuable for revealing mathematical structures at secondary level for all students.

We have produced guidance for some of the most useful representations for Key Stage 3 mathematics. Each guidance document details:

  • what they are
  • why they are important
  • how they might be used.

Click the following links to download the guidance documents.

Easy-download: Representations (all nine guidance documents in one easy-to-download zip file).

We have also produced explainer videos for algebra tiles and Cuisenaire® rods, which you can view via the links below.

Algebra tiles

  1. What are algebra tiles?
  2. Using algebra tiles: adding and subtracting directed numbers using zero pairs
  3. Using algebra tiles: simplifying expressions by collecting like terms
  4. Using algebra tiles: expanding brackets
  5. Using algebra tiles: factorising expressions
  6. Using algebra tiles: solving linear equations

Cuisenaire® rods

  1. What are Cuisenaire® rods?
  2. Using Cuisenaire® rods: modelling additive and multiplicative relationships
  3. Using Cuisenaire® rods: modelling decimals and fractions
  4. Using Cuisenaire® rods: exploring factors and primes

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

  • Secondary mathematics specialists: Clare Dawson; Pete Griffin; Alison Hopper; Carol Knights; Pete Sides
  • Educational consultant: Dr Alf Coles, University of Bristol
  • Editorial and production: Natasha Chippendale; Charlotte Christensen; Tracey Cowell; Bronwyn Enright; Jackie Mace; Bill Mantovani; David Mantovani; Andrew Young
  • Illustrations: Steve Evans
  • Video development and production: Pam Jones, Eight Interactive Ltd



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25 November 2019 09:08
They're in a different format, but have a look at https://www.ncetm.org.uk/resources/50639
23 November 2019 07:48
Is there a similar set of documents for Key Stage Two?
By KJL33
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