The most useful resource for this investigation would be a large number of cut out shapes. Children may also find dotty/squared paper useful.

If you talk about shape properties with the specialist language we use, then this will help your pupils to use the right vocabulary. Encourage the pupils to talk about what they are doing, perhaps with a partner, and report their findings back to the class frequently.

In order for a shape to tessellate, the angles where they come together are important. Try to question the children in such a way so as to lead them to explore this, perhaps by drawing their attention to a particular part of the tessellation. For example, use lots of coloured tiles to build a pattern like this:

Tessellation.

At the point marked by the arrow you could try asking questions like:

This should prompt your pupils into considering the angles within the individual shape itself, which can be extended to discussion about the sum of the angles at the point shown.

Perhaps you could also challenge the children to make tessellating patterns using more than one type of shape.

This work can make a lovely display!