Fun with Tessellations

Tessellations is a mathematical idea to do with tiling. It’s part of Geometry and young children will first learn about it in Key Stage 1. Basically it involves working with shapes that tile exactly to cover and surface without any gaps. The fun part comes in finding ‘tessellations’ in the real world.

A regular tessellation is made by repeating the same regular (all sides the same length) 2D shape.

Track them down wherever tiles get together (kitchens, bathrooms, pavements, shopping centres, etc).

Squares tessellate, and patterns using squares are easy to find:

Children should also be able to find examples of triangles tessellating too:

Regular hexagons work too:

A semi-regular tessellation is made by repeating two or more regular 2D shapes:

These might be found in more complex tiling patterns:

Next time you are out and about, and you spot a tiled pattern talk about the shapes used. Younger children may be able to name some of the shapes used or talk about the colours. Older children could think of the type of shapes and the type of pattern. It might also be useful to talk about the angles of some of the shapes.

Tessellation patterns can also involve non-regular shapes, making tiling patters with these types of shapes can be the most fun. This type of tessellation can be seen in the works of M.C. Escher.

Escher’s work is incredibly complex and mesmerising… but children can create similar patterns. Here’s a good way to make simple Escher-like patterns.

For older children, here’s a more advanced version of the same idea:

Children can also use this online tool to play around with simple tessellating patterns.
Finally, one of our readers sent in details of a great way to introduce Tessellations through story. Emily Grosvenor wrote in with details of her own story book “Tessalation! A Children’s Picture Book about Tessellations“. The book, which was published earlier this year following a successful Kickstarter campaign, tells the story of young Tessa, who discovers wonderful patterns wherever she goes. The work is gentle, colourful introduction to the world of pattern. See Emily’s video, below, or go to her website to find out more details.