Lesson Topic: Pythagorean Theorem
Instructional
Objectives:
Students will be able to:
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Use the Pythagorean Theorem to solve for the unknown
sides of a right triangle.
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VSC Addressed:
8.2.A.1.b. Identify and describe the relationship among the parts of a right triangle
ASSESSMENT LIMIT: Use the hypotenuse or the legs of right triangles
8.2.A.2.b. Apply right angle concepts to solve real-world problems
 ASSESSMENT LIMIT: Use the Pythagorean Theorem
Time Frame
Materials/Equipment:
1-2 days
Markers
Construction Papers
Graph paper
Cardboard squares of various sizes
Scissors
Colored pencils
Rulers
Document Camera
Computers
LCD Projector
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Prior Knowledge:
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Vocabulary
right triangle
hypotenuse
leg
right angle
Pythagorean Theorem
formula
substitute
square
square root
Pythagorean triple
LESSON
Warm-up
Mixed exercises on classifications and parts of triangles.
Fluency test on finding the square roots of a number.
Types of triangles
Describe angles
Right triangles
Powers of integers
Estimating square roots
Group Investigation Activity:
 Have the students work in groups of 4 to complete this activity.
 Give each group graph paper and have each member draw one
right triangle.
 Students will then find squares that fit on each side of the right triangle
(in other words, three squares, each with side lengths equal to one side of the
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triangle).
Measure the sides of the squares.
Calculate the areas of the squares (l x w).
Compile the group’s data into the table provided.
Look for patterns in the calculations done.
Complete the chart and answer the discussion questions.
Explicit Teaching/Modeling:
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Show a flipchart on Pythagorean Theorem and some examples and
have the students identify the parts and the missing side.
Have a walk through on the steps in finding the missing side of a right triangle
using the Pythagorean Theorem.
Guided Practice:
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The WORK
SESSION
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Differentiation
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Modifications
I do - Using a flipchart, show a real-life application problem and
model the procedures in finding the length of the unknown side.
We do – Have another example and have the students solve the
problem either independently or with a partner, while a volunteer
student solves on the promethean board.
You do – For the last example, give another problem and have the
students work on their own and check for correctness.
Think- Tac-Toe
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Have the students complete the Pythagorean Think-Tac-Toe
worksheet.
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The Think-Tac-Toe allows for differentiation by readiness, interest,
and learning profile.
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Students with IEP will work with a special educator or co-teacher
during the modeling and the group investigation activities. Utilize the
following websites during the activity for the students to see the proof
and examples of Pythagorean Theorem visually and interactively.
Have the students use the promethean board on these websites.
http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html
http://www.pbs.org/teachers/connect/resources/6329/preview/
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Accomodations
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Have the students work with a partner when completing the ThinkTac-Toe
Use of calculating devices
Process Chart on Pythagorean Theorem
Extended Time
Frequent Breaks
Reduced Distractions
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Formative
Assessment
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Homework:
Reflection
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Exit Ticket:
Vocabulary Graphic Organizer on Pythagorean Theorem
List Down 5 Pythagorean Triples. Show your work using the Pythagorean
Theorem
PROCESS CHART
PYTHAGOREAN THEOREM
 The hypotenuse is the longest side of the
right triangle and the side opposite of the
right angle. The sides that form the right
angle are called legs. For any right
triangle, the Pythagorean Theorem is true:
The square of the hypotenuse equals the
sum of the squares of the legs.
hypotenuse
leg
leg
WALK-THROUGH STEPS
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Identify the right angle, legs, and hypotenuse of the
right triangle.
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Plug in the value of the legs for a and b in the
Pythagorean Theorem.
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Evaluate the exponential expressions.
Take the square root of each side of the equation to
solve for c.
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GROUP INVESTIGATION WORKSHEET
Directions:
1. Each group has a set of right triangles and squares to sort.
2. For each right triangle, label the shorter leg
a, the longer leg b, and the
hypotenuse c.
3. Find squares that fit on each side of the right triangle (in other words, three
squares, each with side lengths equal to one side of the triangle).
4. Compile your group’s data into the table below by finding the length of each
side of the right triangle and the area of each square on each side.
Right
Triangle
Leg
(a)
Leg
Hypotenuse Area
(b) (c)
Leg
(a2)
Area
Leg
(b2)
Area
Hypotenuse
(c2)
1
2
3
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What do you notice about the values you found for the areas?
 Is there any relationship between the areas of the squares on the legs and the
area of the square on the hypotenuse?
PYTHAGOREAN THEOREM THINK-TAC-TOE
WORKSHEET
Compose a rap on
Compose a poem on
Create a comic strip on
Pythagorean Theorem Pythagorean Theorem
Pythagorean Theorem
with emphasis on its
with emphasis on its
with emphasis on its
real life application and real life application and real life application and
how to solve for the
how to solve for the
how to solve for the
unknown side.
unknown side.
unknown side.
INTERACTIVE
Complete a
Pythagorean Theorem
WorD Problems. Draw
the figure, label its
parts, and show your
work.
ACTIVITY
Select and complete one activity from each horizontal row to demonstrate your
understanding of the Pythagorean Theorem.
Go to www.ixl.com and
complete the problems
on solving for the
unknown side of a
triangle using the
Pythagorean Theorem.
Complete a BCR on
Pythagorean Theorem.
Go to
www.studyisland.com
and complete 15
problems on solving
for the unknown side
of a triangle using the
Pythagorean Theorem.
Complete a worksheet
on solving for the
hypotenuse of a right
triangle.
Research on the life
and contributions of
Pythagoras and make a
powerpoint
presentation with 6-10
slides.
Name_________________________________________ Date ________________
Use the Pythagorean Theorem to solve the problems below.
Draw a picture to help you!!
1. A ladder is leaning against a house. The base of the ladder is 5 feet
from the house. The top of the ladder rests 12 feet up. How long is
the ladder?
2. A cable that is 45 feet long is attached to the top of a vertical pole.
The cable is anchored to the ground 36 feet from the base of the
pole. How tall is the pole?
3. Ms. Walker tells you that she is drawing a right triangle with a
hypotenuse of 13 inches and leg of 5 inches. How long is the other
leg?
4. Mr. Shoales rests a ladder against a wall with the base 6 feet from
the wall. The ladder is 10 feet long. How high is the wall where the
pole rests against?
5. Point A is 9 miles from Point B, and 12 miles from Point C, with a
right angle at Point A. A road directly connects Points B and C. How
many miles is this road?
BCR ON PYTHAGOREAN THEOREM
A. Ms. Reid wants to cover a bulletin board. She puts a boarder on the
diagonal of the bulletin board. How many feet of boarder does she
need?
23
feet
38
feet
____________________________
B.
 Use what you know about triangles to explain how you found your
answer. Use numbers, words, and/or symbols in your explanation.
_________________________________
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_________________________________
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SOLVE FOR THE HYPOTENUSE
Complete the Pythagorean Triples by giving the value for the hypotenuse.
3, 4, ___
7, 24, ___
9, 12, ___
6, 8, ___
5, 12, ___
15, 20, ___
Do the side lengths below form a right triangle? Show your work. If yes,
circle the hypotenuse.
a)
9, 12, 15
b)
8, 14, 12
c)
12, 5, 13
d)
11, 7, 9
Solve for the hypotenuse in the right triangles below. Show your work!
x
6
4