WebQuest
Pythagoras' Theorem
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..
Task 1. Find out facts about Pythagoras. (It will make by the biographer)
Your report should answer most of these questions and include anything else you discover that you find interesting.
- Where and when was Pythagoras born? Did he live there all his life? How old was he when he died?
- What pursuits did Pythagoras dedicate his life to?(
- Where did he get his schooling? According to Pythagoras, how could the world be best understood?
- In what other science did the make a contribution and what was it?
- What were the members of Pythagoras' Philosophical and Religious School expected to do?
- 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.
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pythagoras.html
http://en.wikipedia.org/wiki/Pythagoras
http://www.iep.utm.edu/p/pythagor.htm
http://plato.stanford.edu/entries/pythagoras/
http://scienceworld.wolfram.com/biography/Pythagoras.html
http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
Task 2. Concepts (Problem solver)
What’s a Right Angled triangle?A right angled triangle has a right angle of 90° as one of its interior angles. In the image here the right angle is marked with the white square.
Any triangle like this is a right angled triangle, it doesn't matter which side the right angle is on or what size the triangle is - the rule applies to all of them.
This is what makes the theory so useful as it can be applied to shapes as small as this one or those which are many miles wide.
What’s the Hypotenuse?
According to some sources the word hypotenuse derives from the Greek words for hypo (under) and teinein (stretch) or tenuse (side).
The hypotenuse is the longest side of a right angled triangle. As you can see, the hypotenuse is the side marked in purple on the image above.What are the other two sides?
Now you know which side the hypotenuse is then this is then this is easy, it's the two other sides marked in orange on the picture above.
OK, so now we know which side is which, what use is it?
Well, understanding the rule means that you can calculate lots of things without having to know the exact exact length of each side?
For example, if you knew that side x was 3 metres and side y was 4 metres long then you would be able to work out the length of the hypotenuse quite easily?
On the image here the hypotenuse is z and the other 2 sides are x and y .
Firstly you need to work out the sum of the squares of both x and y:
X² is 3 x 3 = 9
Y² is 4 x 4 =16
Z² = X² + Y² (25)
The sum of the other 2 sides squared is 25
The length of the hypotenuse therefore is the square root of 25
√25 = 5 ( 5 x 5 = 25)
So you have now calculated that the length of the hypotenuse is 5 metres
Task 3: Use the Pythagorean Theorem to solve problems.Prover.
You will receive a worksheet from your teacher which needs to be turned in for your grade.
Task 4: Create your own real world problem in Power Point presentation that will be presented in class .Prover-solver-biographer).
You will have class time to go on the computer and research the project.Every student of the group will bring his information to complete the Power Point).
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.
http://www.pbs.org/wgbh/nova/proof/puzzle/baseball.html
http://www.pbs.org/wgbh/nova/proof/puzzle/ladder.html
http://www.themathlab.com/Algebra/pythagorean%20theorem%20intro%20to%20trig/pythgpbs.htm
http://www.regentsprep.org/Regents/math/fpyth/PracPyth.htm
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