introduction | tasks | process | group member roles | bio links | proof links | problem links | evaluation
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:
after this assignment students will be able to:
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!!!!
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.
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
your report should answer most of these questions and include anything else
you discover that you find interesting.
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: 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://jwilson.coe.uga.edu/emt668/emt668.student.folders/headangela/essay1/pythagorean.html
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.
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 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.
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
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!!!