These pages provide a set of self-study units that will help to strengthen planning and teaching of important aspects of geometry, including developing mathematical arguments, formalising notation and working towards proof.

The materials are organised into four units.

Visualisations

Introduction to geometrical visualisations as a key tool for developing pupils’ spatial awareness and geometrical language:

- seven examples of visualisations that can be explored by teachers and tried out in the classroom

- audio files of the visualisation scripts.

Build-ups

Introduction to the idea of a ‘Build-up’ – a simple way of structuring a geometrical argument using visual resources. A series of seven build-ups is presented in two formats:

- acetate overlays that can be used with a visualiser (document camera), an overhead projector or at a desk

- electronic versions, using various dynamic geometry packages.

Sample problems

A selection of problems involving geometrical reasoning, which can be incorporated into unit plans. The problems are organised into three categories:

- problems with diagrams

- problems where a diagram has to be drawn

- extended problems to investigate.

Planning for geometrical reasoning

Advice and examples of how visualisations, build-ups and problems can be incorporated into unit plans, including a partly completed example unit plan.