## 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Copyright | Unpublished copyright work © 2005, David McAdams, Orem Utah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.

- From Utah Educator Network:
- 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
- Review
- Reintroduce the Pythagorean Theorem. Work several problems on the board of missing angles in right triangles.
- Activate prior knowledge of proofs by reviewing what constitutes a proof.
- Work one of the many proofs of the Pythagorean Theorem. Show how each step builds on the last.

- State the problem and objective
- State that at least 367 proofs of the Pythagorean Theorem have been found.
- State that each student (group/team) will attempt to discover one of the proofs.
- 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.

- Introduce the materials and begin the discovery process
- 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.
- 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.
- Have the students begin and circulate.

- Informal Assessment
- Circulate among the students, offering insight and encouragement.

- Summarize
- Invite various students or groups to present their proofs. Provide critical analysis of the strong and weak points of each proof.

- Reinforce the nature of a proof.
- Pass out the sheet giving the Chinese proof. Review it with the students to make sure they understand.

- Formal Assessment
- Pass out the worksheet for homework or class work.

- Review
- 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
- cut-the-knot.org
- 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.
- 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
- 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
- Development of Mathematics in Ancient China, http://www.saxakali.com/COLOR_ASP/chinamh1.htm

- Materials Masters
Download Manipulative and information sheet.