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Tessellations are a fascinating topic that students of all ages find intriguing. The real world applications of tiling and the opportunity for creating beautiful patterns provide a hook to engage students and stimulate their curiosity, while the interactive environment allows them to quickly test out ideas and make conjectures.
Finding all the possible tessellations provides a context for students to practise working out interior angles of polygons and angles around a point.
Introduce the interactivity to the class, and ask them to consider which shapes you might choose if you wanted to tile an area (with just one type of shape) without leaving any gaps or overlaps.
Why do some shapes fit together and others don't?
Students could begin by exploring tessellation of quadrilaterals, paying particular attention to the angle properties.
Suggest students read Shaping up with Tessellations.
Move on to three dimensions: Which Solids Can We Make?