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# 6. Geometry

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

## 6. Geometry

Theme 6 is Geometry. 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.

• 6 Geometry
Theme 6 explores the properties of various geometrical shapes, the key transformations of translation, rotation, reflection and enlargement, and standard ruler and compass constructions

• 6.1 Geometrical properties
This core concept covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem

• 6.2 Perimeter, area and volume
This core concept covers how the various formulae for perimeter, area and volume are derived and connected, and the importance of reasoning mathematically in order to solve a wide range of problems

• 6.3 Transforming shapes
This core concept introduces the transformations of translation, rotation, reflection and, finally, enlargement. It highlights and discusses the degrees of freedom available, with regards to what does and doesn’t vary for each one

• 6.4 Constructions
This core concept explores the following constructions: triangles of given lengths; a perpendicular bisector of a line segment; a perpendicular to a given line through a given point; an angle bisector

## 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; 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

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