Lesson plan

Lesson 4  The Pythagorean Theorem

By: Shan Huang

Subject: Mathematics Grade: 8		Lesson Number: 4 of 10 Time: 75 minutes
Big Idea: Students will understand that... What does Pythagorean Theorem mean geometrically and algebraically? We can describe, measure, and compare spatial relationships.
Objectives: SWBATs Understand the geometrical and algebraic meanings of Pythagorean Theorem Use the theorem to explain the project
Content: The formula of Pythagorean Theorem: a^2 + b^2 = c^2 . a^2 is the expression of the area of a square with side length a, and so do b^2 and c^2.	Curricular Competencies: Visualize and describe mathematical concepts Explain, clarify, and justify mathematical ideas		Language Objectives: Use mathematical vocabulary and language to contribute to mathematical discussions. Communicate in a variety of ways. Develop mathematical understanding through concrete, pictorial, and symbolic representations
Materials/equipment needed: Pre-designed PPT; projector; scissors, paper, and pen/pencil.
Assessment Plan: Sharing, talking, listening, and summarize group discussion results within class
Adaptations: 1.       Students’ mathematics levels vary 2.       Students may be able to make the large square but fail to explain 3.       Students may not be able to make the large square Modifications: 1.       Ask/invite students to explain with classmates 2.       Appropriately use the pre-designed PPT to demonstrate the process 3.       Allow students to walk around, ask, and observe Extensions: More proofs of the theorem

LESSON COMPONENTS

               

Hook and Introduction (15 minutes)

1.       Quiz on previous topics

2.       Quiz collection and explanation                                                            

Development (50 minutes)

1.       Lecturing (10 minutes)

a.       Vocabulary: leg, hypotenuse, right triangle, Pythagorean Theorem

b.       Formula: a^2 + b^2 = c^2, where a and b are the lengths of the two legs, and c is the length of the hypotenuse.

2.       History of the theorem (10 minutes)

a.       Brief History of the Pythagorean Theorem (video, 5 minutes): https://www.youtube.com/watch?v=PrjTkWGLk2Q

b.       Other story of the theorem (5 minutes)

3.       Cut and make (Blake Peterson’s activity (2009), 30 minutes)

a.       Students in pairs will make two squares. These squares can be with any dimensions, but for convenience, they had better have different and drawable sizes

b.       In each pair, assume the smaller square is with side length a, and the larger is with side length b.

c.        When two squares are put adjacent to each other, the total area of the two squares are a^2 + b^2

d.       Cut the two squares as shown on figure 1. Then each pair will have five shapes.

Figure 1

e.        Move these shapes to make a larger square.

f.        The result will be similar as figure 2.

Figure 2

Closing (10 min)

1.       Feedback of the class

2.       What to do next class: various proofs of the theorem and applications of the theorem

Reference:

Peterson, B. E. (2009). Teaching the Pythagorean Theorem for understanding. The Mathematics Teacher, 103(2), 160-160.