The Pythagorean Theorem

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A WebQuest for 9th Grade

Based on a template from The WebQuest Page

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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.

Introduction

Introduction

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Process

Evaluation

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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.

Title

The Task

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.

The Process

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.

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Evaluation:The Pythagorean Theorem

Teacher Name: J FalckStudent Name:     ________________________________________         

CATEGORY 4 3 2 1Mathematical Concepts

Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).

Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.

Mathematical Reasoning

Uses complex and refined mathematical reasoning.

Uses effective mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.

Explanation Explanation is detailed and clear.

Explanation is clear. Explanation is a little difficult to understand, but includes critical components.

Explanation is difficult to understand and is missing several components OR was not included.

Neatness and Organization

The work is presented in a neat, clear, organized fashion that is easy to read.

The work is presented in a neat and organized fashion that is usually easy to read.

The work is presented in an organized fashion but may be hard to read at times.

The work appears sloppy and unorganized. It is hard to know what information goes together.

Working with Others Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.

Student was an engaged partner but had trouble listening to others and/or working cooperatively.

Student cooperated with others, but needed prompting to stay on-task.

Student did not work effectively with others.

         

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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.

Conclusion

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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/Pythagorean.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 & References