1. The Pythagorean Theorem
WebQuest
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits Based on a template from The WebQuest Page
2. Introduction
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations.
Title 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
Introduction Southern Italy. He is credited with many contributions to mathematics although some of
Task them may have actually been the work of his students.
Process The Pythagorean Theorem is Pythagoras' most famous mathematical contribution.
According to legend, Pythagoras was so happy when he discovered the theorem that he
Evaluation offered a sacrifice of oxen.
Conclusion 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.
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3. The Task
Title You will be traveling all the way back to ancient times
Introduction in Greece to work as a team studying under the great
Task Pythagoras. In your assigned group, you will navigate
Process
your way to proving the Pythagorean Theorem. When
you get back, your last step will be to put together a
Evaluation
presentation including:
Conclusion
1. historical information
2. explanation of the Theorem
3. a picture proof of the Theorem
4. the solutions to two real world problems that use
the Pythagorean Theorem.
5. The challenge: An original real world example of
Pythagorean Theorem. Remember, you have to show
that the Pythagorean Theorem works only for right
triangles, not all triangles.
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4. The Process
Title As you “travel” back in time learning about Pythagoras,
Introduction keep a written record of your group’s work.
Task
Process
Each part of the task should be documented.
• History
Evaluation
• Explanation
Conclusion
• Picture Proof
• Solutions to Problems
• Real World Challenge
Keep track of all websites used to include in a
References slide.
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5. Group Rules
You will be learning together and helping one another
understand the Pythagorean Theorem.
• Remain in your work area
• Listen to each other
• Everyone should be working at all times
• Share the work equally and DO YOUR PART!! Talk
to the teacher ahead of time if someone is not
doing his/her part
• Allow group members to use their strengths
• Save your work on your flash drive and upload to
our class wikispace “Files”
6. Step 1: 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.
7. Step 2: Explanation of Theorem
Now work with your group to describe the
theorem in your own words.
8. Step 3: Picture Proofs
Take your time through this part of your travels. Try
to make sense of these pictures.
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.)
10. Step 4: 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.
11. Step 5: Real World Challenge
Create your own real world problem!
Use the knowledge within your group to show
how Pythagorean Theorem can be used in
your everyday lives.
12. The Presentation
Put this all together in one PowerPoint presentation.
Make it look professional and interesting. Be creative,
but be sure to include information from each of the
previous 5 steps. Use the rubric to make sure you group
will be honored by Pythagoras for proving his work
Content 1st
13. Evaluation:
The Pythagorean Theorem
Title Student Name: ________________________________________
Introduction CATEGORY Exceeds Meets Approaching Does Not Meet
Mathematical Explanation shows Explanation shows Explanation shows Explanation shows
Task Concepts complete substantial some understanding very limited
understanding of the understanding of the of the mathematical understanding of the
Process mathematical mathematical concepts needed to underlying concepts
concepts used to concepts used to solve the problem(s). needed to solve the
Evaluation solve the problem(s). solve the problem(s). problem(s) OR is not
written.
Conclusion Mathematical Uses complex and Uses effective Some evidence of Little evidence of
Reasoning refined mathematical mathematical mathematical mathematical
reasoning. reasoning reasoning. reasoning.
Explanation Explanation is Explanation is clear. Explanation is a little Explanation is
detailed and clear. difficult to difficult to
understand, but understand and is
includes critical missing several
components. components OR was
not included.
Neatness and The work is The work is The work is The work appears
Organization presented in a neat, presented in a neat presented in an sloppy and
clear, organized and organized organized fashion unorganized. It is
fashion that is easy fashion that is but may be hard to hard to know what
to read. usually easy to read. read at times. information goes
together.
Working with Others Student was an Student was an Student cooperated Student did not work
engaged partner, engaged partner but with others, but effectively with
listening to had trouble listening needed prompting to others.
suggestions of to others and/or stay on-task.
others and working working
cooperatively cooperatively.
throughout lesson.
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14. Conclusion
Title GOOD JOB!!! You have successfully convinced the
Introduction disbelievers of the Pythagorean Theorem that is does
Task in fact hold true for right triangles. Now you can begin
Process
to apply the theorem to right triangles in mathematics
and in life.
Evaluation
Conclusion
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.
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15. Credits & References
www.creativecommmons.org
Title
http://www.pbs.org/wgbh/nova/proof/puzzle/
Introduction
Task http://www.arcytech.org/java/pythagoras/history.html
Process http://rubistar.4teachers.org/index.php
Evaluation http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Py
thagorean.html
Conclusion
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.webquest.org/index.php
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