Pythagorean Theorem Webquest
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Transcript Pythagorean Theorem Webquest
Student Page
[Teacher Page]
Title
The Pythagorean Theorem
A WebQuest for 8th Grade (Connected Math 3)
Introduction
Task
Process
Evaluation
Conclusion
Credits
Based on a template from The WebQuest Page
Student Page
[Teacher Page]
Title
Introduction
Task
Process
Evaluation
Introduction
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations.
This famous theorem is named for the Greek mathematician and philosopher, Pythagoras.
Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in
Southern Italy. He is credited with many contributions to mathematics although some of
them may have actually been the work of his students.
The Pythagorean Theorem is Pythagoras' most famous mathematical contribution.
According to legend, Pythagoras was so happy when he discovered the theorem that he
offered a sacrifice of oxen.
Conclusion
Pythagoras needs your help in showing disbelievers that his theorem works for all right
triangles. He has the problem that some people do not believe him because they do not
understand how he explains it. Your job as a group is to find ways to make everyone
believers and show them that the theorem exists in real world examples. Be prepared to
work hard on this project. The people you need to convince are stuck in their ways and not
easily swayed.
Credits
Student Page
[Teacher Page]
Title
Introduction
Task
Process
Evaluation
Conclusion
The Task
You will be traveling all the way back to ancient times in Greece to work as a team studying
under the great Pythagoras. But be careful, the Pythagoreans had many rituals, and they
approached mathematics with an almost religious intensity. Their power and influence
became so strong that some people feared that they threatened the local political
structure, so they were forced to disband. However, many Pythagoreans continued to meet
in secret and to teach Pythagoras’s ideas. This will be your quest, and during it you will be
able to:
build a table of values showing the relation between the sides of a right triangle
apply the Pythagorean Theorem to any triangle
discover the Pythagorean Theorem
show that the Pythagorean Theorem holds true for small right triangles
show that the Pythagorean Theorem does not hold true for any triangle that is not
a right triangle
show to the disbelievers that the Pythagorean Theorem works
apply the Pythagorean Theorem to modern, real world problems
Once you return from your journey, you will use Xcel to build a table that you can present to
any disbeliever to show them the pattern and relationship between the sides of a right
triangle. You will put together a PowerPoint presentation that includes you table and
different triangles, and the solutions to two real world problems that use the Pythagorean
Theorem. Remember, you have to show that the Pythagorean Theorem works only for right
triangles, not all triangles.
Credits
Student Page
[Teacher Page]
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
The Process
We’ve traveled way back to the time of Pythagoras. In your assigned group, you will
navigate your way to proving the Pythagorean Theorem and building a table of values that
will show the pattern of the relationship between the sides of a right triangle. When you
get back, your last step will be to put together a presentation including real world examples
of how to solve them.
1.Meet your fellow travelers. You will be learning together and helping one another
understand the Pythagorean Theorem. Open up a good line of communication.
2.Gather some background information on where you are going and learn a little more
about Pythagoras.
3.Start by discovering the proof of the Pythagorean Theorem. Is this method any different?
What does it say about the triangles it applies to? How can you write down this proof so
that anyone can understand it? (Actually write it down, you need it for later)
4.Build a table of values for the lengths of the sides of a right triangle. Write all different
lengths, but keep it simple. It will be easier to see the pattern if you use small numbers.
Here are some columns you might consider having in your table: length of side 1, square of
side 1, length of side 2, square of side 2, length of hypotenuse, and square of hypotenuse.
5.How does this apply to real world problems?? Check it out, here are some good
problems to solve.
6.Put this all together in one presentation. Make sure to use Xcel to build your table of
values. Make this presentation look professional, you may need to use it at any time.
Student Page
[Teacher Page]
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits
The Pythagorean Theorem
Teacher Name: Dilmore and Keck
Student Name: ________________________________________
Evaluation:
CATEGORY
Mathematical
Concepts
1
Explanation shows
very limited
understanding of the
underlying concepts
needed to solve the
problem(s) OR is not
written.
Mathematical
Uses complex and
Uses effective
Some evidence of
Little evidence of
Reasoning
refined mathematical mathematical
mathematical
mathematical
reasoning.
reasoning
reasoning.
reasoning.
Explanation
Explanation is detailed Explanation is clear. Explanation is a little Explanation is difficult
and clear.
difficult to understand, to understand and is
but includes critical
missing several
components.
components OR was
not included.
Neatness and
The work is presented The work is presented The work is presented The work appears
Organization
in a neat, clear,
in a neat and
in an organized
sloppy and
organized fashion that organized fashion that fashion but may be
unorganized. It is hard
is easy to read.
is usually easy to read. hard to read at times. to know what
information goes
together.
Working with Others Student was an
Student was an
Student cooperated Student did not work
engaged partner,
engaged partner but with others, but
effectively with
listening to
had trouble listening needed prompting to others.
suggestions of others to others and/or
stay on-task.
and working
working cooperatively.
cooperatively
throughout lesson.
Date Created:
4
3
2
Explanation shows
Explanation shows
Explanation shows
complete
substantial
some understanding
understanding of the understanding of the of the mathematical
mathematical
mathematical
concepts needed to
concepts used to solve concepts used to solve solve the problem(s).
the problem(s).
the problem(s).
Student Page
[Teacher Page]
Title
Introduction
Task
Process
Conclusion
GOOD JOB!!! You have successfully convinced the disbelievers of the Pythagorean Theorem
that is does in fact hold true for right triangles. Now you can begin to apply the theorem to
right triangles in mathematics and in life.
Because of your great work on the journey, Pythagoras can once again get back to the study
of mathematics instead of having to worry about proving to everyone that his theorem
holds true. You have done a great service to Pythagoras and all his students and colleagues.
Evaluation
Conclusion
Credits
Your journey may be over, but you now have a presentation you can give to anyone in
modern times that does not believe in the Pythagorean Theorem.
Student Page
[Teacher Page]
Title
Introduction
Task
Process
Evaluation
Conclusion
Credits & References
www.creativecommmons.org
http://www.pbs.org/wgbh/nova/proof/puzzle/
http://www.arcytech.org/java/pythagoras/history.html
http://rubistar.4teachers.org/index.php
http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Py
thagorean.html
Books
Fitzgerald, William M., Susan N. Friel, Glenda Lappan, and Elizabeth D. Phillips. Looking for
Pythagoras, the Pythagorean Theorem. Ed. James T. Fey. Glenview: Prentice Hall, 2004.
Nuzzo, M. (2008, June 20). Life Lessons - A Book Review of "The Ultimate Gift".
Retrieved March 1, 2009, from http://ezinearticles.com/?Life-Lessons---A-BookReview-of-The-Ultimate-Gift&id=1265081
Lesson Plan
Marfitano, L (2007). Pythagorean Theorem Webquest. Retrieved February 28, 2009 from
http://www.slideshare.net/lmarfita/pythagorean-theorem-webquest
WebQwest
http://www.webquest.org/index.php
Credits
[Student Page]
Teacher Page
Title
Introduction
The Pythagorean Theorem(Teacher)
A WebQuest for 8th Grade (Connected Math 3)
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
Based on a template from The WebQuest Page
[Student Page]
Teacher Page
Title
Introduction (Teacher)
Introduction
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
This lesson stems from the book, Looking for Pythagoras used by Poudre School
District in Fort Collins, Colorado. It has been designed to make the lesson more
interactive and for students to use experimental techniques in their learning. Some
students may need additional help and resources from the teacher, and that is
perfectly fine. Other students may begin to want to learn everything using a
WebQuest.
While participating in this WebQwest, students will learn background information on
Pythagoras and ancient times in mathematics, along with how to prove the
Pythagorean Theorem and apply it to modern problem solving.
[Student Page]
Teacher Page
Title
Learners (Teacher)
Introduction
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
This lesson is specifically made for eighth grade mathematics students. It can be
extended to either seventh grade students or ninth grade students, based on their
knowledge and abilities. Students will continue to use the Pythagorean Theorem in
later geometry classes, so it may be useful to modify this lesson for higher level
students studying the benefits of the Pythagorean Theorem.
[Student Page]
Teacher Page
Title
Curriculum Standards (Teacher)
Introduction
Learners
Standards
Process
Resources
Evaluation
Essential Math Standards leading to the outcomes of this activity:
•1.1a Understand the characteristics of irrational numbers.
•1.1b Understand the relative magnitude of square roots (for example, √72
lies between 8 and 9).
•1.6a Estimate solutions with irrational numbers.
•4.5b Apply the Pythagorean theorem to solve real-world problems.
•5.4a Use the Pythagorean theorem.
•6.2a Apply order of operations to evaluate simple expressions with integers.
Teacher Script
Conclusion
Credits
This activity will also teach teamwork and compromise as the students work closely
with their group. Students must use good communication skills to help each other to
discover the Pythagorean Theorem and put together a presentation covering their
discovery. Students may also need to employ creative problem-solving techniques
and critical thinking.
[Student Page]
Teacher Page
Title
Introduction
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
The Process (Teacher)
Students must be split up into groups of four before the activity begins. Be aware of
how they work together and the individual strengths and weaknesses of the students
in the group. They will need to work very closely with each other, so make sure they
will get along for the remained of the project. Multiple classes may be doing this at
one time, so use each one as a learning experience.
We’ve traveled way back to the time of Pythagoras. In your assigned group, you will
navigate your way to proving the Pythagorean Theorem and building a table of
values that will show the pattern of the relationship between the sides of a right
triangle. When you get back, your last step will be to put together a presentation
including real world examples of how to solve them.
1.Meet your fellow travelers. You will be learning together and helping one another
understand the Pythagorean Theorem. Open up a good line of communication.
2.Gather some background information on where you are going and learn a little
more about Pythagoras.
3.Start by discovering the proof of the Pythagorean Theorem. Is this method any
different? What does it say about the triangles it applies to? How can you write
down this proof so that anyone can understand it? (Actually write it down, you need
it for later)
4.Build a table of values for the lengths of the sides of a right triangle. Write all
different lengths, but keep it simple. It will be easier to see the pattern if you use
small numbers. Here are some columns you might consider having in your table:
length of side 1, square of side 1, length of side 2, square of side 2, length of
hypotenuse, and square of hypotenuse.
5.How does this apply to real world problems?? Check it out, here are some good
problems to solve.
6.Put this all together in one presentation. Make sure to use Xcel to build your table
of values. Make this presentation look professional, you may need to use it at any
time.
[Student Page]
Teacher Page
Resources (Teacher)
Title
Introduction
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
To implement this lesson, you may need:
•Class sets of books (Looking for Pythagoras)
•Computers for each student in the class (this could be a building computer
lab or mobile laptop station)
•Access to the internet
•Access to Word, Xcel, and PowerPoint
•Educational websites that advance the learning of the Pythagorean Theorem
for students
•One teacher can effectively implement this lesson, but it is easier to have
additional help for the students when working on the computers
[Student Page]
Teacher Page
Title
Introduction
Learners
Standards
Evaluation (Teacher)
This lesson will be successful if:
•students fulfill the objectives and standards
•work well in groups
•establish effective group communication
•understand the Pythagorean Theorem and area able to use the theorem in
real world problems
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
You will evaluate the progress and understanding of the group using the rubric in the
students section of the WebQwest. You may want to add or take away from the
given rubric to fit your class and students better.
[Student Page]
Teacher Page
Conclusion (Teacher)
Title
Introduction
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits
This lesson is a great way to let students take a hands on approach to learning. It
will allow different learning styles to excel and it will help certain students
comprehend the material better because of the self-exploration piece of the activity.
Students may not fully comprehend the topic, but with the assistance of the teacher,
the students will have the ability to learn about the Pythagorean Theorem in multiple
ways.
[Student Page]
Teacher Page
Title
Introduction
Learners
Standards
Process
Resources
Evaluation
Teacher Script
Conclusion
Credits & References (Teacher)
www.creativecommmons.org
http://www.pbs.org/wgbh/nova/proof/puzzle/
http://www.arcytech.org/java/pythagoras/history.html
http://rubistar.4teachers.org/index.php
http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Py
thagorean.html
Books
Fitzgerald, William M., Susan N. Friel, Glenda Lappan, and Elizabeth D. Phillips. Looking for
Pythagoras, the Pythagorean Theorem. Ed. James T. Fey. Glenview: Prentice Hall, 2004.
Nuzzo, M. (2008, June 20). Life Lessons - A Book Review of "The Ultimate Gift".
Retrieved March 1, 2009, from http://ezinearticles.com/?Life-Lessons---A-BookReview-of-The-Ultimate-Gift&id=1265081
Lesson Plan
Marfitano, L (2007). Pythagorean Theorem Webquest. Retrieved February 28, 2009 from
http://www.slideshare.net/lmarfita/pythagorean-theorem-webquest
WebQuest
http://www.webquest.org/index.php
Credits