Fractal Projects For Geometry Students


Welcome Mathematics Teachers.

Educators often talk about creating conditions that make the "light go on" for their students. This hands-on fractal unit is a way to turn those lights on for all of your students.



Fractals are an example of the extaordinary beauty of mathematics. It is my hope that this process of introducing the beauty of fractals to your students will be extremely exciting. I believe that your students will increase their understanding and love for mathematics as they work on the fractal lessons and projects that follow.


This fractal geometry unit was designed during my studies in the Master of Science Teaching program (MST) at the New Mexico Institute of Mining and Technology (NMT) in Socorro, NM. My goal has been to create for myself and other high school mathematics teachers a fractal unit that will challenge our students with some enjoyable and interesting mathematics activities.

At the beginning of this fractal unit, you will introduce your students to some of the classic fractals by guiding them through the fractal lessons. It is here where they will learn more about fractal characteristics such as "self-similarity" and "fractal dimension." Also, as the students study the perimeter and area of these fractals, they will be able to apply additional higher-level math concepts such as finding "the sum of geometric series" and "limits." In addition, you will model for the students how to design MSW Logo computer programs and how to use the Xaos program to create these fractals.

Then, the most exciting part of the fractal unit begins. Your students will apply what they have learned as you set them free to work in small groups on the hands-on fractal projects. After finishing their project assignments, each group will give a presentation to the class describing what they have learned from their fractal project. Also, there is an assessment test at the

The unique part of this fractal unit is the technology aspect that is included. Computers can help students to understand the process of geometric iteration and to quickly visualize the astounding fractal images. I also believe that students will improve their logical thinking skills by learning some of the basics of computer programming. Here, they can apply all these skills in a way that's fun.

This fractal unit has been successfully tested out with my own students. My students really enjoyed this fractal unit and learned quite a bit. This was a particularly appropriate unit for the end of the school year. At a time when students had tired of textbook activities, the fractal unit refocused their attention and encouraged them to dive deep into an exciting math topic.

I feel that this lesson could be also be used as an independent study project for a gifted student or for a student who has to be home-schooled for a while. Such students would still need occasional guidance from a math teacher, however.

I am grateful to all of my professors and the Master of Science Teaching staff at New Mexico Tech for their help with my studies, and to my family (Carol, Carolene, Craig, Ben, Noah, and Alec) for providing me the time to work on my studies.

Teachers, please contact me if you have any questions, comments, or suggestions about this fractal unit. I will appreciate your responses. In addition, feel free to share this webpage with your colleagues.


Bruce Lewis
Math Department
Thoreau High School
PO Box 96
Thoreau, NM 87323

phone: (505) 721-4500

e-mail: blewis@gmcs.k12.nm.us

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