Technology-Enhanced Activity Plan

Ashley Bailey and Brendan Galioto

Topic: Chaos Game

Connection to Core Curriculum: Geometry

• Similarity, Right Triangles, and Trigonometry
• Understand similarity in terms of similarity transformations

Overview: Students can explore that randomness can create something that is not random.

Objectives:

Materials needed: half sheets of paper with vertices making an equilateral triangle, computer

Technology:

Shodor applet at http://www.shodor.org/interactivate/activities/TheChaosGame/

Youtube video https://www.youtube.com/watch?v=droTYSmSGHg

Role of Technology: Shodor applet will allow students to see what 1000s of dots will make which would be unattainable by hand. Video is a visual way to introduce instructions.

Activity Plan: Show video from the beginning until the one-minute mark. Hand out pieces of paper with 3 vertices that make an equilateral triangle. Students are to randomly choose a point inside the triangle, randomly choose a vertex, and make a new dot half-way between the chosen point and random vertex. At the new point, student is to randomly choose a vertex and make a new dot half-way between the current dot and the newly chosen vertex. Repeat process. We will give students 4-5 minutes with the idea that students should have 30-35 dots on their paper. Bring the class together and probe students if they notice any large gaps where there are no dots. Students will then begin to work with the Shodor applet. The Shodor applet enables students to change the type of polygon worked with and the probability a vertex will be chosen. After coming back together, the teacher will ask follow-up questions such as, “why do we see the Sierpinski triangle with the equilateral triange?”, “why do even numbered polygons have dots in the middle but odd numbered polygons tend to have a blank area in the middle?”, “what was noticed when you changed the probabilities of vertices?”. Wrap-up as time allows.

Included documents: the half-sheet of paper of an equilateral triangle