# 3. Developing problem-solving skills

Having established familiarity with nets, and making cuboid shapes from them, you now move on to ways of helping your pupils to visualise and transform these nets mentally. One way to do this is by using a dice. Another way is to look at shapes in the environment.

A dice is a special kind of cube, where each surface has a unique number between 1 and 6, and where the numbers on opposite surfaces add up to 7. See Resource 3: Dice facts.

In order to correctly number the squares on a cubic net, before it is folded into a cube, the pupil must be able to visualise the transformation from 2D to 3D in their mind’s eye. Case Study 3 and the Key Activity explore these ideas in different ways.

## Case Study 3: Drawing nets for different shapes

Mrs Uwera wanted to develop her pupils’ awareness of mathematics in everyday life and so she took them to the nearby market. She took paper and pencils with her and asked her pupils to find different containers. She asked them to draw a quick sketch of containers with different shapes. Some of Mrs Uwera’s pupils drew tins of sauce tomatoes to show cylindrical containers and boxes to show rectangular prisms.

For homework, she asked them to produce neat drawings of both the containers and what they thought the nets of these shapes would be, as she wanted to hang them in the classroom. The pupils were very pleased with what they produced and so she asked them to invite their parents to come and see their work. Mrs Uwera knows that it is important to have good parent cooperation, as this enhances teaching.

(If there is no market or general store near you, you can ask your pupils to collect used containers such as empty washing powder boxes, different tins etc. and get them to do a similar exercise in class.)

## Key Activity: Making dice nets

Before the lesson, collect up or make several dice to show your class.

Ask pupils in pairs to look at a dice, and look carefully at the numbers – they should be able to identify that each side has a number between 1 and 6; you may have to prompt them to see that opposite sides add to 7. Allow them time to check if this rule is followed on all their dice.

Now give each pair two sets of empty 5 x 5 square grid papers. Ask them to design different nets for a dice: a cube net with numbers written on the squares so that they obey the rules above. When they think they have solved the problem, they may cut out the nets and check that they have ‘correct’ dice.

After the pairs have solved this problem, they could mark dice numbers on some of the other 11 cube nets that they identified.

Ask each pair to make a poster to display the different numbering patterns for each net.

You could extend this activity by asking your class to make a board game about shape and use their own dice to play it.

Resource 4: Numbered dice netshows an example of a correct solution and a template for your more able pupils to investigate how many different ways they can place the numbers on the dice so it still works.

You may wish to use a double lesson for this activity.

2. Using group work to understand ‘nets’

Resource 1: Net of a tin (a cylinder)