Create a tessellation pattern

This activity is designed for KS3 students and involves formulating a rule that can be used to create tessellation patterns. It will help students develop an understanding of the tessellation that will be required to design interlocking units.

This lesson plan could be taught in maths or as part of graphics within design and technology.

Students will be supplied with cut-outs of triangles, squares, and hexagons, allowing them to craft captivating, tessellated patterns. The key requirement is that all individual shapes possess identical side lengths, allowing seamless interlocking.

Once comfortable with these basic shapes, students will be introduced to pentagons and heptagons, which, unlike the former, do not tessellate perfectly.

To deepen their understanding, students will create a table, plotting the interior angles of each shape against the corresponding polygon. Through observation and analysis, they will endeavour to formulate a rule distinguishing which shapes can tessellate and which cannot.

Students will be encouraged to predict whether 10, 11, and 12-sided shapes can tessellate to challenge their comprehension further.

This activity promises an exciting blend of hands-on exploration, critical thinking, and geometry, fostering a deeper appreciation for the captivating world of tessellations.

Tessellation is a geometric concept in mathematics and art that involves covering a surface with repeated, non-overlapping shapes. These shapes, called tiles or polygons, fit together seamlessly, creating a pattern extending infinitely across a surface. Tessellations can be found in various forms in nature, art, and architecture.

The most famous example of a tessellating shape is the regular hexagon, which can fit together perfectly to cover a plane without leaving any gaps or overlaps. Other common tessellating shapes include squares, triangles, and other regular polygons.

The ‘Engineering Process’ scheme of work gives students an in-depth understanding of some engineering materials and how they are being developed in industry. This scheme was inspired by the casting process used to make the D3O smart material into a ‘usable’ form; this links to industrial practices such as quality control, standardisation, and casting manufacture. It is designed to challenge the students by requiring them to apply their knowledge and understanding of engineering materials through a ‘batch’ production experience.