Lesson Plan - Pythagorean Theorem Using the Chinese Proof

Pythagorean Theorem Lesson Plan
Developed by	David McAdams
Last update	5 Dec 2005
Grade Level	9
Subject	Geometry
Digital version	http://www.lifeisastoryproblem.org/lesson/index.html
Copyright	Unpublished copyright work © 2005, David McAdams, Orem Utah This document may be reproduced for non-commercial educational use only. All other rights reserved.
Contact	Contact the author at DEMcAdams@usa.net.

Goal(s)/Standards
- From Utah Educator Network:
  - Algebra Objective 2.2.3 - Apply Pythagorean Theorem to find the missing measures of right triangles.
  - Geometry Objective 3.2.3 - Develop the distance formula using the Pythagorean Theorem.
  - Standard 3 - Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.
Specific Objectives
At the end of the lesson the student will be able to:
- State the Pythagorean Theorem
- Apply the Pythagorean Theorem to find the missing measures of right triangles.
- Develop the distance formula using the Pythagorean Theorem
- Describe a proof of the Pythagorean Theorem
Materials/Preparation
- The teacher should have manipulatives used to find proofs the Pythagorean Theorem.
- Each student will receive a set of manipulatives.
- Each student will need scissors to cut out the manipulatives.
Prerequisite Vocabulary
- Right triangle is a triangle containing one 90 degree angle.
- The Pythagorean Theorem states that for all right triangles, the length of the hypotenuse squared is equal to the sum of the length of the other two sides squared (C2 = A2 + B2).
Prerequisite Methodology
None
Instructional Procedure
1. Review
  1. Reintroduce the Pythagorean Theorem. Work several problems on the board of missing angles in right triangles.
  2. Activate prior knowledge of proofs by reviewing what constitutes a proof.
  3. Work one of the many proofs of the Pythagorean Theorem. Show how each step builds on the last.
2. State the problem and objective
  1. State that at least 367 proofs of the Pythagorean Theorem have been found.
  2. State that each student (group/team) will attempt to discover one of the proofs.
  3. State and write on the board that at the end of the lesson, the student will be able to give a proof of the Pythagorean Theorem.
3. Introduce the materials and begin the discovery process
  1. Pass out the manipulatives for the trial. State that this particular set of triangles and squares are from the Chinese proof of the Pythagorean Theorem.
  2. State that the student may create other manipulatives that they may find useful, such as squares that are size A x A and C x C.
  3. Have the students begin and circulate.
4. Informal Assessment
  1. Circulate among the students, offering insight and encouragement.
5. Summarize
  1. Invite various students or groups to present their proofs. Provide critical analysis of the strong and weak points of each proof.
6. Reinforce the nature of a proof.
  1. Pass out the sheet giving the Chinese proof. Review it with the students to make sure they understand.
7. Formal Assessment
  1. Pass out the worksheet for homework or class work.
Differentiation for Diverse Student Needs
- Blind students will need the manipulatives pre cut on card stock to facilitate working by feel.
- Students that are limited in motion may need assistance with cutting out the manipulatives.
- Students with cognitive difficulties will need additional assistance bridging from the concrete to the abstract.
- Cognitively advanced students may be encouraged to develop additional proofs, or find proofs on the Internet.
Assessments
- An informal assessment will be performed by watching students attempt to develop proofs.
- Students will describe their proof as a formal assessment.
- Students will complete a worksheet as a formal assessment. The worksheet may be used as a substitute for a quiz.
Other Resources
1. cut-the-knot.org
2. Teresa Gonczy, Student at University of California, San Diego, Ancient Chinese Mathematics: Right Triangles and Their Applications, Spring 2003, http://math.ucsd.edu/programs/undergraduate/history_of_math_resource/history_papers/math_history_01.pdf, Last accessed 9/2/2005.
3. David E. Joyce, Professor, Clark University, Mathematics in China, Initial work December, 1994. Latest update Sept 17, 1995, http://aleph0.clarku.edu/~djoyce/mathhist/china.html
4. J J O'Connor and E F Robertson, The Ten Mathematical Classics, December 2003, http://www-groups.dcs.stand.ac.uk/~history/HistTopics/Ten_classics.html
5. Development of Mathematics in Ancient China, http://www.saxakali.com/COLOR_ASP/chinamh1.htm
Materials Masters
Download Manipulative and information sheet.

Pythagorean Theorem Lesson Plan