Teacher: Cassie Cooper
Unit: The Pythagorean Theorem
Lesson: Proof with Jellybeans
I.
Common Core State Standards
 8.G.B.6—Explain a proof of the Pythagorean Theorem and its converse.
II.
Learning Objectives
 The learner will be able to construct and explain a proof of the Pythagorean
Theorem using a physical model.
 The learner will be able to write a formula to represent the Pythagorean Theorem
with 100% accuracy.
III.
Anticipatory Set
 For a warm-up, the students will be asked what they know about right triangles.
They will be given around 5 minutes to brainstorm all the ideas that they have about
the characteristics of right triangles. After the 5 minutes, the teacher will construct a
concept map on the board. The words “right triangle” will be at the center and
students will contribute ideas to construct subsequent bubbles. The teacher will
build upon these ideas and focus mainly on the ideas that right triangles must have
a right angle, as well as the fact that the two sides touching the right angle are
called “legs” and the remaining side is the “hypotenuse.” These vocabulary words
will be crucial for the lesson.
IV.
Purpose/Rationale
 “Yesterday, we talked about distance between points on a plane, as well as squares
and square roots. If you struggled with the idea of square roots, you can look back
at the worksheet. Today, we are going to learn about how to find the ‘flying’
distance between points on a plane. This is just talking about the direct distance
between any two points. Before Discovery Education tests, we talked about the
Pythagorean Theorem. Today, you’re going to actually prove this theorem and see
how and why it works!”
V.
Input
A. Task Analysis
i.
The students will complete a warm-up requiring them to brainstorm ideas about
characteristics of right triangles. They will work independently.
ii.
After 5 minutes, the teacher and students will collaboratively construct a
concept map of right triangles, focusing on the vocabulary needed to be
successful in the lesson.
iii.
State the objectives and purpose of this lesson.
iv.
Students will get into groups of 3. The teacher will distribute the Activity Page,
jellybeans, and cardboard constructions. They will then explain the directions
stated at the top of the worksheet to students.
v.
Students will work to complete the Activity Page using the given manipulatives.
vi.
The teacher will be circulating the room, ensuring students are on task, assisting
with questions, and asking questions for understanding.
vii.
viii.
ix.
x.
xi.
As students finish the Activity Page (or with 10 minutes left of class), the teacher
will bring the class back together as a whole. They will ask students to find
someone who was not in their group to compare their formula to.
The teacher will then ask for ideas of what students concluded, writing many of
them on the board. They will then write the standard formula for the
Pythagorean Theorem and explain the similarities and differences between that
and student responses.
The teacher will then explain explicitly how the activity proves the Pythagorean
Theorem.
The teacher will ask students to think about how you could use side lengths to
determine if a triangle is, in fact, a right triangle. As a class, they will conclude
that you could see if they satisfy the Pythagorean Theorem. If they do, the
triangle is right.
The teacher will then pass out the homework on Pythagorean Triples. Any extra
time will be used to work on this.
B. Thinking Levels
i.
Knowledge— Students will recognize the formula of the Pythagorean Theorem.
ii.
Comprehension—Students will explain the Pythagorean Theorem and its’
relation to area of squares.
iii.
Application—Students will apply the converse of the Pythagorean Theorem to
determine if a triangle is a right triangle from given leg lengths.
iv.
Synthesis—Students will construct a geometric proof of the Pythagorean
Theorem and the formula that describes the conclusion.
C. Learning Styles
i.
For students who are not understanding, I will work with them in their groups
on how the manipulatives and hands-on aspects relate to the formula. I will also
work with them to understand how the converse of the Pythagorean Theorem
works and how it can be used to determine if triangles are right.
ii.
As an extension, there is a Bonus Challenge at the end of the Activity Page.
Students will be asked to create their own model not using squares that could
prove the same theorem. They can draw it and give an explanation on the back
of the page.
iii.
Hands-on learners will be able to physically construct a proof of the
Pythagorean Theorem.
iv.
As the teacher circulates, they can also ask students questions so that they can
answer orally, as opposed to verbally.
v.
Visual learners will be able to see the different shapes involved in the proof of
the Pythagorean Theorem, as well as see the different formulaic
representations of the same concept.
VI.
Modeling
 When giving directions to the Activity Page, the teacher will demonstrate to
students what they are expected to do, without the use of jellybeans. That is, they
will use the cardboard construction and the Activity Page to detail what students are
to do and what questions they should be able to answer at the end.

The teacher will also model how to use the converse of the Pythagorean Theorem to
determine if a triangle is right. They will write an example on the board before
students are to do it on their homework.
VII.
Checking for Understanding
 How does this activity actually prove the Pythagorean Theorem?
 How is the Pythagorean Theorem related to area?
 Could this same activity be done with other shapes besides squares?
 How does the formula you wrote relate to the activity?
 Would this work with triangles that weren’t right triangles? Could you test this?
 Is the “c” square always going to be on the hypotenuse? Why or why not?
VIII.
Guided Practice
 Students will work on the activity in class, with assistance from the teacher and their
group members as needed.
 The teacher will also demonstrate an example of using the converse of the
Pythagorean Theorem to determine if a triangle is a right triangle.
IX.
Independent Practice
 Students will complete the Pythagorean Triples Homework independently.
X.
Closure
 With around 10 minutes left of the lesson, the class will come together to discuss
the importance of this theorem. Questions to ask:
i.
How does this activity prove the Pythagorean Theorem?
ii.
How does the formula relate to what we did today?
iii.
Would this work with triangles that weren’t right triangles?
iv.
Is the “c” square always going to be on the hypotenuse? Why or why not?
 The teacher will then discuss how we could work backwards, this time determining
if a triangle was a right triangle from given leg lengths. They will explain that this
notion is the converse of the Pythagorean Theorem and can be used to determine if
any three leg lengths are Pythagorean Triples.
 The teacher will reflect and evaluate the lesson after it is implemented to make any
necessary changes to make the lesson more effective.