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1. The structure of the number system

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

1. The structure of the number system

Theme 1 is The structure of the number system. It comprises four 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.

  • 1 The structure of the number system
    Theme 1 explores the key structures of number and the number system, such as place value, factors, multiples and powers
  • 1.1 Place value, estimation and rounding
    This core concept covers the structure of our place-value system (particularly as it relates to decimals) and rounding numbers to a required number of decimal places or significant figures
  • 1.2 Properties of number
    This core concept focuses on factors, multiples and primes. It explores various representations to support understanding of highest common factors and lowest common multiples. Positive integer exponents and associated real roots are also explored
  • 1.3 Ordering and comparing
    This core concept covers the conversion of decimals to fractions (and vice versa), ordering positive and negative integers, fractions and decimals, and the expression of numbers in standard form
  • 1.4 Simplifying and manipulating expressions, equations and formulae
    This core concept concerns the generalisation of number structures, the use of algebraic symbols and techniques for their manipulation. The rearranging of formulae is also explored by linking it to the manipulation of number sentences

Easy-download: Theme 1 (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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