Instructional Activity# Regular Tessellation for Other Polygons

Lesson 2. Unit 9. Grade 8 Open Up Resources

Open Up Resources15 min(s)

This Instructional Activity is a part of the Lesson 2, Unit 9, Grade 8. The goal of this activity is to show that only triangles, squares, and hexagons give regular tessellations of the plane. The method used is experimentation with other regular polygons. The key observation is that the angles on regular polygons get larger as we add more sides, which is a good example of observing structure. Since three is the smallest number of polygons that can meet at a vertex in a regular tessellation, this means that once we pass six sides (hexagons), we will not find any further regular tessellations. The activities in this lesson now show that there are three and only three regular tessellations of the plane: triangles, squares, and hexagons.