Chaos Theory:  Everything's A Pattern

A WebQuest for 7th
Grade Mathematics

Designed by

Ken Keech

[email-masked]

Introduction

The
Chaos Theory shows the idea that everything in the world, no matter how random
or unexplainable, happens because of some pattern.  This means that even something as
intricate and seemingly random as the path of a river can be understood by
evaluating many patterns.

So,
what is the BIG QUESTION?  This
WebQuest is centered around the search for the understanding of advanced
patterns.  Are you able to see how
the world can be explained through patterns?

The
Task

After
completing this WebQuest, you should have complete understanding of the
Fibonacci sequence, and basic understanding of both fractals and the Chaos
Theory.  You will also have created
a three-page paper hypothesizing how the Fibonacci sequence can be seen in
nature.

The
Process

1.
First learn about fractals by clicking HERE. Make sure you
complete the quiz!  Write down a
copy of each question as well as the answer to hand in.

Next,
click HERE to get a more
in-depth look at fractals.  Complete
either the “Jurassic
Park” project or
the     “Koch’s
Snowflake” project, following the directions that are provided in the
links on the website.

2.  Now
take a look HERE
to learn about the Fibonacci Sequence.
Take a few minutes to write out the Fibonacci Sequence to the fifteenth
term neatly on the sheet where you created the fractal in number one.  Next, click HERE
to see how the Fibonacci Sequence relates to nature.

3.  The
Sierpinski Triangle is a very interesting (and easy to draw) fractal.  Click HERE to learn about and take
a look at the Sierpinski Triangle.
Now create your own Sierpinski Triangle on a poster.  You may use markers, colored paper, or
anything else in order to make your fractal the coolest one in class.  If you wish, you may choose to make your
poster of “Koch’s Snowflake” or the “Jurassic
Park” fractal instead; just make sure that if you do this you make a
Sierpinski Triangle for part one.

Think about it!

How
would you explain the relationship between the Sierpinski Triangle and
Fibonacci Sequence? (Hint: Think about how both the Sierpinski Triangle and
Fibonacci Sequence show growth.)
For extra credit, include this explanation on your poster.

4.  Now
let's make some connections and see how fractals and the Fibonacci Sequence
relate to the Chaos Theory.  Click HERE
for a brief introduction to the Chaos Theory.  Now look HERE to learn a little bit more about
how fractals and patterns relate to the Chaos Theory.

Now for the final part of the WebQuest.  Write a three-page essay in which you
hypothesize at least three new ways you can see the Fibonacci Sequence in
nature.  You may use pictures,
models, or other methods to support your paper, but these do not count as far
as length is concerned.  You may
also conduct research on the internet beyond sites included in this WebQuest,
provided you cite all sources.  Hand
in this last assignment to Mr. Keech to complete your WebQuest.

Evaluation

The rubric for the
evaluation of the essay can be found HERE.

The rubric for the
evaluation of the poster can be found HERE.

Conclusion

Each group should turn in the following:

Completed quiz with correct answers.  (One for each student in the group)

One fractal (not a poster, one for each student in
the group)

One poster (one for the whole group, explained in
process step 3)

A rough draft of the essay (handwritten, due
Thursday)

Final draft of essay (three pages, not including
pictures or diagrams)

All of this (except for the rough draft) is due on
Monday, March 27, 2006.

After completing this assignment, are you
constantly identifying patterns in nature that you have never thought about
before?  You should be!  Math helps you think about ordinary
things in extraordinary ways!

Resources

http://library.thinkquest.org/26242/kids/

http://www.techlar.com/fractals/websys.exe?file=explore/tutorials/kids11a.html

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html

http://math.rice.edu/~lanius/fractals/

http://www.ga.k12.pa.us/Academics/US/Math/Geometry/stwk99/danc/backgrnd.htm

http://www.orgmind.com/chaos.html

Based on a template from The
WebQuest Page

Edited by Ken Keech