This project is quite unique because it juxtaposes elements of technology and education to culminate in an impressive portfolio assignment in which students will use technology as their basis for obtaining, analyzing and presenting information.   Students will be immersed in Pythagoras - the man, the myths, his life, contributions, and his theorem.   Students will acknowledge that mathematicians are people too! The main goal is for students to become familiar with the theorem in a manner that is untraditional and will spark students' interest and curiosity.  

Objectives:

Students will:

• Obtain various biographies of Pythagoras

• Have a better understanding of what happened in the days when Pythagoras was alive

• Engage in interactive lessons about Pythagoras' theorem

• Prove why his theorem works and to be able to explain it in their own words

• Figure out the type of triangle which can be created, depending on the sides given.

• Determine if the triangle created by various sides will be acute, right, or obtuse

• Be able to self-evaluate whether any three numbers will satisfy the theorem

• Create a story using a word processor that has a mathematical problem wherein a character in the story has to use the Pythagorean theorem to solve the problem

• Enhance their narrative with pictures using Microsoft Word

• Employ a proof from the Internet lesson or another one they come up with to show the Pythagorean theorem works.

Objectives :

• To obtain various biographies of Pythagoras
• To have a better understanding of what happened in the days when Pythagoras was alive
• To engage in interactive lessons about Pythagoras' theorem
• To prove why his theorem works and to be able to explain it in their own words

My educational goals :

•  To have students use the Internet as a source of valuable information

•  To have the students gain better knowledge of who Pythagoras was

•  To get students to see the man as he was

Materials :

•  Computers

•  Handouts with questions that will lead students to discover the world of Pythagoras

•  Pencils

Motivation:

            For this first lesson, going to a new environment - the computer lab - will motivate students.   Students will also be motivated by working with a partner in a nontraditional decorum to breach unknown concepts.

Internet Addresses Involved :

•  http://geocities.com/Athens/2092/paper1.htm

•  http://rit.edu/~flwstv/presocratic.html

•  http://perseus.tufts.edu/GreekScience/
Students/Tim/Pythag'sTheorem.html

•  http://cut-the-knot.com/pythagoras

•  http://encarta.msn.com/find/Concise.asp?z=
1&pg=2&ti=761563435

•  http://historyforkids.org/learn/greeks/science/
math/pythagoras.htm

• http://sunsite.ubc.ca/LivingMathematics/V001N01/
UBCExamples/Pythagoras/pythagoras.html

Instructional Procedure :

            Students will be given a copy of the handout and will be asked to answer the given questions using the provided websites.   Answers will be recorded and turned in for a grade.  

Activity :

•  Using the first URL, find the answers to these questions:

•  True or False - Pythagoras was a vegetarian but wisdom trivia says that he sacrificed about 100 oxen because he was happy about discovering what has come to be known as his theorem

•  Describe the mystical symbolism of the Pythagorean Triangle and some important facts about the 3-4-5 triangle

•  Using the second URL, find the answers to the following questions:

•  What was Pythagoras' cult about?

•  What does this site say his greatest scientific success was?

•  What did he discover about the stars?

•  Using the third URL, answer:

•  What does this site say about what he did in his excitement of discovering the theorem, and how does it differ from the first URL?

• Write 10-15 sentences describing the life of Pythagoras.   Include at least two of his mathematical accomplishments.   Include some of his beliefs.

•  Using the fourth URL, put in your own words five out of the thirty-eight proofs of why Pythagoras' theorem works.

•  Using the fifth and sixth websites, compare the two biographies of Pythagoras.   Note similarities and differences between the language of the two sites.

•  Use the seventh site to demonstrate how the theorem works.   Watch the animation, and tell what happens to show that a 2 + b 2 = c 2

Closure :

Students and teacher will regroup and verify accurate information.

Homework :

Using your answer to question five in your worksheet, create a Venn diagram that compares the two biographies from the website.  

Assessment Measures :

• Did students answer the questions properly?
• Can students explain the Pythagorean theorem?
• Can students demonstrate the Pythagorean theorem?
• Can students relay information concerning Pythagoras' biography?
  

Objectives :
Students Will:

• Figure out the type of triangle can be created, depending on the sides given
• Determine if the triangle created by various sides will be acute, right, or obtuse

My educational goals :

•  To have students use their knowledge of squares and triangles to elicit the Pythagorean theorem

•  To have students understand the theorem in a novel way, using a constructivist approach

Materials :

•  Glue and scissors

•  Various colored graph paper

•  Markers and pens

•  Chart paper to display results

Motivation:

            Students will be motivated by the question, "Can any three numbers make a triangle?"   Students will be asked to cut out various squares and label the area of each.   This will motivate the students by deviating from the traditional lecture approach.

Instructional Procedure :

•  I will begin by asking students if any three numbers can be used to create a triangle.

•  Students will then be led to create the various squares using the colored graph paper.

•  Students will use the handout to be able to answer the aim.

Activity :

•  Students will work in groups of four to answer questions on the handout collectively.

•  Each student will take part in answering the questions together.  

•  Students will use the various-shaped squares to explore what kind of triangle would be formed by the edges of the squares.

•  Students should be instructed that squares MUST not overlap.

•  After the discovery is made, students will paste their examples on chart paper and attach the table to the paper.   Names and standards will be written on the paper.

Closure :

One student from the class will come up and give an oral presentation and example of what happens when squares are combined to form a triangle and the type of triangle that is formed.

Homework :

Students will write a paragraph explaining how the three types of triangles are formed and give an example of each.

Assessment :

•  Finished product is displayed on bulletin boards and then placed in portfolio along with the task and standards.

Objective :

•  Upon completion of this lesson, students should be able to self-evaluate whether any three numbers will satisfy the theorem

Materials :

•  Computer with MS Excel and 3 ½" disk drive

•  Disks

•  Paper, pencil/pen

•  Results of Lesson # 2

Motivation :

Students will easily be motivated via the use of the new environment in the computer lab, along with the excitement of why not all numbers can work and which numbers do satisfy the theorem.

Instructional Procedure :

•  I will begin by asking, "What is the Pythagorean theorem?  

•  Then, "Can any number be a, b, and c?"

•  The students would be asked to open an Excel document and put in the appropriate headings.  

•  Students are then led into the activity.

Activity :

•  Students would then be asked to pick various numbers for a, b, and c and see if the theorem is satisfied.  

•  Students would look for patterns to see when the theorem works.

•  Students then edit columns to make it pleasing to the eye and easy to read.

Closure :

Students will engage in whole-group instruction and will discover that multiples of triplets will also satisfy the theorem.

Homework :

Write as many Pythagorean triplets as you found and see if you can find at least five more, using what you learned about multiples.

Assessment :

•  Finished product is displayed on bulletin boards and then placed in portfolio along with the first draft

Objectives :

•  Upon completion of this lesson, students should be able to create a story using a word processor that has a mathematical problem wherein a character in the story has to use the Pythagorean theorem to solve the problem

•  Students will enhance their narrative with pictures using Microsoft Word

Materials :

•  Computer with MS WORD, graphics, and 3 ½ disk drive

•  Disks

•  Paper, pencil/pen

Motivation :

Students will be asked the question that they ask to all teachers - "When are we going to use this in everyday life?"   Also, the experience in the computer lab will also be motivation for them in this lesson.

Instructional Procedure :

•  I will begin by asking:

•  How can we tell which is the hypotenuse?

•  Will this always work for any triangle?

•  Which ones will it work for and why?

•  How can we use this theorem in everyday life?

•  Two common examples will be presented to students: (1) To find the height of a tree given its distance to a point and away from the point.   (2) To find the length of a ramp given the height of a wall and its distance from the endpoint of the ramp to the base of the wall.  

Activity :

•  Students will be asked to be creative and come up with other problems that involve the Pythagorean theorem.  

•  They will then be asked to come up with a story that involves one of the characters using the theorem to solve a real-world problem.

•  Students decide what types of pictures can enhance their narrative.

Closure :

Students will be asked to share their applications at random concerning when the theorem can be applied.  

Homework :

            Students will be asked to proofread, have someone else do the same and initial it, and then type their stories on Microsoft Word or another word processor.   Pictures will also be included in final draft.

Assessment :

•  Teacher grades draft version of narrative, makes necessary changes based on a rubric, hands back to students, and grades final version

•  Finished product is displayed on bulletin boards and then placed in portfolio along with the first draft

Aim : How can we use the mathematical proofs we saw in the first lesson to demonstrate our own proof?

Objectives :

•  Upon completion of this lesson, students should be able to employ a proof from the Internet lesson or another one they come up with to show the Pythagorean theorem works.

•  Students should enhance their presentation with graphics and sound from the Internet or another source to make it more appealing to the eye.

Materials :

•  Computer with MS PowerPoint or other presentation software, graphics, and 3 ½" disk drive

•  Disks

•  Websites from Internet component

Motivation :

Students will be shown an animated proof that I created on MS PowerPoint and will be challenged to create a better visual and stunning presentation.

Instructional Procedure :

•  I would begin by asking, "When can we use the Pythagorean theorem?"

•  "How can you prove to a third- or fourth-grader that this theorem is true?"

•  "Would you put all your information on one slide?"

•  "How can you use the animation feature, graphics, and sounds to help keep your audience interested?"

Activity :

Students would work individually or in dyads to demonstrate a proof of why or how the theorem works.   Students may choose to recreate one of the thirty-eight proofs they saw during the Internet lesson if they cannot come up with one on their own.   Students are challenged to explain their proof in words.   Finished product is displayed during a mini-conference for the class, parents, principal or assistant principal.  

Closure :

            Students will be asked to display their draft version to the class and teacher.   This can help to prepare them for the mini-conference on Pythagoras' theorem.

Homework :

•  How would you change your presentation to make it clearer and more interesting?

•  Evaluate two other person's presentations and tell them what they can improve.

• Internet Handout
• Venn Diagram
• Excel Handout
• Constructivist Handout
  

Students will combine the results from the compilation of the five lessons and put it in their portfolio.   Additionally, a unit test will be given.   The unit test will sample the intended content because each lesson will be assessed in the unit test.   Additionally, all the instructional objectives will be assessed.   Homework, classwork, and portfolio assessments are also employed throughout the unit.   Although each lesson in the unit is assessed separately, some more than others, this assessment tool - the test - will enable the teacher to understand, in the traditional approach, that the students understood the concept of the Pythagorean theorem.  

Use the Unit Test that Christina created to accompany this project.