A ROTATION TESSELATION

Lesson Designed By:

Janet Mae Zahumeny
Roselle Park High School
e-mail: 74620.2745@compuserve.com

TOPIC:

A Rotation Tesselation

LEVEL:

Secondary Plane Geometry

GEOMETER'S SKETCHPAD PROFICIENCY:

Beginner / Intermediate

CLASS TIME:

1 class period (42 minutes)

GEOMETER'S SKETCHPAD SKILLS NEEDED:

Students should be familiar with the CONSTRUCT and TRANSFORM menus.

NOTES TO TEACHER:

To begin this activity students should be familiar with the terms rotate and equilateral, or have access to a dictionary or geometry book.

This activity can be done with any figure that tesselates. However, you must keep in mind that the size of the angle you rotate by must divide evenly into 360. [This assumes that you rotate by the number of degrees in the angle you are rotating around.]

i.e. The example here begins with an equilateral triangle with a 60 degree rotation of the figure. A square would rotate 90 degrees, and a hexagon would need a 120 degree rotation.

This activity was adapted for use with The Geometer’s Sketchpad - from Geometry (1994 Teacher's Edition), Jurgensen, Brown, & Jurgensen, by Houghton Mifflin Company.

ACTIVITY: A ROTATION TESSELATION

CONSTRUCTING THE BASIC SHAPE

  1. Draw equilateral triangle ABC.
  2. Alter the shape of side AB by placing and connecting a series of points along the side - DELETE the original side AB. (FIGURE 1)
  3. Rotate the new curved side AB about point B by 60 degrees.
  4. This now creates a new, curved side for BC . DELETE the original side BC.
  5. Connect the points A and C. Add artwork (eyes, feathers, etc. - if you feel creative!)
  6. Rotate 60( about the point B.
  7. Answer the questions on the last page.

*** YOU CAN ALTER THE ORIGINAL FIGURE AT ANY TIME ***

NOTE: Only 1 point was moved to change the figure on the left into the figure on the right.

CONSTRUCTION FOR THOSE WHO ARE FEELING BRAVE!

  1. Follow steps 1 through 4 above in the BASIC directions.
  2. Locate the midpoint of side AC.
  3. Alter the left half of side AC.
  4. Rotate the shape drawn in step 3 through 180 degrees about the midpoint of side AC.
  5. Connect the points A and C. Add artwork (eyes, feathers, etc. - if you feel creative!)
  6. Rotate the entire new shape 60 degrees about the point B.
  7. Answer the questions on the next page.

ROTATION TESSELATION QUESTIONS:

  1. Why did the directions specify that you rotate around point B if the triangle was equilateral/equiangular?
  2. Try rotating about a different vertex to verify your conjecture.
  3. You were directed to rotate using an angle of 60(. Would other angles work also? Why or why not?
  4. Investigate using different angles of rotation.
  5. Select 1 point and move it. Notice that ALL 6 of your transformed images react. WHY?