Cynthia Lanius

A Pretty Fractal     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.
Table of Contents


  Why study fractals?
    What's so hot about
    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
            Using Java

  Fractal Properties
    Fractional dimension
    Formation by iteration

  For Teachers
    Teachers' Notes

    My fractals mail
    Send fractals mail

  Fractals on the Web
    The Math Forum

  Other Math Lessons
    by Cynthia Lanius

Grade Levels: 4-8

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.

Copyright 1996-2007 Cynthia Lanius