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- 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. Credits
- 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. Credits
- 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. Credits
- 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.)
- 9. Step 3: More Proofs Proof 1 Proof 2 Proof 3
- 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. Credits
- 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. Credits
- 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 Credits

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