In Search of Pythagoras

and the theorem named for him!?!

(a webquest for Geometry B)

Pythagoras

You've probably heard the name before, right?
In this webquest you're going to find out who he was and why his name is so important in mathematics.

California Math Standards:

14.0 Students prove the Pythagorean theorem.

15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

Big Idea: Understanding the properties of right triangles.

Essential Questions:

• How can we find a missing side of a right triangle if we know the other two sides?
• How can this information be used in real life situations?

After this assignment Students will be able to:

• Prove the Pythagorean Theorem
• Use the Pythagorean Theorem to find missing sides and distance

Introduction

Pythagoras made many contributions to Mathematics and Physics but the contribution that we will be exploring is:The Pythagorean Theorem.

The Pythagorean Theorem is a formula that can be used only when working with right triangles. It can help you find the length of any side of a right triangle.

Pythagoras wasn't the first to discover this formula. The Babylonians and the Chinese worked with this concept years before Pythagoras.

Pythagoras gets most of the credit for it though because he was the first to prove why it works. Several other proofs came about after his.

So, are you ready to learn something new?!!! Well take out a pen or pencil and a piece of paper and lets get started!!!!

• Find out facts about Pythagoras. These facts will be presented by your group in an oral presentation and each student is required to write a 1 page typewritten (double spaced) paper summarizing what they have learned about Pythagoras.
• Demonstrate a proof of the Pythagorean Theorem. This presentation will be made by your group with each member having a significant part in the presentation.
• Use the Pythagorean Theorem to solve problems. Each student will turn in the worksheet provided with the answers to the problems.
• Create your own real world problem and challenge the class. Each group will create a problem that can be solved by using the Pythagorean Theorem and challenge the class to answer it. The group will submit a sketch of the problem and its solution.

The Process:

You will work in groups of three (assigned by the teacher). Each person in the group will be responsible for turning in their own written paper and the worksheet problems. The group will make an oral presentation (about 5 minutes long) in which they give facts about Pythagoras’ life and each group will be responsible for selecting a proof of the theorem and explaining it to the class. You will be graded as a group for the presentations and as an individual on your written paper and worksheet. You may use any visual aids you like including PowerPoint for the presentation.

Roles of Group Members:

Each member of the group will take on a different responsibility. Choose in your group who will take on each role.

Biographer - This person will receive all the facts about the life and times of Pythagoras from the rest of the group along with his/her own and decide which are the key facts for the oral presentation. Will lead the group in discussions on how best to present the material and assign tasks to others like making posters, downloading pictures, writing a skit, organizing a powerpoint, etc.He/she will produce this part of the presentation.

Prover: This person will be in charge of putting the proof part of the presentation together. All students in the group will research a proof and present it to their group for discussion. The Prover will then pick the one to show the class and be responsible for organizing the presentations.He/she will produce this part of the presentation.

Problem Solver: This person will collect the individual problems from all the group members and decide which problem is the most interesting problem and which will be presented to the class. He/she will organize the method of presentation and produce this part..

Your report should answer most of these questions and include anything else you discover that you find interesting.

1. Where and when was Pythagoras born? Did he live there all his life? How old was he when he died?
2. What pursuits did Pythagoras dedicate his life to?
3. Where did he get his schooling?
4. According to Pythagoras, how could the world be best understood?
5. In what other science did the make a contribution and what was it?
6. What were the members of Pythagoras' Philosophical and Religious School expected to do?
7. Pythagoras had several rules for his members. What were some of the rules?

You can use the following links or any others you find to get your information. Make sure you write where got your information.

Task 2: Demonstrate a proof of the Pythagorean Theorem
The following link has 72 different proofs of the theorem. Choose one you understand and explain it to the class.
http://www.cut-the-knot.org/pythagoras/index.shtml

Here are some more links with proofs and explanations:

http://mathforum.org/isaac/problems/pythagthm.html
http://standards.nctm.org/document/eexamples/chap6/6.5/index.htm
http://www.math.hmc.edu/funfacts/ffiles/10007.2.shtml
http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html
http://www.pbs.org/wgbh/nova/proof/puzzle/theoremsans.html

Task 3: Use the Pythagorean Theorem to solve problems.

Task 4: Create your own real world problem and challenge the class
You will have class time to go on the computer and research the project.
Here are some links to give you ideas about the types of problems you can create and the applications of the Pythagorean Theorem to real life situations. Use these to give you ideas. Do not present one of these problems.

The Evaluation:
Your grade for this assignment is based on your ability to meet the above tasks. Below the tasks have been broken down into five overall objectives. Read below to see what you think your score would be. I hope you are all in the green.

Individual Achievement

 Beginning 1 Developing 2 Accomplished 3 Exemplary 4 Score Identify five facts about Pythagoras and incorporate them in your paper. Unable to identify any facts Able to identify at least one fact Able to identify at least three facts Able to identify at least 5 fact Presentation of Paper Paper is handwritten and has no real content. Paper is handwritten and contains limited content. Paper is typewritten and clearly states facts about Pythagoras Paper is type written and shows insight and details about the life of Pythagoras State the Pythagorean Theorem, identify and define its parts, and its applications (when can it be used Unable to state the theorem, identify any parts, nor any time it can be used Able to state the theorem Able to state the theorem and define its parts. Able to state the theorem, identify and define all three parts, and know when it can be applied Complete worksheet on applications Unable to complete any problems on the worksheet Able to complete at least 50% of worksheet Able to complete at least 75% of worksheet Able to complete at least 90% of worksheet.

Group Work

 Beginning 1 Developing 2 Accomplished 3 Exemplary 4 Score Demonstrate a proof of the theorem and the real world applications. Unable to identify or demonstrate proof or applications Able to identify a proof and/or real world application Able to identify and demonstrate proof or application Able to identify and demonstrate the proof and application as well as explain in own words Sketch problem and answer the initial hypothesis Unable to sketch problem and answer the initial hypothesis Able to sketch problem (inappropriately labeled) or find solution but not both. Sketch appropriately labeled picture but can not solve accurately Sketch appropriately labeled picture and solve accurately Oral Presentation Facts about Pythagoras No interesting facts are given Some interesting facts are given but no visual aids used. Several facts are given and supported with visual aids. Many facts are given. Group uses visual aids and shows imagination and creativity in presentation.

Conclusion:
So how did you do? I hope you found Pythagoras’ life interesting and that you can now solve and understand what the meaning of the theorem is.

This is not Pythagoras!!!