Section 2: Practical ways from sheet to cube

Key Focus Question: How can you help pupils ‘see’ and mentally transform geometric shapes?

Keywords: nets; geometry; visualisation; transformation; boxes; dice; investigations

Learning Outcomes

By the end of this section, you will have:

• explored practical ways to use the local environment and simple nets to help pupils understand 3D objects;
• used investigation and problem solving to extend your pupils’ thinking about the different nets to make cubes;
• used dice to encourage mental visualisation and transformation of cubic nets.

Introduction

Imagine you have to draw a shape on a piece of paper, which can be cut out and folded into a cube. On the paper you will draw the six squares that will fold up to make the six sides of the cube. Can you imagine the shape you would draw on the paper to make the cube?

It is not easy to do, as this imaginary exercise requires two important mathematical skills – mental visualisation (being able to ‘see’ with your mind’s eye a two-dimensional [2D] or three-dimensional [3D] mathematical image) and mental transformation (being able to ‘manipulate’ or change that image in some way).

This section explores practical ways to develop these skills in your pupils as they make nets. (A net is a 2D representation of a 3D shape, with dotted lines to represent folds, and solid lines to represent cuts.) Manipulating a real object will help your pupils visualise the transformations of this object and relate their understanding of shape to their own life.

Resource 2: A mathematical dictionary

1. Organising an investigation of 3D shapes