The Pythagorean Theorem

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The Pythagorean Theorem
A WebQuest for 9th Grade
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
Based on a template from The WebQuest Page
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Introduction
The Pythagorean Theorem was one of the earliest
theorems known to ancient civilizations. This
famous theorem is named for the Greek
mathematician and philosopher, Pythagoras.
Pythagoras founded the Pythagorean School of
Mathematics in Cortona, a Greek seaport in
Southern Italy. He is credited with many
contributions to mathematics although some of
them may have actually been the work of his
students. The Pythagorean Theorem is Pythagoras'
most famous mathematical contribution. According
to legend, Pythagoras was so happy when he
discovered the theorem that he offered a
sacrifice of oxen. Pythagoras needs your help in
showing disbelievers that his theorem works for
all right triangles. He has the problem that
some people do not believe him because they do
not understand how he explains it. Your job as a
group is to find ways to make everyone believers
and show them that the theorem exists in real
world examples. Be prepared to work hard on this
project. The people you need to convince are
stuck in their ways and not easily swayed.
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
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The Task

• You will be traveling all the way back to ancient
  times in Greece to work as a team studying under
  the great Pythagoras. But be careful, the
  Pythagoreans had many rituals, and they
  approached mathematics with an almost religious
  intensity. Their power and influence became so
  strong that some people feared that they
  threatened the local political structure, so they
  were forced to disband. However, many
  Pythagoreans continued to meet in secret and to
  teach Pythagorass ideas. This will be your
  quest, and during it you will be able to
• investigate the history of Pythagoras and his
  Theorem,
• illustrate the Theorem with picture proofs,
• discover how different ancient cultures
  discovered and used the theorem,
• and find real life examples of the Theorem in
  action.
• Once you return from your journey, you will put
  together a presentation that includes historical
  information, explanation of the Theorem, a
  picture proof of the Theorem, cultural
  connections, and the solutions to two real world
  problems that use the Pythagorean Theorem.
  Remember, you have to show that the Pythagorean
  Theorem works only for right triangles, not all
  triangles.

Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
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The Process

• Weve traveled way back to the time of
  Pythagoras. In your assigned group, you will
  navigate your way to proving the Pythagorean
  Theorem. You will
• investigate the history of Pythagoras and his
  Theorem,
• illustrate the Theorem with picture proofs,
• discover how different ancient cultures
  discovered and used the theorem,
• and find real life examples of the Theorem in
  action.
• When you get back, your last step will be to put
  together a presentation including real world
  examples of how to solve them.

Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
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Step 1 Meet your Group

• Meet your fellow travelers. You will be learning
  together and helping one another understand the
  Pythagorean Theorem. Open up a good line of
  communication. You will be receiving a group
  grade, so be sure to divide up the work equally
  and DO YOUR PART!! Talk to Mrs. Falck ahead of
  time if someone is not doing their part of the
  project. Be sure to keep track of who does which
  parts of the preparation.
• Keep a list of all websites that you use!!!

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Step 2 History

• Gather some background information on where you
  are going and learn a little more about
  Pythagoras. See also more history. There are many
  other websites that you can use to find
  information about Pythagoras.
• Write down the answers on the hand-out. Take
  notes on the back of the paper.

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Step 3 Picture Proofs

• Start by discovering the proof of the Pythagorean
  Theorem. Is this method any different? What
  does it say about the triangles it applies to?
  How can you write down this proof so that anyone
  can understand it? (Actually write down a
  picture proof, you need it for later.)

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Step 4 Ancient Culture

• What cultural proof was assigned to your group?
  Be sure to find a proof and explanation from that
  particular culture. How did that culture use the
  Pythagorean Theorem? (you will need to do some of
  your own research to find this information)

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Step 5 Real World Applications

• How does this apply to real world problems?
  Check it out, here are some good problems to
  solve. You must solve at least 2 problems and
  include them in your presentation. You can find
  problems from other sources, or even make up your
  own!

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Step 6 Presentation

• Put this all together in one presentation. Make
  this presentation look professional, and
  interesting. You may use PowerPoint, Movie
  Maker, or another form of presentation. Be
  creative, but be sure to include information from
  each of the previous 5 steps.

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Evaluation
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
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Conclusion
GOOD JOB!!! You have successfully convinced the
disbelievers of the Pythagorean Theorem that is
does in fact hold true for right triangles. Now
you can begin to apply the theorem to right
triangles in mathematics and in life. Because
of your great work on the journey, Pythagoras can
once again get back to the study of mathematics
instead of having to worry about proving to
everyone that his theorem holds true. You have
done a great service to Pythagoras and all his
students and colleagues. Your journey may be
over, but you now have a presentation you can
give to anyone in modern times that does not
believe in the Pythagorean Theorem.
Title
Introduction
Task
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Conclusion
Credits
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Credits References
www.creativecommmons.org http//www.pbs.org/wgbh/
nova/proof/puzzle/ http//www.arcytech.org/java/p
ythagoras/history.html http//rubistar.4teachers.
org/index.php http//jwilson.coe.uga.edu/EMT669/S
tudent.Folders/Morris.Stephanie/EMT.669/Essay.1/Py
thagorean.html Textbook Fitzgerald, William
M., Susan N. Friel, Glenda Lappan, and Elizabeth
D. Phillips. Looking for Pythagoras, the
Pythagorean Theorem. Ed. James T. Fey. Glenview
Prentice Hall, 2004. WebQwest http//www.webque
st.org/index.php
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits