The Mathematics of Wallpaper

CONTENTS OF CURRICULUM UNIT 10.04.01

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Objectives
  4. Strategies
  5. The hierarchy of quadrilaterals
  6. Tessellation
  7. Activities 1
  8. Activity 2
  9. Activity 3
  10. Activity 4
  11. Notes:
  12. Appendix A: Annotated Bibliography
  13. Appendix B: Implementing District Standards
  14. Appendix C: Collection of Problems

Geometry and the Real World

Shamsu Abdul-Aziz

Published September 2010

Tools for this Unit:

Activity 4

This is more like a class project. This activity can be used as a pre-activity before introducing the concept of symmetry. Through the course of the class, as you teach the concepts, the students will look back at their results and make changes, if necessary, to their observation and results. Students will use the knowledge of symmetry and isometry to group different types of wallpaper.

Procedures:

1. Each student will bring to class different wallpaper patterns they can find.

2. Students should be grouped into groups of three.

3. Lay all the wallpapers on a table.

4. Each group should group the different wallpaper patterns into different piles. Make sure that each pile you create has a peculiar characteristic. Example, pile A should contain all the wallpaper patterns that has reflective symmetry, pile B should have only rotational symmetry, pile three should have only translational symmetry. Some piles can have more than one characteristic.

5. The following questions need to be answered by each group after making their piles. Seek the help of your teacher if necessary.

  • How many piles did you get?
  • Name the piles according to the type of symmetry seen in the pattern.
  • Are there any piles that have the same type of symmetry seen in the pattern? If yes why?
  • How many piles have rotational symmetry?
  • Is there any pattern that has a different order of rotational symmetry other than 1, 2, 3, 4, and 6? If yes, explain why?

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