# Teacher's Guide

Objective:
Students will know how to use KaleidoTile.
Students will be able to sketch the polyhedra shown.
Materials:
Launch:
• Hand out the Introduction to KaleidoTile Activity Sheet
• Explain how to load the KaleidoTileprogram.
• Let the students play with the program. (They will do so anyway.)
Explore:
• After the students have played with the program for a while, direct them to the questions on the worksheet. Make sure the students have the faces button turned off when making their sketches so the "hidden" edges can be seen.
• You can print any of the objects shown in the Tiling window by going under the File menu at the top of your screen. You could easily make any transparencies of these that you like. (Of course if you have a computer linked up to a large monitor or overhead, even better.)
Summary:
Have the students share their sketches with others, either in small groups or as a class.

Pose these questions to the class:

• Can you see the 3-dimensional aspects of the polyhedra in your drawings?
• Did your sketches look the same as other people's?
• What did all the shapes have in common that used the (2,3,3), (2,3,4), and (2,3,5)buttons?

```Answer:  All of the shapes made with these buttons were polyhedra.
(These symmetry groups tile the sphere.)```
• How was using the (2,3,6) button different than the previous three?

```Answer:  This made flat patterns.  (They tiled the Euclidean
plane.)```
• Can anyone tell what happened when you used the (2,3,7)button and moved the figure around?

```Answer:  It looks like the shapes are in the plane but are
distorted.  (This is actually one view of hyperbolic space.  We will not
study hyperbolic space in these materials, but feel free to explore.)```
• Who found the soccer ball? How did you find it?

```Answer:  The soccer ball is the truncated
icosahedron  It is found using the (2,3,5) Symmetry Group by
placing the base point in the Basepoint window in the middle of
the left side of the triangle.```

Connections:
If you have done lessons on building physical polyhedra models, this would be a good place to connect those seen on KaleidoTile with the models.