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While some shapes fit together to make a two-dimensional repeating pattern that leaves no gaps, this is not possible for other shapes.

Compare how squares and circles fit together in a rectangular pattern.

A blank rectangular grid of twelve equally sized squares in a three by four pattern.

A rectangular grid of squares.

Three rows of four circles touching each other in a rectangular pattern.

A rectangular array of circles.

A pattern of shapes that fit together without any gaps is called a tessellation. So squares form a tessellation (a rectangular grid), but circles do not.

Tessellations can also be made from more than one shape, as long as they fit together with no gaps.

A tessellation formed by fitting regular octagons together, with squares fitted in the gaps.

A tessellation of squares and octagons.

Through exploring how shapes fit together, students can learn much about those shapes. They can learn about the number and lengths of the sides of each shape, as well as the angles at the corners. They can also encounter concepts such symmetry, congruence, similarity and parallels.

Triangles tessellate

Many geometrical ideas can be found in a triangle tessellation.

Making tessellations

Tessellations can easily be investigated with pattern blocks (with or without digital technology).

Growing patterns can tessellate

The video Let's Make a Pattern! can inspire students to create their own two-dimensional growing patterns.

Curriculum links

Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features

Year 2: Describe and draw two-dimensional shapes, with and without digital technologies

Year 3: Identify symmetry in the environment