**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.

**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. **

- Where and when was Pythagoras born?
- What is the significance of Pythagoras' travels to Egypt?
- What subjects and ideas were taught at the school started by Pythagoras in Croton, Italy?
- Pythagoras believed that "all relations could be reduced to __________________."
- Was Pythagoras the first to discover the theorem named for him? Explain.
- Why was the Pythagorean Theorem named for Pythagoras?
- Who were the Pythagoreans? Describe their way of life and interests.
- 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. **

- What is the relationship (proved by Pythagoras) among the hypotenuse and legs of a right triangle?
- What is the formula that represents this relationship? What does each letter in the formula represent?
- What do the a
^{2}, b^{2}, and c^{2}represent? (Hint: squares, area) How does this relate to the theorem? 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

**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 problems__. You 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://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.

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

**T**

**ask 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**

| 0 | 1 | 2 | 3 | Score |

Content (Pythagoras) | Incorporates 0-3 facts about Pythagoras’ life | Incorporates 4-6 facts about Pythagoras’ life | Incorporates7-9 facts about Pythagoras’ life | Incorporates 10 or more facts about Pythagoras’ life | |

Content(Theorem) | Does not state the theorem, explain its 3 parts, nor state when it can be used | States 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. |

| 0 | 1 | 2 | 3 | Score |

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

| 0 | 1 | 2 | 3 | Score |

Content | Unable to sketch and solve the problem | The sketch is inappropriately labeled and the solution is inaccurate | Appropriately 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 |

| 0 | 1 | 2 | 3 | Score |

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