## Fractals Teachers' Notes

These lessons, written to comply with the NCTM Standards, use fractal geometry to introduce students to modern mathematical research and to reinforce the arithmetic and geometry skills that they study in school.

Why study fractals?
fractals, anyway?

Making fractals
Sierpinski Triangle
Using Java
Math questions
Sierpinski Meets Pascal
Jurassic Park Fractal
Using JAVA
It grows complex
Real first iteration
Encoding the fractal
World's Largest
Koch Snowflake
Using Java
Infinite perimeter
Finite area
Anti-Snowflake
Using Java

Fractal Properties
Self-similarity
Fractional dimension
Formation by iteration

For Teachers
Teachers' Notes
Teacher-to-Teacher

My fractals mail
Send fractals mail

Fractals on the Web
The Math Forum

Other Math Lessons
by Cynthia Lanius

Lesson Procedures: Students will study properties of fractals by utilizing online resources. The lessons are designed for students to work independently or with guidance from the teacher.

Mathematics Topics: Patterns, ordering fractions, area, perimeter, similarity, measurement, exponents

Connecting Mathematics:

• Connects math, art, writing, history, and careers
• Connects arithmetic and geometry

Materials and media: None other than a computer with Internet access and graphics capabilities, although triangle grid paper and posterboard is helpful. Every lesson has a version without links or navigational bar which can be printed for classroom use.

Suggested Assessment: Questions are included with most sections. A mini research project could be assigned after completion of the lesson. Students would complete an on-line portfolio that includes examples of other fractals, a paper describing what they have learned, a biography of a mathematician who does research on fractals, etc. Be sure to have them include a bibliography of the urls they used.

Suggested Teacher Resource: A really fine lesson on chaos and fractals is Robert Devaney's Chaos in the Classroom.