### Penta Place

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

### Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

### Tetrafit

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

# Shapely Tiling

## Shapely Tiling

Below is a pattern which can be created using a pair of compasses and a ruler, and a photograph of an Islamic Star.

Use the interactivity to make this Islamic star and cross design.

Can you produce the following tessellations:

• regular octagons with two different types of triangle?
• irregular hexagons with triangles and squares?

Click on a region of the pattern to change its colour. The colours will cycle between white, green, purple and orange if you keep clicking.

Use the CLEAR button to change everything back to white.

Full screen version

This text is usually replaced by the Flash movie.

Printable version of the above interactivity

### Why do this problem?

This problem will give learners the opportunity to become acquainted with less familiar two dimensional shapes. This is an accessible activity at which all children could have a go.

### Key questions

What shapes can you see?
Can you see another one which is a different size?
If you make these touching shapes the same colour, what shape have you made?

### Possible extension

Learners could create their own tessellations using this template.

### Possible support

The interactivity will be useful for children who don't like making mistakes and those who find colouring difficult.