The Topic: 
Tessellations

Easier - A tessellation is created when a shape is repeated over and over again. All the figures fit onto a flat surface exactly together without any gaps or overlaps.
 
Harder - A tessellation is a repeating pattern composed of interlocking shapes (usually polygons) that can be extended infinitely. The tiling for a regular (or periodic) tessellation is done with one repeated congruent regular polygon covering a plane in a repeating pattern without any openings or overlaps. Remember 'regular' means the sides of the polygon are all the same length, and 'congruent' means that the polygons fitted together are all the same size and shape. A semi-regular (or non-periodic) tessellation is formed by a regular arrangement of polygons, identically arranged at every vertex point. 
 
 
Totally Tessellated (A ThinkQuest Project) 
http://library.advanced.org/16661/index2.html
Website gives a comprehensive introduction to tessellations, explaining the basic mathematics underlying tessellations, as well as allowing you to browse through many examples of tessellations in real life. Note: The gallery section contains an unmoderated student forum.
 
Tessellation Tutorials (A Math Forum Web Unit by Suzanne Alejandre) 
http://mathforum.org/sum95/suzanne/tess.intro.html
This site explains what they are, the math concepts involved, the historical and religious connection, and provides tutorials and templates for making your own tessellations. Also provides numerous links to related resources.
 
Tessellation 
http://www.hbschool.com/glossary/math/definitions/tessellation7.html
Contains an brief, clear and concise introductory definition along with an animated graphic.
 
Karen's Tessellation Page
http://www.coolmath.com/tesspag1.htm
What are tessellations?
  
Find Tessellations in the World. After exploring the Tessellation Tutorial and Tessellation sites, find tessellated shapes in everyday life. You might start by looking for patterns in man-made materials, artwork, architecture, and the like. What about near-tessallations, designs and patterns that do not perfectly match the definitions? Take photographs of your findings and put together a display of the results. Can you identify the time period in which they were created? Did you find some tessellations in nature? There are some (honeycomb). For some examples of man-made tessellations, look in the gallary section at Totally Tessellated.
 
Construct Your Own Tesselations. Make your own tessellations. You can follow instructions found at Tessellation Tutorials and Creat Tesselations using ClarisWorks. Decorate your creations by adding attractive colors and design shapes. Show your completed tessellations.
 
Compare and Judge Tessellations. Find and look at many tessellations. You can find lots of examples at the websites below. Remember to check some of the linked sites also. Pick and choose the best or your favorite design. Print out and display your choice(s). Explain why you like and chose the tessellation as being best.
 
Make a Tessellation Quilt Block. Design and construct a quilt block that uses a tessellated pattern. Display the finished work.
 
Create Tesselations Using ClarisWorks
http://mathforum.org/sum95/suzanne/cwtess.html
Create computer-generated tesselations using ClarisWorks
 
Tessellations -Step by Step
http://www.wsd1.org/lgc98/teach/Paint/makefish.htm
Contains instructions for creating tessellating art using Paintbrush or Paint software on Windows
 
Tessellate
http://www.shodor.org/interactivate/activities/tessellate/index.html
Allows you to generate a new tessellating shape starting from a rectangle, triangle or sexagon. 
 
How to Create a Tessellation
http://arttech.about.com/c/ht/00/07/How_Create_Tessellation0962934009.htm?am=dpile&terms=Weaving+Tessellations
A simple how to on creating tessellations.
 
World of Escher 
http://www.WorldOfEscher.com/
Learn more about the life and work of M.C. Escher, a Dutch graphic artist, recognized for spatial illusions, impossible buildings, repeating geometric patterns (tessellations), and his incredible techniques in woodcutting and lithography.
Another Escher site:
http://www.mathacademy.com/pr/minitext/escher
 
Tessellations 
http://www.tessellations.com/
Explore the world of tessellations.
 
Student Tessalations
http://mathforum.org/alejandre/students.tess.html
Samples of student work.
 
Examples of Tessellations
http://www.iusb.edu/~abrown/tessellations.html
 
Tantalizing Tessellations Grade 5
http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html
Mainly for teachers; a series of lesson plans involving tessellations
 
Investigations of Tessellations
http://mathforum.org/sum95/suzanne/active.html
Investigating tessellations using pattern blocks links to activities using pattern blocks in colour.
 

'tiling'
dissection
vertex
shape
congruent
quilt
pattern
border
geometry
M.C. Escher
reflection
direction
graphic
embellishment
plane
polygon
translation
rotation
color
irregular
design
interlocking
intersection
computer-generated
angle
mosaic
infinite
edge
periodic
symmetry

 
Created by Annette Lamb and Larry Johnson, 1/99. Updated by Nancy Smith 3/02