The Greedy Triangle by Marilyn Burns

Mathematical Strand:

Geometry

Mathematical topic:

Students will discover which regular polygons can be used to tile a plane.

Grade level:

4th - 6th grade

Lesson Created by:

Joy Heinrichs Theodore Roosevelt Elementary, Manhattan, KS

Lesson Description

Material

• 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

1. Read the book
   
2. There was one shape in the book that fit in as floor tiles. Do you remember which one?
   
3. 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

1. Tiling means covering a flat surface with shapes that fit together without any gaps.
   
2. Discuss the definition of regular polygon, edge, and angle.
   
3. Use a set of regular polygons- triangles, squares, pentagons, hexagons, and octagons- to figure out which of these will tile a flat surface.
   
4. Consider tiling in which all the polygons are the same and tiling patterns that combine 2 or more different polygons.
   
5. Make sketches of combinations that work and combinations that don't work.
   

3. Summarize/Discussion/Elaboration

1. Have groups draw their combinations that work and don't work on the board or overhead projector.
   
2. Why do squares, triangles, and hexagons work?
   
3. 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.