Pythagorean Theorem: Prove It
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This lesson provided by:
Author: Shannon Ashworth
System: Madison County
School: Central School

General Lesson Information
Lesson Plan ID:
32199
Title:

Pythagorean Theorem: Prove It
Overview/Annotation:

During this lesson, eighth grade students will be introduced to the Pythagorean Theorem: a^{2} +b^{2} =c^{2} . They will construct a right triangle on graph paper and draw squares on each side of the triangle.

Associated Standards and Objectives
Content Standard(s):
MA2015 (8) 21. Explain a proof of the Pythagorean Theorem and its converse. [8-G6]

MA2015 (8) 22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. [8-G7]

Local/National Standards:

Primary Learning Objective(s):

At the end of this lesson, students should know and be able to explain the attributes of a right triangle. They should be able to apply their new found knowledge of the Pythagorean Theorem to a real life scenario.

Additional Learning Objective(s):

Preparation Information
Total Duration:

Time Not Specified

Materials and Resources:

graph paper (1 cm)

colored pencils

copies of Pythagorean assignment (one per student)

Each group of three needs one of the triangle lengths.

Technology Resources Needed:

Interactive Whiteboard

Computer with access to the following video: Pythagorean Theorem demo (attached)

Access to the following Internet website: http://www.quia.com/cc/65631.html

Background/Preparation:

Student Prerequisite Knowledge needed:

Students need to understand how to square numbers as well as the inverse operation: square roots.

Students should have a list of perfect squares through 225.

Students should understand that the hypotenuse is the longest side in a right triangle. It is also opposite the largest angle.

Teacher Preparation:

Cut out triangle side lengths attachment. Make sure that you have one for each group of students.

Procedures/Activities:
1.) To begin, review how to find the perfect square of a number by playing the following interactive game: http://www.quia.com/cc/65631.html . If using an interactive whiteboard, students may come up to the board and tap to find matching pairs.

2.) Students will watch the demo video on the Pythagorean Theorem (attached)

3.) Use an interactive whiteboard to display the Pythagorean Theorem. Lead a class discussion to see what conclusions the students can draw about the relationship between the sum of the squares of the legs and the square of the hypotenuse.

4.) Divide students into mixed-ability cooperative groups. Groups of three would be ideal for this lesson.

5.) Remind the students that the hypotenuse is the longest length because it is opposite the largest angle. The "right" angle should be between the other two side lengths.

6.) Students will test this theory with different size triangles. Hand out a slip of paper with three lengths on it to each group. Students will use these lengths to build a triangle. They will apply what they saw in the video to this particular lesson. They will build squares off of each side of the triangle and see if it does prove to be a right triangle.

7.) Students will complete attached assignment to assess their understanding of the application of the Pythagorean Theorem.

Attachments: **Some files will display in a new window. Others will prompt you to download.

Assessment
Assessment Strategies

Students will complete the attached assignment. This assignment requires them to read and interpret a real life scenario. They will need to be able to represent their mathematical thinking in words as well as pictorially.

Acceleration:

Intervention:

Each area below is a direct link to general teaching strategies/classroom
accommodations
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.

Be sure to check the student's IEP for specific accommodations.