Lesson Plan
Curated OER

Investigating the Sierpinski Triangle

For Teachers 9th - 11th
Students solve and analyze the sierpinski's triangle. In this geometry lesson, students identify properties and theorem of triangles. They solve problems involving angles and sides of triangles.
Lesson Plan
Curated OER

CHAOS AND COMPUTERS

For Teachers 9th - 12th
Students discuss the Chaos Theory and how it came into existence.They observe order and compare it to the randomness of chaos. The lesson features the playing of a game to reinforce concepts.
Activity
University of Massachusetts

Fractal Project: Exploring Fractals

For Students 9th - 10th
A good beginner's site for fractals - the language is straightforward and requires only minimal experience to be able to understand the topic. (Note: When clicking on links on archived site, they may pause and appear not to be found...
Unit Plan
Boston University

Fractal Geometry of the Mandelbrot Set Ii

For Students 9th - 10th
This web site addresses counting and adding in fractal operations, as well as the role of the Fibonacci sequence in fractal geometry.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: I, It, Itera, Iteration

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson introduces students to the notion of Brownian motion and has students graph a sample Brownian particle. In Brownian motion, each "step" depends on the "steps" taken previously,...
Handout
Wolfram Research

Wolfram Math World: Fractals

For Students 9th - 10th
This page briefly illustrates and discusses fractals, which are closely linked to the concept of iteration (repitition.) Site links to well known pictured fractals.
Lesson Plan
Shodor Education Foundation

Shodor Interactivate: Lesson: The Mandelbrot Set

For Teachers 9th - 10th
In this lesson students will explore Julia sets and the Mandelbrot set. In the process they will learn about fractals and explore complex numbers and function iteration.
Unit Plan
Boston University

Bu: Fractal Geometry of the Mandelbrot Set

For Students 9th - 10th
This site progresses in iterations through Mandelbrot and Julia sets to explain fractals and the mathematics behind them.
Unit Plan
Boston University

Boston University: Chaos, Fractals and Arcadia

For Students 9th - 10th
This is an interesting site for information on chaos and fractals. Includes links to interactive activities to learn more.
Lesson Plan
Shodor Education Foundation

Shodor Interactivate: Lesson: Fractals

For Teachers 9th - 10th
This site provides some links to activities and lesson plans dealing with fractals and chaos.
Activity
Other

Research Pages: Circle Inversion Fractals

For Students 9th - 10th
This site introduces the iteration of circle inversions and describes the associated properties.
Unit Plan
Other

Eal: Fract Ed

For Students 9th - 10th
A great resource for beginners. The site begins with a definition of iteration of functions, and proceeds from there to discuss fractal dimension.
Interactive
Shodor Education Foundation

Shodor Interactivate: Two Variable Function Pump

For Students 9th - 10th Standards
Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form.
Article
Other

Julia Sets, Complex Deterministic Fractals

For Students 9th - 10th
Here's an example of "What a 2 Dimensional Julia Set will look like using modern computers with their sophisticated graphical displays." Gaston Julia published his theories long before computers and as the site's author remarks, "What a...
Activity
Shodor Education Foundation

Shodor Interactivate: The Chaos Game

For Students 9th - 10th Standards
Play the Chaos Game by experimenting with probabilities. Learn about an apparently random process with a not-so-random, geometric fractal result.
Unit Plan
CK-12 Foundation

Ck 12: Geometry: Self Similarity

For Students 9th - 10th
[Free Registration/Login may be required to access all resource tools.] Apply the concept of self-similarity.
Unit Plan
CK-12 Foundation

Ck 12: Geometry: Self Similarity

For Students 9th - 10th
[Free Registration/Login may be required to access all resource tools.] This concept introduces students to self-similarity and presents several common examples of self-similarity.
Handout
CK-12 Foundation

Ck 12: Geometry: Self Similarity Study Guide

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] This study guide looks at several examples of self-similarity.
Graphic
Curated OER

Research Pages: Circle Inversion Fractals

For Students 9th - 10th
This site introduces the iteration of circle inversions and describes the associated properties.
Graphic
Curated OER

Research Pages: Circle Inversion Fractals

For Students 9th - 10th
This site introduces the iteration of circle inversions and describes the associated properties.