Download The Pythagorean Theorem

The Mystery of the Pythagorean Theorem
Developed by Miss Jill Keeve
Teacher Overview
The lesson is about the student’s understanding of the Pythagorean Theorem.
They will research and describe the background information of the theorist.
Content area: Mathematics/ Geometry
Grade level: High School
Standard - 2.10.11.A: Identify, create, and solve practical problems involving right
triangles using the trigonometric functions and the Pythagorean Theorem.
Anchor Descriptor - M11.C.1.4: Solve problems involving right triangles using the Pythagorean
Theorem.
Standard - 2.9.11.A: Create justifications for arguments related to geometric
relations.
Anchor Descriptor - M11.C.1.4: Solve problems involving right triangles using the Pythagorean
Theorem.
Standard - 2.9.11.B: Use arguments based on transformations to establish
congruence or similarity of 2- dimensional shapes.
List any special resources needed in the classroom or in the media center for the
students to complete the activity. For example, print resources in the media
center, art reproductions, or video and audio materials.
Introduction
Congratulations! You have just been hired as a detective to the case of the Pythagorean. It is
your job to act as a detective to find out who developed the Pythagorean Theorem. Find the
specifics of the mastermind behind this discovery and explain the 5 essential Ws. Who, what,
when, where and why should all be analyzed. Become proficient in the theorist’s background,
motives, and any cohorts in the case. All information that is found will be presented to your
supervisors. Be sure to include 5 of the Pythagorean proofs to prove that he has correctly
proved his hypothesis.
Here is some information that was found before the previous detective caught a dead end:
“Geometry is knowledge of the eternally existent.”
Form groups of 3 for this case, assigning each person to a specific part of the theorist’s
background. Each person will create essential questions corresponding to their assigned area.
These questions will be answered at the end of this inquiry and will help the group fill in the
blanks on this difficult case. Based on previous knowledge, what information do you expect to
find on the theorem?
After the initial inquiry, begin constructing a rubric. Attached to this assignment is a sample
rubric dealing with the content.
Investigation
These websites will help you to achieve the correct answers that your group has
developed for the case. The sites are a starting point to the project, write additional
websites you find on the lines below with a short explanation of the collected
information.
URL: http://www.shodor.org/interactivate/activities/PythagoreanExplorer/
Description: Visit shodor interactive to practice the Pythagorean theorem. Answers are
displayed after it’s plugged in.
URL: http://mathworld.wolfram.com/PythagoreanTheorem.html
Description: This site offers information on John Glenn's recent Space Shuttle mission. It
discusses how the age barrier for astronauts has been broken, as well as the tremendous
physical demands that space travel places upon the human body.
URL: http://www.cut-the-knot.org/pythagoras/index.shtml
Description: This site demonstrates the proofs of the Pythagorean Theorem.
URL: http://www.thebigview.com/greeks/pythagoras.html
Description: This site gives a brief history of Pythagoras and how he developed the theory.
URL: _______________________________
Description: _________________________________________________
URL: _______________________________
Description: _________________________________________________
Write down all information that each individual finds on his or her specialization of the
case. This evidence will be needed to prove to your supervisor that it is credible
information.
Gathering & Sorting
Using your detective abilities, use the library’s resources such as internet databases and
reference material to find additional background information. The complexity of the case
requires a complete analysis of all information on this theory. Work to answer the previously
developed questions and add additional questions as more material is discovered.
Gather pictures and evidence (the 5 proofs) to inform the police is who the culprit of this
theory. Save all websites and descriptions of additional materials as further investigation as
reference to those materials may be necessary. (lines are above)
Make sure to include any influence the Pythagorean Theorem has on mathematical theorists
and theorems. Take into account how the theorem can be used in a real world context and
what mathematical findings rely on the mathematical theorem.
The Portfolio
Use the index card folder in the front of the classroom to expand your research. The portfolio
includes research and clues from the previous detective that will help you to solve the case.
Make sure to use library books, bibliographies, articles, magazines, models and videos/pictures
to make your presentation more appeasing.
If additional resources are found that are not in the portfolio, take a blank note card from the
pile and write
-Group member’s names
- URL of website/ title, author and publication information of the print
-Description of the material
Sharing
The group of detectives needs to decide how the information will be presented to the
supervisor (teacher). Combine all information on the background information on the theorist,
the theory, and the 5 proofs that the theory exists.
Each individual student should attach their findings from the Internet and additional databases
on a word document/ paper into the portfolio. Staple the group’s documents together and
then place them in a section of the portfolio. Be sure to include each student name and group
name. Make sure to include a cover page, each content area of the group’s members including
5 proofs with explanations, and reflective questions.
Groups can use a PowerPoint, poster board, chalkboard, and any types of media in order to
present the evidence to the class. Make sure to include the prepared essential questions and
answers. Provide an extensive review of the theorist’s background and the required 5 proofs.
There should be enough detail that a complete stranger will have a concrete understanding of
the information after the presentation.
A reflection should also be included in the PowerPoint including the questions:
What did you enjoy about the project? What would you do differently if you were to do the
project again? How effectively did you work in your group? Did you work better with specific
people?
Evaluation
Previous examples are available for review.
Using the rubric developed in the initial stages, your supervisor will analyze your presentation
of the Pythagorean theory, theorist, and 5 essential proofs.
In addition, your presentation and findings will be evaluated according to the designated rubric
below.
Final Grades will be assessed using:
-Presentation Rubric
-Group Performance Grade
-Note Card Assessment
-Personal Reflection
Beginning
1
Developing Accomplished
2
3
Exemplary
4
Description of
Stated
identifiable
Objective or performance
Performance characteristics
reflecting a
beginning
level of
performance.
Description of
identifiable
performance Description of
characteristics
identifiable
reflecting
performance
development characteristics
and
reflecting
movement
mastery of
toward
performance.
mastery of
performance.
Description of
identifiable
performance
characteristics
reflecting the
highest level
of
performance.
Description of
Stated
identifiable
Objective or performance
Performance characteristics
reflecting a
beginning
level of
performance.
Description of
identifiable
performance Description of
characteristics
identifiable
reflecting
performance
development characteristics
and
reflecting
movement
mastery of
toward
performance.
mastery of
performance.
Description of
identifiable
performance
characteristics
reflecting the
highest level
of
performance.
Description of
Stated
identifiable
Objective or performance
Performance characteristics
reflecting a
beginning
level of
performance.
Description of
identifiable
performance Description of
characteristics
identifiable
reflecting
performance
development characteristics
and
reflecting
movement
mastery of
toward
performance.
mastery of
performance.
Description of
identifiable
performance
characteristics
reflecting the
highest level
of
performance.
Description of
Stated
identifiable
Objective or performance
Performance characteristics
reflecting a
beginning
level of
performance.
Description of
identifiable
performance Description of
characteristics
identifiable
reflecting
performance
development characteristics
and
reflecting
movement
mastery of
toward
performance.
mastery of
performance.
Description of
identifiable
performance
characteristics
reflecting the
highest level
of
performance.
Total
Score
PROVE THE SCARECROW WRONG IN THE WIZARD OF OZ: The sum of the square roots of any
two sides of an isosceles triangle is equal to the square root of the remaining side. Oh, joy! Oh,
rapture! I've got a brain!"