Tessellations & Transformations Project
Developed in collaboration with Luke Cioffi
This lesson will guide you to a few different places on the World Wide Web. My goal is for you learn about tessellations and transformations. Most of your correspondence with me for this project will be done through the use of email. (kkane@fcsuvt.org)
Objectives:
- Students will be able to recognize five different transformations in a plane.
- Students will be able to discuss and construct different types of tessellations by hand and with the use of technology.
- Students will explore the mathematical history of transformations and tessellations.
- Students will be able to make connections between mathematical concepts and their every day lives.
Assignment:
The assignment, which needs to be completed by March 27th, has a few parts to it:
- Browse this page and all links thoroughly.
- Use a search engine to find at least one website that contains tessellations and email the URL to me. (Websites already on this page cannot be used.)
- Complete the "Dueling Pinwheel" activity. On your Sketchpad sketch, answer ALL parts to each question completely, save your sketch on your H-drive and email the completed activity to me. (Make sure to carefully label each part and question.) (Scoring rubric)
- Draw and label, on one posterboard (22" x 28"), four semi-regular tessellations OR draw the four semi-regular tessellations and for them into an accordian book (see me for details) OR construct one tetrahedron that is covered with four semi-regular tessellations. These four tessellations must be drawn by hand. If you wish to use Geometer's Sketchpad to create the tessellations, you must create SIX tessellations instead of four. (Scoring rubric)
- Create a unique, Escher-type, tessellation using Geometer's Sketchpad. Please include the type of tessellation you have created. (Specifically, what shape did you start with and what transformations did you use to alter it.) Save your tessellation and email it to me. (Translation Tessellation Instructions) (Rotation Tessellation Instructions) (Scoring rubric)
- Type a (double-spaced, 12pt font, minimum of four pages) paper about tessellations and transformations. This paper needs to be transmitted to me digitally. Be sure to include the following:
- Definitions, diagrams/illustrations, and complete explanations of each term. (These must include, but are not limited to: rigid transformation (isometry), non-rigid transformation, translation, rotation, reflection, glide reflection, tessellation, regular tessellation, semi-regular tessellation, tiling, and monohedral tiling.)
- A detailed description of how transformations and tessellations are related to art and science.
- A discussion of the history of tessellations.
- Real-life examples of transformations/tessellations.
- A "works cited" page. (You must have a minimum of 10 sources.) (Scoring rubric)
I expect correct spelling and grammar and for the paper to be in your own words!
Getting Started:
Through your exploration of these links, you will be able to obtain some very useful information. You will need to do some additional research too! UNIT 7 IN YOUR TEXTBOOK will be a valuable resource.
What are these things called transformations?
Find some great definitions of the transformations, as well as some other interesting mathematical thoughts, while you look for some wallpaper.
Tessellation links from Suzanne Alejandre's collection.
More tessellations at Tessellation.org.
For a little history on tessellations try, Totally Tessellated, or one of the "tessellation masters", MC Escher.
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