About cookies

The NCETM site uses cookies. Read more about our privacy policy

Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.


Personal Learning Login

Sign Up | Forgotten password?
Register with the NCETM

2. Operating on number

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

2. Operating on number

Theme 2 is Operating on number. 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.

  • 2 Operating on number
    Theme 2 is about students understanding the structures underpinning calculation using each of the four operations. It includes the solving of equations, which is essentially concerned with operations on, as yet, unknown numbers
  • 2.1 Arithmetic procedures
    This core concept offers guidance on developing a strong understanding of the mathematical structures that underpin the standard procedures for calculation with decimals, fractions and directed numbers
  • 2.2 Solving linear equations
    This core concept explores how linear equations are effectively the formulation of a series of operations on unknown numbers and how the solving of such equations is concerned with undoing these operations to find the value of the unknown

Easy-download: Theme 2 (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; Gwen Tresidder; 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



Comment on this item  
Add to your NCETM favourites
Remove from your NCETM favourites
Add a note on this item
Recommend to a friend
Comment on this item
Send to printer
Request a reminder of this item
Cancel a reminder of this item



There are no comments for this item yet...
Only registered users may comment. Log in to comment