Tessellations

Tessellations

A Web Quest for 7th Grade Mathematics

Bethany Anderson
bethany_anderson@charleston.k12.sc.us

Introduction
Congratulations! You are about to embark on one of the most exciting and fun projects that you will do in math this year! You are going to make a tessellation. What is a tessellation? Click here!

The Task

By the end of this project, you will have created your very own tessellation! Now that you know what a tessellation is, it is time for you to check out math's impact on the world of art. Check out some really awesome professional art pieces that were created using tessellations and fractal patterns! See below for a few examples, but also visit this page. Particularly, look at "really cool stuff," and "mathematical art." Don't forget, the top five tessellations from my classes will become a part of the Anderson Ceiling of Fame!

The Process

Now it is time for you to make your tessellation! You will need the following materials:
        one 3 in x 5 in index card
           scissors
           pencil
           a textured or thick 11 x 18 in piece of white paper
           colored pencils or markers
           scotch tape

First, you must make your tessellation card. Follow these steps:
             1) At the top of your index card, draw any kind of line that starts at the left corner, and ends at the right corner. It can be swirly, pointy, squiggly, or whatever kind of line you want.
             2) Cut out your line.
             3) Slide your cut out to the bottom of your index card. Line up the straight edge of your cut out with the straight edge of the bottom of your card. Make the edges meet perfectly, and tape them together. What was cut out of the top of your card should now be added to the bottom of your card.
             4) On the left side of your index card, draw any kind of line (as in step one), that starts at the top corner and ends at the bottom corner.
             5) Cut out your line.
             6) Slide it to the right side of your index card. Line up the straight edge of the cut out with the straight edge of the right side of the card. When the edges meet perfectly, tape them together.

You now have your tessellation card! Twist it and turn it, and try to imagine what shape or object it looks like to you. Can you picture what your tessellation is going to be? Check out some other tessellations here to get ideas.

Now it is time for you to trace your tessellation on your paper! Remember to use pencil. Start in the middle of the page, and trace your object over and over, making each piece fit perfectly into the next like a puzzle. Tessellate the shapes over and over (off the edges), until the entire page is covered. Add your artwork by creating your imaginative objects! Don't forget to add plenty of color!

Evaluation
Here is the rubric I will use to grade your tessellation project. The first category is worth 30 points. Creativity can earn you up to 20 points. Neatness can also earn you up to 30 points, and you can earn up to 20 points for artistic ability. Remember, if you're good at the math, you're good at the art!!! This calculates to a grand total of 100 points.


	Poor Work 1	Fair Work 2	A Good Job 3	Excellence 4
How well does the object tessellate?	The objects on the page do a poor job of tessellating. Half or more do not fit together like a puzzle. There are many gaps or overlays.	There are several objects that do not fit together well. There are several gaps or overlays.	Almost all objects fit together perfectly like a puzzle. Only one or two objects do not fit perfectly.	Every object on the sheet perfectly fits into all surrounding objects with no gaps or overlaps.
Creativity	The artist created a design out of his/her tessellation shape that reflects poor work ethic and no imagination.	The artist created a design out of his/her tessellation shape that is not creative, but shows some effort put forth.	The artist created a somewhat unique and different design out of his/her tessellation shape.	The artist created a very unique and different design out of his/her tessellation shape.
Neatness	The tessellation shows a great lack of time and effort put into the project. The project appears unfinished or sloppy.	The tessellation shows a hint of neatness, but also has great qualities of messy work.	The tessellation project is very neat. There may be one or two areas that reflect messy or untidy work.	The tessellation is extremely neat and well put together. The coloring and tracing of the project is beautifully finished and reflects great work ethic.
Artistic Ability	The tessellation project shows no reflection of artistic ability. The artwork may appear loose or disheveled.	The project reflects some artistic ability. The artist shows some attempt at making the project attractive.	The art in the project is attractive. The artist reflects good ability in creating a good looking piece of art.	The artwork is exceptional. Not only did the artist produce very neat and attractive work, there is a natural ability to create art reflected in this piece.

Conclusion
Now that you have created your own tessellation, you have mastered the art of translation! Translation, reflection, and rotation are very important mathematical values that are integrated into everyday life. Hopefully, you had a lot of fun creating your tessellation project, and are proud of the artwork you mathematically produced! How well did you do? Do YOU have a shot at joining your tessellation in the Anderson Ceiling of Fame?

Credits & References

Links, images, and information provided by the following:
http://members.cox.net/tessellations/index.html

http://www.coolmath.com/tesspag1.htm

http://www.kenston.k12.oh.us/khs/math/top4.html

http://mathforum.org/sum95/suzanne/whattess.html

http://mathforum.org/sum95/suzanne/tess.intro.html

A very special thank you to Ronnie Continenza, web master of Kenston High School's web site, and to Robert Fathauer, artist and web master of the Tessellations web site, who both gave me personal permission to use their web sites and images in this Web Quest.