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# 3. Multiplicative reasoning

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

## 3. Multiplicative reasoning

Theme 3 is Multiplicative reasoning. 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.

• 3 Multiplicative reasoning
Theme 3 addresses the idea that any two numbers can be connected by multiplication. This gives rise to ideas of ratio, proportionality, percentage increase and decrease, rates of change, enlargement, similarity and trigonometric ratios

• 3.1 Understanding multiplicative relationships
This core concept explores fractions, percentages, ratio and proportion (direct and inverse) as contexts in which multiplicative relationships are used

• 3.2 Trigonometry
This core concept introduces the trigonometric functions through the unit circle. Ideas of similarity, scale factor and multiplicative relationships are integrated to show how trigonometry can be used to solve a wide range of problems

## 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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