Transcript The Pythagorean Theorem

The Pythagorean Theorem
Title
A WebQuest for 9th Grade
Introduction
Task
Process
Evaluation
Conclusion
Credits
Based on a template from The WebQuest Page
Introduction
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
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.
The Task
Title
Introduction
Task
Process
Evaluation
Conclusion
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 Pythagoras’s 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.
Credits
The Process
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
We’ve 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.
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!!!
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.
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.)
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)
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!
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.
Evaluation:
The Pythagorean Theorem
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
Teacher Name: J Falck
Student Name: ________________________________________
CATEGORY
Mathematical
Concepts
4
3
2
1
Explanation shows Explanation shows Explanation shows Explanation shows
complete
substantial
some understanding very limited
understanding of the understanding of the of the mathematical understanding of the
mathematical
mathematical
concepts needed to underlying concepts
concepts used to
concepts used to
solve the problem(s). needed to solve the
solve the problem(s). solve the problem(s).
problem(s) OR is not
written.
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.
Conclusion
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Introduction
Task
Process
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.
Evaluation
Conclusion
Credits
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.
Credits & References
Title
Introduction
Task
Process
Evaluation
Conclusion
www.creativecommmons.org
http://www.pbs.org/wgbh/nova/proof/puzzle/
http://www.arcytech.org/java/pythagoras/history.html
http://rubistar.4teachers.org/index.php
http://jwilson.coe.uga.edu/EMT669/Student.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.webquest.org/index.php
Credits