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 2

In this activity you will be using Geometer's Sketchpad to draw a figure and the figure will be "flipped" over a line of reflection. You will make observations that compare the new figure with the original.

Materials/Resources:

Geometer's Sketchpad on a computer

Procedure

1. Open Geometer's Sketchpad program on your computer and draw a half head as shown below.

image 10.04.01.13

2. Double click on the line of reflection.

3. Select the entire half head. (With the arrow tool, click and drag a rectangular region around the half head.)

4. Choose Reflect from the Transform menu.

5. Drag around any points or segments on the figure. What do you notice? Comment on the lengths of the segments, the size of each side and the angles on each side of the line of reflection.

6. What do you notice about the two red segments when you drag the earring? (Hint: to measure a segment, select the segment and choose Length from the Measure menu.)

7. Can you make the angle at one earring different from the angle at the other earring? (Hint: to measure an angle, select the 3 points that make up the angle and choose Angle from the Measure menu.) Why or why not?

8. Describe the relationship between the segments and angles on each side of the line of reflection.

9. Click Next. Now you are going to try to create a reflection yourself, without the help of Sketchpad! Use the segment tool to draw what you think the other side of the "half-shape" should look like. When you are done, use Sketchpad to reflect the "half-shape." How well did you do? If you want to try again, choose Undo from the Edit menu and start again.

10. Now it's your turn to create a reflected shape. Click Next to go to a blank sketch. Use the segment tool to draw a new "half-shape". Reflect your half-shape using Sketchpad.

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