You are at your grandma's house for the weekend but you've decided you're
ready to go home. Your mom says the only way you can come home is if you
tell her exactly how many miles is the shortest distance from Grandma's
before you can leave. She tells you that your street and Grandma's
street meet to form an L at your school. Grandma's house is two miles
east of the your school and your house is one mile north of your school.
She also tells you the shortest distance home does not involve passing
your school again. How can you do this? Why not let Pythagoras help
you home?
The Tasks:
To find the shortest distance to your house, you will complete the
following steps:
find facts about Pythagoras,
demonstrate proofs of the Pythagorean
Theorem,
practice using the Pythagorean
Theorem to solve problems,
use the theorem in other real
world applications and think of your own real world application, and
sketch a picture of the problem
you're trying to solve and solve it.
Pythagoras
(530 BC)
The Process:
Now, let's begin. Below are a few sites that will help you meet your tasks.
Instructions are given as to what you are to do at each site. You will
need your pencil, a couple of sheets of paper, and a calculator.
1. By now, I'm sure
you're wondering exactly Who
is Pythagoras? Where and when did he live? What was his famous
theorem pertaining to? You will find the answers to your questions here.
Visit here and take brief notes.
2. What is the Pythagorean
Theorem? When does it apply? What can we use it for?
All of your questions and more can be answered through this link.
Pay close attention to the names of the parts of the theorem and how they
are used in the theorem. Also you may clarify the names of the
Parts of the Right Triangle.
3. Many mathematicians
have researched the validity of the Pythagorean Theorem. In their
attempts, they have found various ways to show that the Pythagorean Theorem
definitely works.Pythagorean
Theorem Proofs shows thirty-six of the many proofs that have been
published. Follow the instructions for demonstrating the interactive
proofs. Pick the one you like best. Be prepared to give your interpretation.
4. Go to Practice
for Students to practice using the Pythagorean Theorem. Mini-lessons
and worksheets about pre-algebra are given here. You will provide
two lengths of a triangle and the site will calculate the third (this may
be both legs or a leg and the hypotenuse). Practice working a few
letting the site work them for you. Then go to the Worksheet
and complete it.
5. The Pythagorean Theorem is
used in real life in many different ways. Nova
Online demonstrates two real world applications in particular.
One involves throwing a runner out from home plate and the other involves
climbing a ladder up the side of a house. Go here and try these applications.
When you are complete, think of a real world application other than those
given on the site. Tell how the theorem could be used in your situation.
Write it on your paper. Then if time permits try the Super
Challenge. Otherwise you may take it home and finish
for extra credit.
6. By now, you've learned
that right triangles meet to form an L (right angle). Knowing this, use
the Template
to sketch a picture of the triangle needed to solve the problem.
Label each leg appropriately, and label each vertex (corner of the triangle)
with a picture of the school, grandma's house and your house. Now
solve the problem.
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.
Beginning
1
Developing
2
Accomplished
3
Exemplary
4
Score
Identify
three facts about Pythagoras
Unable to identify any facts
Able to identify one fact
Able to identify two facts
Able to identify three facts
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
Demonstrate a proof of the theorem and the real world
applications
Unable to identify or demonstrate proof or applications
using the interactive site
Able to identify a proof and/or real world application
Able to identify and demonstrate proof or application
using site
Able to identify and demonstrate the proof and application
as well as explain in own words
Complete worksheet on applications
Unable to complete any problems on the worksheet
Able to complete worksheet at least 50% without assistance
or 75% with assistance of computer or teacher
Able to complete worksheet at least 75% without assistance
or 100% with assistance from computer or teacher
Able to complete worksheet 100% without any assistance.
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
Conclusion:
So how did you do? I hope Pythagoras was a big help getting you home.
I also hope you chose to complete the super challenge. It's lots
of fun. Let's not forget the practical applications of Pythagoras' theorem.
You never know when you may need this information at home.
Credits & References:
I would like to thank my partners who assisted me while I completed this
project, Amy Bobbitt and Romond Arnold. Also, I would like to thank Background
City for their use of the background.
Teacher Advice:
This lesson is designed for eighth grade Pre-Algebra but can be extended
to seventh or above eighth grade. Either way it should require an individual
effort. It is necessary that students have access to calculators
and a knowledge of squares and square root. If they choose to do the super
challenge they will need to print a page and a pair of scissors to cut.
For grades higher than eighth, the super challenge is recommended as part
of their grade.
You may give them a worksheet of problems to complete on the Practice
for Students. This way they can write their answers on the sheet
and you can monitor effectively.
Completing this WebQuest should take one to two fifty minute classes
or one traditional block. It is probably best to question students
after they are complete as to the effectiveness of the site. Students
should also be encouraged to describe the proof that was the easiest to
comprehend. After completing this lesson, however, students should be prepared
to use the Pythagorean Theorem effectively. Slower learners should
be provided the time to rework the WebQuest, if time permits. If
not, I recommend printing a copy of the sites from Step 2 in the Process,
the worksheet from Step 5, and the template from Step 6. They can complete
these without the assistance of the internet.
This WebQuest stimulates critical thinking based on on the three general
skills: evaluating, analyzing and connecting. It promotes evaluating
by having students verify the Pythagorean Theorem with interactive proofs,
analyzing by classifying right triangles in order to apply the theorem,
and connecting by using the theorem in real life situations.
In addition, you can have students develop their own scenario for the
real world application they decided on. They can take turns presenting
each to the class or switch with a partner and have them solve.
find facts about Pythagoras,
1. By now, I'm sure you're wondering exactly Who is Pythagoras? Where and when did he live? What was his famous theorem pertaining to? You will find the answers to your questions here. Visit here and take brief notes.
2. What is the Pythagorean Theorem? When does it apply? What can we use it for? All of your questions and more can be answered through this link. Pay close attention to the names of the parts of the theorem and how they are used in the theorem. Also you may clarify the names of the Parts of the Right Triangle.
3. Many mathematicians have researched the validity of the Pythagorean Theorem. In their attempts, they have found various ways to show that the Pythagorean Theorem definitely works. Pythagorean Theorem Proofs shows thirty-six of the many proofs that have been published. Follow the instructions for demonstrating the interactive proofs. Pick the one you like best. Be prepared to give your interpretation.
4. Go to Practice for Students to practice using the Pythagorean Theorem. Mini-lessons and worksheets about pre-algebra are given here. You will provide two lengths of a triangle and the site will calculate the third (this may be both legs or a leg and the hypotenuse). Practice working a few letting the site work them for you. Then go to the Worksheet and complete it.
5. The Pythagorean Theorem is used in real life in many different ways. Nova Online demonstrates two real world applications in particular. One involves throwing a runner out from home plate and the other involves climbing a ladder up the side of a house. Go here and try these applications. When you are complete, think of a real world application other than those given on the site. Tell how the theorem could be used in your situation. Write it on your paper. Then if time permits try the Super Challenge. Otherwise you may take it home and finish for extra credit.
6. By now, you've learned that right triangles meet to form an L (right angle). Knowing this, use the Template to sketch a picture of the triangle needed to solve the problem. Label each leg appropriately, and label each vertex (corner of the triangle) with a picture of the school, grandma's house and your house. Now solve the problem.
