Detailed Lesson Plan
Student Intern’s Name: Malynta Masby
Lesson Title: Pythagorean Theorem
Lesson Planned Time: 2 days (50 minutes)
Objectives
Upon completion of the lesson, the students should be able to:
 Objective 1: Identify the Pythagorean Theorem formula and prove it using the areas of
squares to find the sides of a right triangle.
 Objective 2: Use the Pythagorean Theorem to find the hypotenuse of right triangles.
 Objective 3: Make observations of the use of right triangles in architecture.
 Objective 4: Recognize that the hypotenuse of a right triangle is always the longest side,
and be able to compare imperfect squares to other integers.
Georgia Performance Standard Alignment
8.NS The Number System
- Know that there are numbers that are not rational, and approximate them by
rational numbers.
8.EE Expressions and Equations
- Work with radicals and integer exponents.
8.G Geometry
-Understand and apply the Pythagorean Theorem.
Essential Questions, Knowledge & Skills
What is the Pythagorean Theorem and what
Students will know how to round numbers to
polygon is it used with?
the nearest hundredth.
How can the Pythagorean Theorem be proven
Students will know how to solve equations that
and used?
involve several steps.
Differentiated Instruction
Discuss alternate or additional strategies, resources, or activities to engage students at
varying levels of readiness, modalities and/or interests.
I will use different stations that all require students to practice using the Pythagorean Theorem to
solve problems. The stations will include board games, manipulatives, and online activities to
appeal to the diversity of interests. Some activities will also have extension questions to
challenge those students who have advanced knowledge of the content.
Materials/Preparation
What materials will you use?
-The Pythagorean Theorem Board Game (dice, tangrams, question cards, and computation table)
-Prove It! Worksheet
-candy (skittles)
-Smart board & tablet
- 120 drinking straws
-graphing paper
-masking tape
-electrical tape or duct tape
How will you arrange the desks?
The desks will be arranged in groups of approximately four students per group. Students will
rotate through each station remaining in their cooperative teams.
Warm-up Exercise: 10 minutes
How will you get the students’ attention?
I will employ a kinesthetic activity to get the students’ attention. Students will begin the warmup by drawing a number line diagram using only positive integers. Once this is drawn, I will ask
students to rewrite each integer on the number line as the square root of a perfect square. For
example, students will write √1 below 1 on the number line, √4 below 2 on the number line, √9
on the number line below 3, and so on. Once this is completed up to 17, I will tell students that
oftentimes the hypotenuse is not a perfect square, but we can estimate what two numbers it falls
between based on the conversion of whole numbers into the square root of perfect squares. I will
then give a few examples and see if students can estimate what two numbers it falls between.
For example, students should be able to position the √40 between 6 and 7. Afterward, I will ask
a student to draw and label the type of triangle used for the Pythagorean Theorem. I will then
write the lengths of each leg and hypotenuse, and ask students if the triangle was not drawn
could they determine which number is the hypotenuse. Students should be able to answer that
the hypotenuse is the longest side; and therefore, it is the greatest number. Select students will be
given numbers then asked to locate their position on a number line taped to the floor. Once
positioned, I will tell the class that these three numbers represent the two legs and hypotenuse of
a triangle. I will then ask the class which number represents the hypotenuse and have them
explain their reasoning. After a few rounds, students should realize that the hypotenuse is the
length of the longest side of a right triangle and should be able to identify the hypotenuse when
three numbers are presented without the diagram of the triangle accompanying them.
How will you connect this lesson with their previous knowledge and/or the real world?
This lesson will be connected to student’s previous knowledge and real world applications
through the type of word problems presented. For example, during the online game station,
students will be asked a question involving a television and entertainment system. Within this
question, students will determine if the television will fit within the entertainment system.
Students will also answer a real world question for their ticket out the door. Students will
compute the quickest route to return home from their friend’s house using actual street names
within the McNair community for relevancy. One station will also present real-world buildings
and architectural structures.
Body: 30 minutes
How will you present the new content?
I will use stations to present the Pythagorean Theorem. The Pythagorean Theorem was
introduced at the beginning of the week, so through this lesson students will receive ample
practice using the Pythagorean Theorem during different activities. Playing cards will be used to
divide students into four groups. Students will rotate through each station in groups of 3 or 4
students. One student in each group will be the designated leader of the group. They will be
responsible for coming to me with any questions the group has while I am assisting other
stations. I will rotate through each station in a clockwise cycle, spending three minutes at a time
at each station. Students will spend 15 minutes at each station, completing two stations the first
day, and rotating through the other two stations the following day.
What examples will you use?
There will be four separate stations. At the first station students will work at the Smart Board
and use the tablet to complete different online activities. Students will review some of the
Pythagorean Theorem concepts and compute the length of the hypotenuse using the following
website: http://jmathpage.com/middleschoolmath/jmsmpythagoras.html . More advanced students,
once having received adequate practice, will have the option to play a Jeopardy game of the
Pythagorean Theorem at the following website:
http://www.math-play.com/Pythagorean-Theorem-Jeopardy/Pythagorean-Theorem-Jeopardy.html
At the second station students will play the Pythagorean Board Game. Students will roll the dice and
use those two numbers to represent the lengths of the legs of a triangle. They will then use the
Pythagorean Theorem to find the hypotenuse, rounded to the nearest whole number. Students will
progress forward the number of spaces that is equivalent to the length of the hypotenuse they
calculated. Students may also land on a space that requires them to answer a trivia question about the
Pythagorean Theorem and the history of Pythagoras. Students will show their work on the worksheet
provided.
At the third station students will use round sized pieces of candy as manipulatives to illustrate one
method of proving the Pythagorean Theorem. They will take the candy to cover the squares made using
the sides of the two legs of a right triangle. They will then only use those pieces of candy to cover the
area of the square made using the length of the hypotenuse of the triangle. This activity should help
students to further conceptualize the fact that the Pythagorean Theorem states that the sum of the area
of the two squares made from the length of the legs of the right triangle is equal to the area of the
square made from the length of the hypotenuse of the right triangle. Students will answer the questions
on the Prove It worksheet to further guide their understanding.
At the fourth station students will construct towers using straws and masking tape. The group will be
given 30 drinking straws and will be required to use right triangles in their design to construct the tallest,
sturdiest tower that will remain standing for at least one minute (long enough to measure its height).
Prior to construction, students will sketch their designs on graphing paper and identify right triangles in
different historical architectural buildings including the pyramids that Pythagoras observed when
formulating his theorem.
Transitioning to the Abstract
What potential questions or problems do you anticipate?
I anticipate students having difficulty understanding why the theorem uses the areas of squares
instead of the lengths of the sides of the triangle. I anticipate students having questions about
which numbers to plug into which part of the formula for the Pythagorean Theorem. I anticipate
students having difficulty performing multiple step equations and showing their work in an
orderly fashion. I anticipate students having difficulty rounding numbers to different specified
place values. I anticipate students having difficulty articulating the inverse operation of squaring
a number or variable, which is taking its square root. I also anticipate students having difficulty
estimating the square root when it is not a perfect square without using a calculator.
What teaching points do you want to remember to emphasize?
I want to remember to emphasize the fact that the Pythagorean Theorem only applies to right
triangles. I want students to have a deeper depth of understanding of the Pythagorean Theorem
and not just memorization of the formula. Students should understand that the Pythagorean
Theorem involves adding the areas of the squares made from the lengths of the legs of the right
triangle to find the area of the square made from the length of the hypotenuse. I also want to
remember to emphasize the fact that the inverse operation of squaring a number is finding its
square root.
Close: 10 minutes
How will you summarize and pull together the content taught?
I will remind students that the Pythagorean Theorem is not simply a formula to memorize. It is a
method that involves using the information you have to solve for the unknown. Pythagoras
found patterns and similarities between right triangles of different sizes, and after much
observation he developed a simple formula that is very useful. It is not only useful but vital for
architectural design and the engineering of buildings.
How will you lead into the next lesson?
I will tell students that while we have been using the Pythagorean Theorem to find the length of
the hypotenuse, it can also be used to find the length of a leg of the right triangle which involves
using the same formula, but solving for a different variable. We will learn more about this the
upcoming week.
Assessment: 5 minutes
How will you evaluate this understanding of learned material?
I will evaluate the understanding of the learned material by asking students open-ended and
directed questions throughout class. Students will also complete worksheets for some stations
that will be collected. These worksheets will provide me with insight into their current
understanding and misconceptions. Students will also be assessed with a ticket out the door.
Technology Connection/Integration (if applicable)
How will technology be integrated into the instructional plan?
The Smart Board and a tablet will be used at one station. At this station, students will navigate
through the activities, using a different medium to compute the Pythagorean Theorem. The
activities will have graphics and provide students with immediate feedback.
What does the technology add to the lesson?
Technology offers students an interesting and different medium to compute problems involving
the Pythagorean Theorem. The websites also provide more real world applications for the
Pythagorean theorem. The technology provides additional opportunities to practice using the
formula, which is presented in slightly different ways to help students to recognize it in different
contexts.
Warm Up
INTERACTIVE NUMBER LINE
Three students at a time will be given a small dry erase board and will position themselves on the
number line drawn on the floor. The class will then determine which number is the length of the
hypotenuse. The following Pythagorean Triples will be used:
5, √144, 13
√9, 4, 5
8, 17, 15
1, √1, √2
9, 12, √225
Station 2
https://sn2prd0102.outlook.com/owa/attachment.ashx?attach=1&id=RgAAAACNmrV1XIbRT5y3
GHxzgKVnBwCNxsSnZ1TOT4HKooo1DMiWAAAAVwIWAACNxsSnZ1TOT4HKooo1DMiWAA
Au0kaKAAAJ&attid0=EAB%2boaoYjsNPToIfAMYhtxjf&attcnt=1
THE PYTHAGOREAN THEOREM BOARD GAME
Exact Value of The
Hypotenuse
The Approximate
Value of the
Hypotenuse
(Rounded to the
nearest whole number)
= 36
=16
36+16= 52
7
Station 3
PROVE IT!
1. What is the formula for Pythagorean Theorem? ____________________________________
2.
can be said as A to the second power. How else can
3.
be said?_____________________
can be said as a to the second power plus b to the second power equals c to the
second power. How else can this formula be said?___________________________________
4. Fill in the blank: All sides of a square are __________.
5. What is the formula for the area of a square, with side s? _______________________
s
6. If the area of a square is 25 square feet, what is the length of one side?______________________
7. If
= 25 what inverse operation must I use to find c?
Fill in the blank: Take the __________________ of both sides.
8. Draw three squares that connect to TRIANGLE 1. Use side a of TRIANGLE 1 to draw SQUARE A.
Use side b of TRIANGLE 1 to draw SQUARE B. Use side c of TRIANGLE 1 to draw SQUARE C.
a
c
1
b
1. Take only the amount of candy needed to fill in square a and square b on the triangle found
below.
2. Use only the candy pieces from square a and square b to fill in square c.
3. You do not need any additional candy. DO NOT EAT THE CANDY UNTIL THE ACTIVITY IS
COMPLETED.
4. Why does a triangle with these sides work so well with the candy activity? What do all the
squares have in common?
The table below includes triangles with sides that form perfect squares. Complete the Table:
RIGHT TRIANGLE
AREA OF SQUARE a
AREA OF SQUARE b
AREA OF SQUARE c
LENGTH OF
HYPOTENUS
12
5
9
12
8
15
EXTENSION:
If
, does
? Explain and provide an example for your reasoning.
Does the candy activity work well with a triangle where a=1 and b=1? Draw a diagram to explain your reasoning.
Formulate a real world situation that requires the use of the Pythagorean Theorem.
Station 4
Which architectural structure did Pythagoras observe when formulating his theorem? Identify
right triangles in the structures.
The Great Pyramid of Giza in Egypt, Africa
Chichen Itza Ball Court Watchtower Was Ancient Mayan Observatory, South America
The Eiffel Tower
TICKET OUT THE DOOR
Kamaria went over Biko’s house to study for their math class. Kamaria lost track of time and
realized that she had ten minutes to get home before the street lights came on or she would
miss her curfew and be punished. Kamaria’s house is diagonally across from Biko’s house on
Northfield Boulevard. How far is Kamaria’s house from Biko’s home, if Jolly Road is 8 feet long,
and Old National is 15 feet long? Both Jolly Road and Old National Highway form a right angle
connecting to Northfield Boulevard.
Biko’s House
Northfield Blvd
Old National
Jolly Road
Kamaria’s House
TICKET OUT THE DOOR
Will a 36 inch tv (which is the measure of the diagonal of the tv screen) fit within a
entertainment center that has a compartment for the tv that is 25 inches long and 25 inches in
height? Show your work.
25
36
25
television
entertainment center