From an Enrichment Coordinator

Message 1

Date: Thu, Nov 16, 1995
Dear Suzanne,

Where do you teach?

(Suzanne answered): I am in Rialto, California (inland from LA) and actually I am a computer/newspaper teacher but I have taught math and I mentor in math!
I found your HyperCard directions but I still don't quite understand the symmetry idea. Could you help?
(Suzanne answered): The three symmetries that can be shown in the three tessellation exercises are:
translation
rotation
glide reflection
(but doesn't include reflection and I think reflection is the normal symmetry that we teach...the idea of the butterfly or the Batman sign where you can draw a line and fold and the two pieces match up with each other)

To me the idea of a translation is so simple that it doesn't really seem like a mathematical concept (...but...some mathematical concepts are very simple and basic!!). Maybe to really demonstrate the idea of a figure that tessellates is best understood by one that does not. If you take a circle and try to copy and move it to the side ...no matter what you do you can fit them all together! Only quadrilaterals will do this (including quadrilaterals that have been distorted).

Hexagons are the best figure to show symmetry by rotation.

Triangles are the best figure to show symmetry by glide reflection (flip and slide).

Look at the Where's the Math pages again...but...just look at the examples that have the R diagrams....a great way to show them with the class would be to make an overhead transparency of the letter and slide or rotate it around (actually several R's might help).

Message 2

Date: Wed, 13 Dec 1995
Suzanne,
I work in a school district outside of Rochester, NY. I coordinate an enrichment program which brings me to three elementary schools. I work along side classroom teachers.

I recently lead two workshops with fourth graders using your lesson plans. The kids loved them. I had first introduced the transformations to three classses with your "Where's the Math" as my background. I also used "Tessellmania" to demonstrate how these are used to build tessellations, and a slide show of Escher paintings for the kids to see them in art.

A smaller group from these classes came to the HyperCard workshops the next week and the week after. The kids made some beautiful tessellations. We followed your steps for for building tessellations with two types of translations (I think we used the translation and glide reflection). The computer teacher and fourth grade teachers were impressed. I have used tessellations as an enrichment topic before, but this is the first time I was confident with taking the kids further. It was also the first time we created computer generated products.

Thanks for the help!