The Greedy Triangle by Marilyn Burns
Students will discover which regular polygons can be used to tile a plane.
4th - 6th grade
Lesson Created by:
Joy Heinrichs Theodore Roosevelt Elementary, Manhattan, KS
- Book The Greedy Triangle by Marilyn Burns, paper, pencil, chalkboard and chalk, or overhead projector and transparency film and marker, CMP shapes set- 1 per group (available through Dale Seymour Publications.) The set includes many 2-D polygons that kids can explore tiling.
1. Launching the lesson
- Read the book
- There was one shape in the book that fit in as floor tiles. Do you remember which one?
- Hexagon! Why do you think they mentioned floor tiles for a hexagon, but no other shape? Can all shapes tile a floor?
2. Exploring the lesson
- Tiling means covering a flat surface with shapes that fit together without any gaps.
- Discuss the definition of regular polygon, edge, and angle.
- Use a set of regular polygons- triangles, squares, pentagons, hexagons, and octagons- to figure out which of these will tile a flat surface.
- Consider tiling in which all the polygons are the same and tiling patterns that combine 2 or more different polygons.
- Make sketches of combinations that work and combinations that don't work.
- Have groups draw their combinations that work and don't work on the board or overhead projector.
- Why do squares, triangles, and hexagons work?
- Could introduce shorthand notation for describing regular polygons in tiling patterns. Tiling triangles is written 3,3,3,3,3,3. The 3 means 3 sides and 6 are written because 6 triangles surround each vertex.