Pyramid in the Desert  (Kmz file)

Objectives

  1. •Describe a fractal pattern

  2. •Construct a 3-4 stage Sierpinski triangle in Google Earth

  3. •Express ratios and the area of a Sierpinski triangle mathematically

  4. •Contribute a part to a larger project


Lesson Description

This lesson introduces students to the concept of fractals with a simple fractal curve.  The Sierpinski Triangle is a basic example of fractals because it uses the familiar triangle with a pattern that shows self-similarity at any scale.  Starting with a blank equilateral triangle, the middle fourth of the triangle is found by joining the midpoints of each side in a shaded triangle.  Each repetition of this process constitutes a stage of the fractal.


The download file includes the vertices and polygons of a partially completed Sierpinski triangle.  Students will add to this triangle by continuing the pattern for 3-4 stages in the incomplete triangles. There are 18 vacant triangles in the included file (as shown above).  The vertex coordinates or placemarks of the different triangles can be assigned to students so that the entire class is contributing to the finished product.  Note that individual pieces of the given triangle can be removed or added in the file if needed, and the triangle can be expanded in subsequent years by other students as an ongoing creation.


Discussion should follow as to what properties fractals have and theories of how they can be used.  Additionally, students should try to express the pattern mathematically.  This is best done with by describing the area of the triangle that is NOT shaded with fractions at different stages.  A student worksheet that covers these questions is available for download below.


Downloads:

Pyramid in the Desert - Google Earth Kmz file

Teacher document - Word.doc

Student Assignment Sheet - Word.doc



You may find these links helpful:

Fractal Lessons by Cynthia Lanius - (link)

Chaos in the Classroom by Robert Devaney - (link)

Java Applet by Jacobo Bulaevsky - (link)



Back to Exploratory lessons’ page

 

Concepts used:

Fractals

Measurement

Similarity

Area

Fractions

Algebra


Grade level:

Grades 6-9


Subject areas:

Math


Standards

NCTM

- Geometry

- Measurement

- Connections

  1. -Representation

  2. -Technology


NETS*S

1b, 3a, 3b, 4a, 6b


Tutorial

Videos