Fractals Lesson Plan

Instructor: Corrie Boone

Corrie holds master's in elementary education, taught elementary ESL in the public schools for 5 years, and recently was teaching EFL abroad.

Your students will explore fractals in math, both from the viewpoint of art and in numbers, such as exponents. A fun art activity will surely get them engaged and learning!

Learning Objectives

After this lesson, students will be able to:

  • Create a complex pattern by repeating a simple process.
  • Generate and analyze patterns.
  • Use operations to explain patterns in arithmetic.


90 minutes

Curriculum Standards


Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


  • Fractal
  • Self similarity
  • Gosper iIland
  • Koch snowflake
  • Box fractal


  • Sierpinksi Triangle template for each student
  • Crayons, markers, colored pencils, etc.
  • Copy of lesson quiz for each student

Lesson Instructions

Introduction (10 minutes)

  • Begin the lesson by reviewing with your students the concept of patterns. Discuss where in nature or life you can see patterns. Guide your students to discuss patterns with numbers, not just shapes and figures.
  • Tell your students that today you are going to learn about a new type of pattern: fractals. Fractals are never ending patterns that can occur in art and shapes, as well as in numbers and fractions.

Direct Instruction (40 minutes)

  • Show your students the video lesson Fractals in Math: Definition & Description.
  • Tell the students that now they are going to create their own Sierpinksi triangle, which is a common fractal image but was not shown in the video. (You may want to show your students examples of Sierpinksi triangles from the Internet so they know what they are trying to create.)
  • Give each student a Sierpinksi triangle template. Tell your students follow these steps:

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