Investigating Tessellations

Using Activity Pattern Blocks

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About This Project ||  What is a Tessellation? ||  Tessellation Tutorials ||  Tessellation Links
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Go to Warm Up Activity Using Activity Pattern Blocks,
an exercise designed to familiarize the student with the vocabulary of polygons.
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Go to Activity Pattern Block Student Tessellation Samples,
photographs of Activity Pattern Block creations made by students at
Frisbie Middle School, Rialto, California.
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Go to Pattern Blocks applet
by National Library of Virtual Manipulatives (NLVM)
Experiment online with the shapes.

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Objectives: [NCTM Grade 6-8 Standards: Geometry, Reasoning and Proof, Communication and Connections]

  1. To manipulate triangles, squares, hexagons, trapezoids, and rhombuses to see how they might combine to form patterns in the plane.

  2. To consider which of these patterns are tessellations and which are not using the definition that a tessellation is a tiling with shapes that cover the plane without gaps or overlaps.

  3. To consider which of these patterns are regular tessellations and which are not using the definition that a regular tessellation is a tiling with shapes that cover the plane in a regularly repeating pattern without gaps or overlaps.

Materials - Activity pattern blocks including:

Procedure:

  1. Instruct the students to make patterns with the blocks, making certain that they leave no gaps or spaces.
  2. After each student or group of students has a pattern, have all of the students rotate around the room to view each others' products.
  3. Discuss the patterns.
  4. Discuss the relationships between the blocks.

Questions:

  1. Which shapes fit together easily?
  2. Which shapes don't seem to fit with the others?
  3. Which patterns could be repeated over and over again in the plane?
  4. What shapes fit together making a pattern using only one type of block?
  5. What shapes fit together making a pattern using two blocks that are different?
  6. What shapes fit together making a pattern using three blocks that are different?

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