Pythagorean Theorem
David Gelman
 

 
 
 
 
 
 
 
 
 


 
 
 
 
 
 
 
 
 
 
 


 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 


 
 
 
 
 
 
 
 
 
 
 
 
 
.
 Introduction
Students will understand what is a right angle and right triangle. They will perform WebQuests searching for similar figures.

Students will also learn to solve for the length of one of the sides given the other two.  JavaScript will be used to make this part of the lesson more interactive.

Subject: Algebra I and Geometry
Topic: Pythagorean Theorem
Grade Level: 9-12
Student Lesson URLS:
  • http://ctap295.ctaponline.org/~dgelman/lessons/lesson1.html
  • http://ctap295.ctaponline.org/~dgelman/lessons/lesson2.html
  • http://ctap295.ctaponline.org/~dgelman/lessons/lesson3.html
  • http://ctap295.ctaponline.org/~dgelman/lessons/lesson4.html
    • Standards Addressed
    California Standards for Mathematics This file is 544k and requires Acrobat Reader.
    Algebra 1
    2.0) Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand the rules of exponents.

    Geometry
    15.0) Students use the Pythagorean Theorem to determine distance and find the missing lengths of sides of right triangles. 

    Instructional Objectives
    1) Students know what is a right angle, and a right triangle. 

    2) Students can solve for the hypotenuse given the length of the legs.

    3) Students can solve for the length of one of the legs given the length of the other leg and the hypotenuse.

    Student Activities
    Introductory Activities
    Students are provided three images which have right triangles inside of them.The right triangles are highlighted. The legs and hypotenuse are labeled.
    1) in a street map
    2) in a pyramid
    3) in a baseball diamond

    First Lesson: Right Angle Search
    Students are first assigned to search the internet for webpages that have right angles in them. They type their findings into a form and the information is placed into a database. For all four of the lessons, the student(s) need to type the class period, group number, passcode, and name into the form.

    Second Lesson: Right Triangle Search
    Students are also assigned to search the internet for webpages that have right triangles in them. Again they type their findings into a form and the information is placed into the same database.

    Enabling Activity(ies)
    Third Lesson: Pythagorean Pyramids
    1) Show the students how to calculate the distance from the base to the top of a pyramid using the Pythagorean Theorem. They are given the length of one leg and the hypotenuse of a right triangle. By solving for the height of the pyramid, they are learning to find the length of one leg given the the length of the other two sides.
    JavaScript is used to generate each Pythagorean Triple and take the students through the steps of solving for the hypotenuse, correcting them as they go. For each step, the students type a response in a space of a form and press the appropriate button. An external window appears and "Mr. Right Triangle" tells the students whether the step is done correctly. There is a simple calculator provided as another external window.

    2) The students are given the height and half of the base of a pyramid. They learn to use the Pythagorean Theorem to solve for the hypotenuse of a right triangle given the length of the two legs.
    Once again JavaScript is used to produce the Pythagorean Triples and guide the students as they attempt each step. Students again "Turn in their work" by sending the results to a database. The results got to the database. This page requires browsers which can read the JavaScript. It is unfortunately possible that older browsers will not be able to perform these steps.

    Culminating Activity
    Fourth Lesson: Pythagorean Baseball
    The students are given the distance from the pitcher's mound to home plate and the distance from the pitcher's mound to first base. Show students how to calculate the distance from home plate to first base. Students will learn to solve for the hypotenuse given the length of both legs.
    DHTML is used to simulate a baseball game between green and brown right triangles. For each step there is a response in a "scoreboard" in the upper right corner. When the student has completed this page. The results will be sent into the database if the student uses the "Turn in the Work" form. This page requires browsers capable of reading the dhtml. It is also unfortunately possible that older browsers will not be able to perform these tasks.
     

    Assessment
    Pre-Assessment Pythagorean Worksheet: At the start of the week we did a worksheet. This is a copy. The actual file was typed with a word processor called Lotus Ami Pro in order to include mathematical formulas.

    Post-Assessment Pythagorean Quiz: The students were quizzed at the end of the week. This is also a copy. The actual file was also typed with Lotus Ami Pro.

    Rubric: These are the percentages I used to determine the grades.
    Results
    Pythagorean Results: Here is a bar graph of the student performances on this topic.
     
    Web Resources & Supplementary Materials
    Introductory Activity
    Names of the Sides of a Right Triangle
    Right Triangle Facts

    Enabling Activity
    Baseball and the Pythagorean Theorem
    Luke and Duke's Lake (CTAP 295: Ms. Mindy Cowan)
    Pythagoras (CTAP 295: Mr. Scott Schoepp)

    Culminating Activity
    Generalizing the Pythagorean Theorem: Geometric Interpretations of the Law of Cosines (CTAP 295: Mr. Peter Gerrodette)
    Circles around Pythagoras
    Pythagorean Triples
    Pythagorean Power-Point Presentation

    Gardena High School
    Gardena, California
    DavidX200@aol.com
    Last Revised: 07/01/2001