Tessellations

This webquest is to help you locate and design patterns. "You are a detective trying to identify the mysterious pattern."
Can you find them? What do they look like? Be able to explain it writing, please.

The Tasks:

the student sees the object as a whole--no parts as such,
the students sees the shape as having properties generally single ones,
the student begins to recognize that the properties are linked together, or relationships become apparent
students is able to verbalize some deductive arguments and see new ideas forming, problems to be solved, and positions to be formulated and defended.

The Resources:

Provided below are at least 5 unique places on the Internet with information about tessellations. They include short descriptions so that you can know in advance what you are clicking on. The link will take you directly there, rather than having to navigate through a maze.

1. Ask Us About tessellations Ask your question and get a real-time answer from an actual live person! Be sure to ask at least three questions that deals with tessellations.

2. Math Tessellations An Introductory Unit Based on MECC's Tesselmania! This unit was developed in conjunction with the Tesselmania! software program and the tessellations of M. C. Escher.
3. Quilt Gallery Magazine This web site provides you different types of tessellated patterns and terminology. Also it shows several creative patterns that are used to design quilt.
4. Tetrominoes This web site explain what polyominoes are and to learn how tetrominoes can be related to tessellations. Try a few designs yourself. Are you able to find any patterns like these in the classroom?
5. Symmetry in Tessellations Symmetry in Tessellations list the different types of mathematical symmetry found in tessellations. There are three types, do you know them? After visiting this site you will.

The Process:

It time for you to have some fun. Design your own tessellations. Click and play.

1. Click on Ask Me and ask them what are tessellation used for?

2. Find out who M. C. Escher's is and type a brief summary, turn it in for extra credit.

3. Click on Regular polygon tessellation I. Name the regular polygon figures, make some, cut them out, and design your own tessellation. Follow the rules and it will be worth 150 points.

4. Let's play the Bubbletrouble game, maybe you can match the patterns and numbers.

5. Click on the types of Symmetry and identify and explain each picture you see. What form of symmetry is used?

6. Let's check out a gallery.

Learning Advice:

There are three types of mathematical symmetry that are commonly found in tessellations. These are translational symmetry, rotational symmetry, and glide reflection symmetry. Recall when reading that tessellations extend to infinity; the diagrams are finite portions of infinite tessellations.

Conclusion:

Symmetries create patterns that help us organize our world conceptionally. Symmetric patterns occur in nature, and are invented by artists, craftspeople, musicians, choreographers, and mathematicians.
In mathematics, the idea of symmetry gives us a precise way to think about a particular object or subject. We will talk about plane symmetries, those that take place on a flat plane, but the ideas generalizes to spatial symmetries too.

This page was designed by Charlotte Fields and the page was created February 26, 2000.