Lesson
4 The Pythagorean Theorem
By:
Shan Huang
Subject: Mathematics
Grade: 8
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Lesson Number: 4 of 10
Time: 75 minutes
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Big Idea: Students
will understand that...
What does Pythagorean Theorem mean geometrically and algebraically?
We can describe,
measure, and compare spatial relationships.
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Objectives: SWBATs
Understand the
geometrical and algebraic meanings of Pythagorean Theorem
Use the theorem to
explain the project
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Content:
The formula of Pythagorean Theorem: a^2 + b^2 = c^2 .
of the area of a square with side length a, and so do b^2 and c^2.
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Curricular Competencies:
Visualize and describe mathematical concepts
Explain, clarify, and justify mathematical ideas
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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
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Materials/equipment needed:
Pre-designed PPT; projector;
scissors, paper, and pen/pencil.
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Assessment Plan:
Sharing, talking,
listening, and summarize group discussion results within class
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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
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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.