Sierpinski triangle

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Last modified 3.3.03


Chaos

Audience: Preservice teachers of grades 5-8

Expected time: 60-90 minutes

Overview of Module: In this inquiry-oriented lesson, students generate the fractal called the Sierpinski Triangle (also called the Sierpinski Gasket) through multiple technologies (pencil and paper, graphing calculator, dynamic geometry software, internet simulation program). The study of fractals provides an example of the connection between geometry and nature.

Activities:

  • From Randomness (dice and transparencies, pencil and paper)
  • Examining Fractals (calculator, dynamic geometry software)

Goals:

  • Students recognize and explain how fractals are visual representations of recursiveness.
  • Students discuss and examine examples of fractals in nature.
  • Students explore the ways fractals emerge through random events.

Prerequisites:

  • Students need basic knowledge of measurement, area, perimeter, and similarity.

Math Concepts:

  • Recursion
  • Self-Similarity
  • Area
  • Ratio And Proportion
  • Random Numbers
  • Midpoints
  • Triangles
  • Linear Measurement