This lesson is designed to introduce students to the concept of fractals and show them some examples of fractals in the real world.
- precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
- describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling
- examine the congruence, similarity, and line or rotational symmetry of objects using transformations
- draw geometric objects with specified properties, such as side lengths or angle measures
Teachers will need:
Students will need:
- access to a web browser.
- tape or glue.
- Guided Practice
- Divide the students into small groups so that each group has one
- Allow the students to play with the
Tortoise and Hare Applet.
- Introduce students to the concept of fractals.
- Introduce student to some basic calculus concepts.
- Make the students proficient in recognizing and generating image
- Teacher Input
- Explain how the applet illustrates Zeno's Paradox
- Use Zeno's Paradox to introduce and explain the concept of limits
- Brielfy explain that calculus is the branch of math that deals with
- Allow the students to explore the following applets:
- Encourage the groups to try to figure out how each applet works.
- Discuss how each applet works, inviting groups to explain what they
- Compare the applets to one another.
- Use the applets to help students visualize the concept of limits.
- Pose the question: How many orientations can a piece of paper have
on a flat surface? Explain the concept of transformations.
- Using the transformations handout, ask students to assign a label
to the transformations at the bottom of the page based on their
degree of rotation/reflection with respect to the identity figure.
- Hand out the Geometric Genetic Code worksheet and have the students
identify the codes that correspond to the fractals.
- Hand out two copies of the fractal grid worksheet to each student (or one copy with the grid set printed on both sides). On the first
sheet, give them a starting image and the code they need to create
a full fractal with it.
- Once they are confident with creating a fractal based on a given code,
let them create their own fractal using the other grid set. Once they
complete the fractal, have them determine it's code.
- Compare the algorithm used to generate fractals in the Interactivate
applets with the process the students used to make their own fractals.
- Independent Practice
- Divide the class into groups and give each group a "Making a
Stage 8 Fractal" handout. Follow the instructions to create a giant
fractal, combining each group's stage 7 fractal by taping them
all onto the large sheet of paper.
- Present some examples of fractals in real life, referring to the
"Uses of Fractals and Chaos" worksheet. Other possible examples
include the art of Jackson Pollock and the pattern of the veins in