Transformations and
Tessellations
A Project
developed by Luke Cioffi in collaboration with Karla Kane.
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 is to be completed by March 27, 2012. The entire project will be delivered to Mr. Cioffi digitally, except for #4. Read carefully as this project has a few parts to it:
-
Browse this page and investigate all links thoroughly. There are many links below that will give you insight into the various pieces of this project. You may want to take notes on the material you are reviewing. You might also want to bookmark some these websites for future reference. You might consider one of these bookmarking websites; Google Bookmarks, Digg or Delicious. Be sure to review all of the rubrics prior to completing each part of this project.
- Complete the Dueling Pinwheel activity using Geometer's Sketchpad. Save your GSP file so that you can email it to me at lcioffi@fcsuvt.org. You can answer any questions from the activity in the GSP file. Be sure to label each part of the activity accurately (creating tabs might be useful). Scoring Rubric for Dueling Pinwheel activity.
- Complete a web search to find at least one website that contains examples of tessellations. Send the URL to me at lcioffi@fcsuvt.org. None of the links on this webpage can be used for this part.
- Creating Tessellations: (Scoring Rubric) Choose one of the following to complete
- Draw by hand and label on one poster board (28inx22in) four different semi-regular tessellations using regular polygons. If you wish to use Sketchpad to create them, then you must create SIX semi-regular tessellations instead of the four.
- Construct one tetrahedron that is tiled with four different semi-regular tessellating patterns that are drawn by hand.
- Draw the four semi-regular tessellations and form them into an accordian book. (See Ms. Kane for details) If you wish to use Sketchpad to create them, then you must create SIX semi-regular tessellations instead of the four
- Construct 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?
- Type a double spaced, 12pt font, 4 page minimum paper about transformations and tessellations. The paper should explain what transsformations and tessellations are to a person that has never seen this material before. Be sure to include:
- Definitions and complete explanations of each term. These must include, but are not limited to: rigid transformation (or isometry), non-rigid transformation, tessellation, translations, rotation, reflection, glide reflection, tiling, monohedral tiling, regular tessellation and semi-regular tessellation.
- A detailed description of how this math topic is related to science and art.
- The history of tessellations
- Real-life examples of tessellation/transformation
- Works cited page using MLA format. You must have a minimum of 10 sources, including your textbook.
Bibliography Help:- Proper spelling and grammar.
Getting Started:
Through your exploration of this webpage you discover some very useful information. You will need to do some additional research beyond the links found here! Unit 7 of your textbook will be a great resource.
What are these things called transformations?
Find some great definitions of the four transformations, as well as some other interesting mathemactical thoughts while you look for some Wallpaper.
Tessellation Links from Suzanne Aljandre's collection.
Find out how to construct tessellatins with only a straightedge & compass. This will help you construct a tetrahedron.
Totally Tessellated Thinkquest Project will provide some excellent examples and history of tessellations.
Sir Roger Penrose and M.C. Escher are two individuals that have made large contributions to the study of tessellations and transformations.
A video showing different Escher Tessellations.
Student Found Resources:
Holly http://www.cln.org/themes/tessellations.html
Carly http://www.mathpuzzle.com/Tessel.htm
Olivia
Mariah http://mathandmultimedia.com/2010/03/05/tessellation-mathematics-of-tiling/
Rachel R http://www.cromp.com/pages/tess2.html
Rachel M http://www.princetonol.com/groups/iad/lessons/middle/tessell.htm
Jacob http://www.coolmath.com/lesson-tessellations-2.htm
Dan http://www.mathcats.com/explore/tessellationtown.html
Aaron http://mathartfun.com/shopsite_sc/store/html/Tessellations/SymmetryTess.html
Preston http://www.karenvagts.com/kvtessellations1.html
Ryan
Isabelle http://www.coolmath4kids.com/tesspag1.html
Katie http://www.surfnetkids.com/tessellations.htm
Arnela
Paul http://www.squidoo.com/tessellate
Paxton http://www.shodor.org/interactivate/activities/Tessellate/
Cam http://www.misterteacher.com/tessellations.html
Erin
Anthony
Tiffany http://www.k4.dion.ne.jp/~mnaka/animation.html
Julie http://mathworld.wolfram.com/Tessellation.html
Conner http://aleph0.clarku.edu/~djoyce/poincare/poincare.html
Christa
Kim http://www.opticalillusion.net/category/tessellations/
Cady
Annabeth http://www.teachers.ash.org.au/geparker/examples_of_tessellations.htm
Maya http://www.mathsisfun.com/geometry/tessellation.html
Emily http://gwydir.demon.co.uk/jo/tess/index.htm
Madison http://www.mathsisfun.com/geometry/tessellation.html
Kelly http://tessellation.info/
Robert http://www.kirkwood.k12.mo.us/parent_student/te/mcneelj/reach/challenge/tessellations.htm
Nathan http://gotessellate.webs.com/translating.htm
Mary http://www.laits.utexas.edu/hebrew/personal/toolbox/acm/tess/tess.html
Max http://math.kendallhunt.com/documents/dg4/GP/DG4_GP_07.pdf
JZ http://illuminations.nctm.org/ActivityDetail.aspx?id=202
Collapse All
Expand All