Pythagorean Theorem Lesson Plan

Developed byDavid McAdams
Last update5 Dec 2005
Grade Level9
SubjectGeometry
Digital versionhttp://www.lifeisastoryproblem.org/lesson/index.html
CopyrightUnpublished 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.
  1. Goal(s)/Standards
  2. Specific Objectives

    At the end of the lesson the student will be able to:

  3. Materials/Preparation
  4. Prerequisite Vocabulary
  5. Prerequisite Methodology

    None

  6. 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.
  7. Differentiation for Diverse Student Needs
  8. Assessments
  9. 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
  10. Materials Masters

    Download Manipulative and information sheet.