 |
 |
|
Discovering Fractals - A WebQuest
by Joan Kessler
Broward Schools
|
|
|
| Introduction:
This WebQuest will introduce you to a field of Geometry called Fractal Geometry. Fractals are found in mathematics, art, and nature, and can even be applied to music. You will explore the exciting world of fractals and discover topics in geometry that do not necessarily lend themselves to traditional classroom settings. The internet will enable you to explore the history of fractals, their applications, and how these beautiful and fascinating objects are created. For a look at some fascinating fractals click here. It will open a new page so that you may begin your quest by seeing the beauty in mathematics. The Task: Your task is to investigate Fractal Geometry on the internet, using the links provided. You will work in teams of two or three to explore fractals and use what you have learned from interactive web pages to create a portfolio which includes constructing fractals on paper using geometric tools. After reading through the links you will create a working definition of fractals. You will explore the famous Koch fractals and also explore the Sierpinski Triangle along with the relationship between "arithmetic" and the Sierpinski Triangle using Pascal's Triangle. In your quest you will discover fractals in nature, and those in real life applications. The Process: You and your team members will create a portfolio based upon the following steps. The cover page will have your names on it, along with the title of the WebQuest. Decorate the cover page using one or more of the fractals in the links or in one of the galleries. Each subsequent page will be based upon processes listed below. |
|
1. | Use the links given
below to create a working definition of a Fractal in your own words. The definition should include properties of fractals that are common to all. Be creative with the definition. Do not use a definition from a web site or published source. It should be more than one sentence. This will be page one. |
|
2. | Explore the Sierpinski
Triangle with the linked references in the
Resource section below. Create a Sierpinski Triangle online using online resources. Click here for one of the links. Follow the directions given for this applet. Choose the colors you want and print out just the first page in color. This will be page two. |
|
3.
|
Use the
reference links to find the directions
for making the Sierpinski Triangle on paper. Construct a Sierpinski Triangle on a standard sheet of white 8.5 by 11" piece of paper using geometric tools, such as a ruler, and/or compass. Do four iterations. Start with an equilateral triangle. Color in the triangles to form a unique pattern. Each member of the group must turn one in. Each person must have a different size original equilateral triangle; 6’’ side, 7” side, and, if there are three on the team, an 8” side. Make sure the creator’s name is on the page. Please review how to construct an equilateral triangle. These will be pages 3, 3a, 3b etc. |
|
4. | Explore Pascal's
Triangle and the relationship to the Sierpinski Triangle. Use the links below to first learn about Pascal's triangle. There is information on more than one site. Then click on this link and follow the directions. This will be page 4. |
|
5. | Find examples of
Fractals as seen in nature. Find an example of an object in a magazine or on the web that looks like it has the properties of a fractal. Photocopy it or clip it and paste onto a new page of your portfolio. Do not use broccoli. If you prefer to use your own camera to take a picture of a natural fractal, you may do so and attach it to the page. Find an example of a computer generated fractal online that looks like something in nature. Print this out and place it on the same page as the picture above. Label the pictures. Do not use a fern. This will be page 5. |
|
6. | Each member of the
team is to create a version of the Koch Snowflake on a standard sheet of white 8.5 by 11" piece of paper using geometric tools, such as a ruler, and/or compass. Start with an equilateral triangle with side 6". Each person on the team must have a different size base triangle. Do at least 3 iterations. Use a marker or a colored pencil to trace the outside of the snowflake. The following is one of many links which will help you. Koch This will be page 6, 6a, 6b, etc. |
|
7 | Click on the following link and answer the questions. Scavenger Hunt |
|
8. | E-mail a fractal
postcard to me. Use this link
: Fractal
Postcard Mail to: joan.bookbinder@browardschools.com. Put all the names of the group members on the card or you can each send a unique card. Feel free to e-mail a card to anyone you know (including teachers and principals) and tell them about your WebQuest. |
|
9. | Please
click on this link when you are done with your WebQuest.
Project Evaluation |
Conclusion
| This project was
designed to introduce you to a field of mathematics that would be difficult
to teach and learn in the traditional way. Just as most fractals are computer
generated and difficult to create by hand, some fields of mathematics are
better explored with advanced technology than at a board with markers. You
have also been exposed to online fractal generators and can see the power
and beauty of mathematics develop before your eyes. I hope that this
exploration will give you incentive to explore other topics online. A wonderful
place to begin that exploration is the NCTM (National Council of Teachers
of Mathematics)
Illuminations
site. Let the Journey begin!
|
Rubric Click here
