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Ms. Karakashian's WebQuest:

The Pythagorean Theorem 

So who is Pythagoras and what is his theorem? 

 

His name might sound familiar because he is very important in mathematics.

Today you will find out who he is and learn all about his famous theorem. 

Instructions:  

You will work in pairs (assigned by the teacher) to complete the WebQuest guide sheet.

You will also individually turn in 3 follow-up assignments to be completed for homework.

Task 1:  

First, you will find out some facts about Pythagoras.

On your guide sheet, answer the following questions about Pythagoras.  You may also include any other interesting information that you discover.  

The links below will be helpful, but you may also use any other websites.                                                                                                        

*Make sure you write down all the websites that you used to get your information.   

  1. Where and when was Pythagoras born?
  2. What is the significance of Pythagoras' travels to Egypt? 
  3. What subjects and ideas were taught at the school started by Pythagoras in Croton, Italy? 
  4. Pythagoras believed that "all relations could be reduced to __________________." 
  5. Was Pythagoras the first to discover the theorem named for him?  Explain.
  6. Why was the Pythagorean Theorem named for Pythagoras? 
  7. Who were the Pythagoreans?  Describe their way of life and interests. 
  8. Why do we know so little about Pythagoras' life and achievements?

Links:

http://www.arcytech.org/java/pythagoras/history.html

http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pythagoras.html


Task 2:  

Now you will learn about the Pythagorean Theorem.

On your guide sheet, answer the following questions about the Pythagorean Theorem.  Use the links below.   

*Make sure you write down the websites that you used to get your information. 

  1. What is the relationship (proved by Pythagoras) among the hypotenuse and legs of a right triangle?
  2. What is the formula that represents this relationship?  What does each letter in the formula represent?
  3. What do the a2, b2, and c2 represent? (Hint: squares, area)  How does this relate to the theorem?
  4. Can the Pythagorean Theorem be applied to any type of triangle?  Explain.

Links:

http://www.regentsprep.org/regents/math/fpyth/Pythag.htm 

http://www.mathsisfun.com/pythagoras.html


Task 3:  

It's time to practice solving some problems using the Pythagorean Theorem.

Please visit the following link 

On your guide sheet, write down and solve 3 problemsYou must include a drawing and show all your work for each problem.  You may check your answers there to see if you have solved them correctly.

 

Task 4:

Real-life problem solving!

First, visit the following link that demonstrates a baseball application of the Pythagorean Theorem.  Solve this problem on your guide sheet. 

Class A: 

Now you and your partner will work together to create a real-life problem that can be solved by the Pythagorean Theorem. 

On your guide sheet, brainstorm ideas and start developing and solving your own problem.  The following links may give you some ideas.  (You do not need to solve these problems).

You may not use one of these problems.

Links:

http://tulyn.com/wordproblems/right_triangles.htm 

 

http://regentsprep.org/Regents/Math/fpyth/PracPyth.htm 

Class B:

With your partner, follow this link to another real-life problem on buying a TV that can be solved by the Pythagorean Theorem.  Brainstorm your ideas and start solving this problem on your guide sheet.


Homework:

You have some follow-up assignments on each task to work on individually outside of class.

Task 1 and 2 Assignment - Each student will write a type-written report on Pythagoras and the Pythagorean Theorem using the information from tasks 1 and 2.  A "works cited" page must also be included.

Task 3 Assignment - Each student will complete a worksheet (the teacher will give it to you) on finding missing sides of right triangles by applying the Pythagorean Theorem.

Task 4 Assignment

Class A- 

Each student will submit a final copy of their real-life problem.  This final version should neatly include the problem, a colorful illustration, and worked-out solution on standard white computer paper.  Each pair will present their problem to the class.

Class B- 

Each student will submit a final copy of the given real-life application problem “Buying a TV."  This final version should neatly include the problem, a colorful illustration, and worked-out solution on standard white computer paper.  Your work will be displayed for the class.

 

Please use the rubrics below to guide you on these assignments.

 

What to turn in on the due date: 

1.Task 1 and 2 Homework Assignment

2.Task 3 Homework Assignment

3.Task 4 Homework Assignment

4.WebQuest Guide Sheet

5.Have your presentation of your real-life application problem prepared

Laughing

Task 1 & 2

Paper  

 0

 1

 2

 3

 Score

Content (Pythagoras)  Incorporates 0-3 facts about Pythagoras’ lifeIncorporates 4-6  facts about Pythagoras’ lifeIncorporates7-9 facts about Pythagoras’ lifeIncorporates 10 or more facts about Pythagoras’ life 
Content(Theorem)Does not state the theorem, explain its 3 parts, nor state when it can be usedStates the theorem States the theorem and explains its 3 parts.States the theorem, explains all 3 parts, and states when it can be applied 
 Mechanics  Paper is handwritten and follows no logical sequence.Paper is handwritten and uses some connections/transitions among facts, but is missing a beginning or end.  Paper is typewritten and uses some connections/transitions among facts, but is missing a beginning or end.  Paper is typewritten and follows a clear, logical sequence with a beginning, middle and end. 

 

Task 3 Worksheet Practice Problems

 

 0

 1 

 2

 3

 Score

 Completes less than 50% of the problems on the worksheet correctlyCompletes at least 50% of the worksheet correctlyCompletes at least 75% of the worksheet correctlyCompletes at least 90% of the worksheet correctly  

 

Task 4

Create/Solve a Problem

0

1

2

3

  Score

ContentUnable to sketch and solve the problem The sketch is inappropriately labeled and the solution is inaccurateAppropriately labeled the picture but can not solve the problem accurately Appropriately labeled the picture and solved the problem accurately  
Presentation   Did not present the problem _____ _____Presented the problem 

 

WebQuest Guide

0

1

2

3

Score

 Completed less than 50% of the WebQuest guide Completed at least 50% of the WebQuest guideCompleted at least 75% of the WebQuest guideCompleted 100% of the WebQuest guide  
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