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Interdisciplinary Lesson Plan
I selected a math lesson that was interdisciplinary in the sense that my partner and I were able
to incorporate geography into the lesson as well. I co-taught this lesson to 8th grade students at Hershey
Middle School. I choose this above all the other lesson plans because it was well planned out and gave
students multiple ways to grasp, learn and understand the content through a hands-on activity where
students worked together in groups.
I chose this artifact because it shows not only my skills in creating an assignment that is creative
as well as applicable in the real world but also, because of the corporation and collaboration that my
follow peer and I were able to maintain throughout the entire process.
I would adapt this artifact by making it a two day lesson. Day one students would not only use
the virtual manipulatives but also be given algebra tiles to work with hands-on, specifically for the
kinesthetic learners in the classroom. Time would be permitted on day two for them to finalize their
work and then, we would showcase their work by hanging it on the walls. As a class, we would have a
discussion, students would then be given a sticky note and asked to peer reflect by writing a positive
note or an improvement note for each groups chart. Students would then get back into original groups
and review their peer’s thoughts.
Pythagorean Theorem Name: Katherine Bernardi Grade: 8
Content Area/Subject: Geometry/Geography Duration: 50 minutes
RATIONALE: Last year, the students were briefly introduced to the Pythagorean Theorem. This lesson has been designed to increase
students’ ability to solve problems involving the Pythagorean Theorem and work towards applying it to real world situations involving
different geographic points in the United States of America.
LEARNING OBJECTIVES(S):
The student will be able to solve real world problems involving the Pythagorean Theorem.
The student will identify different locations on a map of the United States of America.
*ASSESSMENT:
The student’s ability to solve problems involving the Pythagorean Theorem will be assessed through a ticket out the door.
The student’s identified points on the map will be formatively assessed through a group chart, and class discussion.
PENNSYLVANIA STANDARDS:
2.3 Geometry
2.3.8.
C.C.2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems
7.1: Basic Geographic Literacy
7.1.8.B: Explain and locate places and regions as defined by human and physical features
Mathematical Practices:
Make sense of problems and persevere in solving them
Model with mathematics
Use appropriate tools strategically
Attend to precision
What the teacher will do
What the students
will do
Differentiation (Content, Process,
Product,
Environment)
Safety Considerations
Materials/Technology
Needed Time
Needed
(5)
INTRODUCTION
1. The teacher will have
students recall:
What they know
about physical and
human features in
geography, and if
they can name any
places they have
gone on vacation
and what they have
observed while on
vacation, specifically
human and physical
features. How long
did it take students
to travel to their
destination? (out of
state or in state)
What the
Pythagorean
theorem is, and why
we use it.
1. Students will
answer the
teacher’s question,
and provide
examples.
5
minutes
> Facilitating to:
Features that are
man made and
nature made.
Examples: The
White House,
Mississippi
River, etc.
The Pythagorean
theorem helps us
find a missing
length of right
triangles. (leg2 +
leg2 =
hypotenuse2) **We will explain to
students that taking
the square root is the
opposite of a number
squared. **
**We will ask
student to think of
another way of
writing the
Pythagorean
Theorem**(a2+b2=c2)
Using a virtual manipulative
the teacher will show
students Garfield’s Proof
(this gives students a visual
as to how the Pythagorean
Theorem works.)
Virtual
Manipulative:
www.cpm.org
Under student support
- Click Technology
Resources.
Under CPM
Connections
eTools & Videos
- Click Geometry
Connections
Under Topics
- Click Chapter 2
- Pythagorean
Theorem
PROCEDURE: 1. The teacher what students
will be doing in today’s
class:
Break into pairs
(groups of three, if
necessary)
Each group will
receive a piece of
chart paper, a map, a
marker, and a
scenario, landmark
pieces (if necessary)
and a bag with pre-
cut triangles of
lengths that match
the scenarios.
** Each scenario
will lead students to
finding a right
triangle somewhere
on the US map. If
students have
1. Students will
break into pairs,
and begin working
on their problem
Students will
be working in
small groups
accommodating
students who
struggle
working alone
with word
problems
Verbal cues
will be given to
students as
needed
Directions will
be read aloud,
as well as
giving students
instructions in
writing.
Directions will
be clarified as
needed.
Chart paper
Markers
Map
Scenario Cards
difficulty the bag of
triangles is there to
help them.
Once students have
their triangle drawn,
they will determine
the length of the
missing side using
the Pythagorean
Theorem.
Students must place
their work on their
chart paper
2. The teacher will circulate
the room while the students
are working, answering any
questions that may come
about, and ensuring that
students are plotting their
points in the right location.
** Directions were given to
students in case they get
confused or lost on what step
to take next or if by any
chance students understood
everything well they could
move ahead. Also, the
teacher will write the steps
on the board and as a class
they will work together in
completing each step.
2. The students
will solve their
problem, recording
their work on the
paper.
In each
scenario card,
the places that
each celebrity
has traveled are
bolded. This
helps students
who struggle,
easily identify
what places to
point.
The scenario
cards range in
level of
difficulty to
challenge
students who
are stronger
with the
Pythagorean
Theorem
Students who
struggle will
receive stencils
of the triangles
that are formed
with each story.
Students that
need the stencil
can read their
scenario and
work towards
identifying the
30
minutes
10
minutes
1. Read Scenario
2. Identify States (put a
point in each state)
3. Find triangle that can
fit within the three
previously plotted
points.
4. Label mileage on
triangle according to
scenario.
5. Determine if you are
solving for a leg or
the hypotenuse.
6. Solve equation for
missing side using the
Pythagorean Theorem
(a2+b2=c2) or
(leg2 + leg2 = hypotenuse2)
** If extra time is allotted,
students will determine the
amount of money spent on
gas**
3. Once students have
completed their problem, the
teacher will instruct each
group to hand in their chart
paper, and the teacher will
collect it for evaluation.
3. Students hand in
their work.
proper triangle
that best fits
their scenario.
Students who
work ahead
will be able to
determine the
amount of
money the
celebrity will
be spending in
gas.
(5 & 6 ELL) (7) ACCOMMODATIONS/MODIFICATIONS:
Students will be working in small groups accommodating students who struggle working alone with word problems
Verbal cues will be given to students as needed
Directions will be read aloud, as well as give students instructions in writing. Directions will be clarified as needed.
In each scenario card, the places that each celebrity has traveled are bolded. This helps students who struggle, easily identify what
places to point.
The scenario cards range in level of difficulty to challenge students who are stronger with the Pythagorean Theorem
Students who struggle will receive stencils of the triangles that are formed with each story. Students that need the stencil can read
their scenario and work towards identifying the proper triangle that best fits their scenario.
Students who work ahead will be able to determine the amount of money that will be spent in gas.
LESSON EXTENTION: If more time is allotted, students will find how much gas was used on the trip if gas cost $3.95 per mile. Also
a worksheet will be given out for them to practice and sharpen their skills at setting up and solving an equation.
4. The teacher will bring the
class back together.
(5) CLOSURE:
1. The teacher will review
what a human and
physical feature is, and
review over what the
Pythagorean Theorem
can help us determine.
2. The teacher will then
review the scenarios that
the students were given.
Asking about the places
the points were plotted,
and discussing if each
feature is a human or
physical feature.
1.Students will
respond to the
teachers question
2. Students will
complete the ticket
out the door.
Ticket out the door
5
minutes
PRE-ASSESSMENT: The teacher will ask students what the Pythagorean theorem is, and what it is used for. The teacher will ask
students if they know what human and physical features are and if they can identify a few in our country.
(5) CONNECTIONS BEYOND THE LESSON:
Students can ask their parents if they have traveled to any of the human or physical features that we have discussed in class.
(5) CITATION:
"Academic standards for mathematics." Pennsylvania core. N.p., n.d. Web. 13 Oct. 2014.
<http://static.pdesas.org/content/documents/PA%20Core%20Standards%20Mathematics%20PreK-
12%20March%202014.pdf>.
"Free Printable Paper." Printable Paper. N.p., n.d. Web. 22 Sept. 2014. <http://www.printablepaper.net>.
GC 2.3.3: The Pythagorean Theorem . (2014). Retrieved from CPM Educational Program : http://studenthelp.cpm.org/m/gc/l/247743-
gc-2-3-3-the-pythagorean-theorem
Pythagoras' Theorem . (2014). Retrieved from Helping with Math:
http://www.helpingwithmath.com/printables/worksheets/geometry/8g6pythagoras01.htm
Scenarios Cards
Hey guys! My name is Christian Hackenberg and I am the
Penn State quarterback. What a rough game against
Northwestern. After that game, I decided I needed to head
home which is directly south, 316 miles to Virginia, the
home state of the Virginia Tech Hokies, where I rejuvenated
for the next big game. A little over a week ago we traveled
803 miles to the University of Michigan, home of the
Wolverines where we lost again. What a game. Now, it’s
directly back to Pennsylvania for to prepare for our next
big game, and hopefully a win!
Where did Christian travel? Draw a triangle that
approximately marks his travels, and find the missing length using the Pythagorean theorem.
If he spent $3.95 in gas per mile, how much money did he spend in gas for his entire trip? If he
has $1,000 to spend on gas, will he have enough to complete his trip? If not, how much more
money will he need?
Hi dolls. My name is Stefani Joanne Angelina
Germanotta. However, many of you know me as Lady Gaga.
As many of you can assume, I live a very busy life.
Traveling all across the United States is what I do on a daily
basis. This week, I left my home, where Disney Land is right
outside my window. I hopped in my limo and traveled
straight across America 2,437 miles to New York, home of the
Statue of Liberty, where I preformed in front of
thousands of people. After my fabulous performance, I drove
directly south 998 miles to Disney World to perform in front
of even more fans. What an exhilarating experience.
Especially with Magic Kingdom as my backdrop.
However, couldn’t enjoy it too long because the next
morning I drove all the way back to Hollywood where I was
able to catch up on some much needed rest and
relaxation.
Where did Lady Gaga travel? Draw a triangle that approximately marks her travels, and find the
missing length using the Pythagorean theorem.
If she spent $3.95 in gas per mile, how much money did she spend in gas for her entire trip? If
she has $1,000 in gas, will she have enough to complete her trip?
What’s up everyone? My name is Tony Romo, and I
am the quarterback of the Dallas Cowboys. This
season has been so exhilarating, but unfortunately I
have not had much time to spend with my family.
This week, I decided to change that and we went on
a favorite places trip. Our car left Dallas, Texas
where we drove directly north 830 miles to South
Dakota. There, I visited one of my favorite places,
Mt. Rushmore. I think it is so breathtaking there. We
spent a couple of days there and then decided to take
our son to Disneyland where he could meet some of
his favorite Disney characters. So we drove directly east 1,139 miles to California for a couple
more days. After enjoying a few days in the sunshine, we drove back down south to Dallas
where I will be getting right back to work preparing for next weeks game.
Where did Tony Romo travel? Draw a right triangle that approximately marks his travels and
find the missing length using the Pythagorean Theorem.
If he spent $3.95 in gas per mile, how much did he spend in gas for his entire trip? If he has
$1,000 in gas will he have enough money to complete his trip?
Hello hello! It’s Iggy Azalea here coming to you
from the fabulous New York City! What a crazy
week it has been. Ever since my hit single, Fancy,
released my life has been non-stop. This week I
traveled directly 203 miles south to the White House
to sing for President Obama. What an amazing
experience that was. After that I was invited to sing
in 2,083 miles away in Las Vegas. That experience
was beyond incredible. However, nothing tops my
favorite, New York! Once my performance ended it
was right back in my limo for a straight shot, right to New York City to see my amazing family
and get back to work on more hit music!
Where did Iggy travel? Draw a right triangle that approximately marks her travels, and find the
missing length using the Pythagorean Theorem.
If she spent $3.95 in gas per mile, how much did she spend in gas for her entire trip?
If she has $1,000 in gas, will she have enough money to complete her trip?
Hi there. My name is Ryan Seacrest. Many of you
know me from a show that has been on for what
seems to be a million seasons: American Idol. It’s
my favorite time of the year again: auditions. We
really meet some interesting people during this time.
This year we started auditions in the south. We
started in the state whose name is also in a major
river in the United States. That was a lot of fun.
Once we found a great group of singers, we headed
directly north 573 miles to Illinois where we found
more talent than I think we have ever seen. Our last
stop was a state known for Dorothy’s home state and
many tornadoes: Kansas. We drove 495 miles east
to Kansas. Once we found even more amazing
vocalists, we traveled back to Mississippi to enjoy a
piece of the south for a few extra days.
Where did Ryan travel? Draw a right triangle that approximately marks his travels and find the
missing length using the Pythagorean Theorem.
If he spent $3.95 in gas per mile, how much did he spend in gas for his entire trip?
If he has $1,000 to spend on gas, will he have enough money to complete his trip?
Hey y’all! My name is Carrie Underwood. Ever since American Idol my life has been a
whirlwind. It has been absolutely amazing! My
life definitely hasn’t slowed down ever since I
was crowned the winner. This week was a prime
example of that. I started by recording a few
songs for my new album in Oklahoma. I am so
excited about this album; I think the fans will
absolutely love it. After recording a few songs, I
traveled directly south 278 miles to Texas to
perform a few of my favorite songs for some
troops at an Air Force base. I always love
performing for troops. After my performance I
decided to take a few days and travel 664 miles
to the worlds famous canyon, the Grand Canyon. Everyone said how breath taking it was, but I
didn’t realize it would be so incredible. What a trip! After my mini trip, I headed straight back to
Oklahoma to get right back to work on my new album!
Where did Carrie travel? Draw a right triangle that approximately marks her travels, and find the
missing length using the Pythagorean Theorem.
If she spent $3.95 in gas per mile, how much did she spend in gas for her entire trip?
If she has $1,000 to spend in gas, will she have enough money to complete her trip?
Hello everybody. My name is Barrack Obama.
Every week I travel all over the country for various
reasons including press conferences, and speeches.
This week I had a few meetings in the Pentagon
where we discussed different situations going on in
the world. However, I was not home for long. I
traveled 215 straight miles north to Pennsylvania
to get the latest information about the Eric Frein
case. After the police filled me in on what is going
on, I traveled 407 miles to Ohio to meet with the
state government. After my meeting I headed
directly east to go home to DC to spend some much
needed quality time with my family. Being
President has a lot of responsibility, but it has been
a great couple of years leading our country.
Where did President Obama travel? Draw a right triangle that approximately marks his travels,
and find the missing length using the Pythagorean Theorem.
If he spent $3.95 in gas per mile, how much did he spend in gas for her entire trip?
If he has $1,000 to spend in gas, will he have enough money to complete his trip?
What’s up guys, it’s Miley Cryus! Many of you may know me as
Hannah Montana, or as the recent singer of the pop song, Wrecking
Ball. This week was a little busy for me. I started the week in my
vacation home in, Red Wood Forest, California. I like to go there
and get a break from the crazy life I live. However, relaxation did not
last long. On Tuesday, I had to drive directly north 493 miles north to
the Space Needle in Seattle to perform live for some fans. That was
such an incredible experience. However, I did not have a lot of time to
enjoy the scenery because the next morning I was driving 1,133 miles
to Las Vegas to meet with my record producer. We are working on my
new album, and I could not be more excited to share it with you! After
a couple meetings, I was able to head back to my favorite vacation spot
directly east in Red Wood. Oh, how I love being in the wilderness!
Where did Miley travel? Draw a right triangle that approximately
marks her travels, and find the missing length using the Pythagorean Theorem.
If she spent $3.95 in gas per mile, how much did she spend in gas for her entire trip?
If she has $1,000 to spend in gas, will she have enough money to complete her trip?
Hey y’all my name is Keith Urban. Some of you may
know me as the famous country singer with the
Australian accent. Others may know me as Nicole
Kidman’s husband. Either way, you all should know, I
am awesome. My wife and I enjoy going on nature walks
together. This week we walked on the San Antonio
River walk. It was breathtaking. Seeing all of nature
surround us was exquisite. After the walk, my wife and I
traveled directly east 471 miles to Louisiana where I
performed in front of my fans. I love performing my
songs in front of fans! Once the concert was over, we
decided to drive 417 miles north to Kansas to visit some
family members. There is nothing like family.
Unfortunately, our visit was very short. It turns out, while
we were in Kansas, I realized that I left my wallet in San
Antonio! So it was directly back to San Antonio we
went. Oh how I can be so forgetful.
Where did Keith Urban travel? Draw a right triangle that approximately marks his travels, and
find the missing length using the Pythagorean Theorem.
If he spent $3.95 in gas per mile, how much did he spend in gas for her entire trip?
If she has $1,000 to spend in gas, will he have enough money to complete his trip?
Hi guys. My name is Tim Allen! Many of you
probably know me as Mr. Claus from the Santa Claus
movies. Making those movies was so much fun. I wish
I lived in the North Pole. Unfortunately, I live a little
far way. I currently live in Colorado. It’s not too bad
here. This week I was not in Colorado long. I like to go
sight seeing, so I decided to go somewhere I have
never been for: the Saint Louis Arch in Missouri. It
was directly east, 916 miles away from my house. That
was amazing. It is cooler in person, than the movies.
After my visit, I decided to travel 1,430 miles to
Montana to see the grizzly bears and wolves at the Grizzly and Wolf Discovery Center. I can’t
even put into words how awesome that was! I loved it so much; I knew I had to bring a piece of
it with me home. So, I purchases a 7 foot stuffed grizzly bear. That was fun to take with me in
the car ride straight home to Colorado.
Where did Tim travel? Draw a right triangle that approximately marks his travels, and find the
missing length using the Pythagorean Theorem.
If he spent $3.95 in gas per mile, how much did he spend in gas for her entire trip?
If he has $1,000 to spend in gas, will he have enough money to complete his trip?
What’s up everybody!! My name is Will Smith. Many of you
may know me from Bad Boys, the Pursuit of Happiness, or
the oh so famous, Fresh Prince of Bel Air. Although I love
acting, the most important thing to me is my family. We love
to go on trips together across the country. This year we
started our trip in Atlanta, and visited the Atlanta
Aquarium. It is the largest aquarium in the United States.
We had a blast. After our visit in Atlanta, we decided to
travel directly north 693 miles to Cedar Point, Ohio to visit
the famous amusement park. It was so thrilling! After we
spend a few days there we traveled 1,152 miles south to see
my very good friend, Tony Romo play football. Go
Cowboys! We had a great trip to Dallas. Once the game was over, we traveled directly east to
Atlanta for a few days to snack on some Georgia peaches. It was a great time. I can’t wait for
next year!
Where did Will travel? Draw a right triangle that approximately marks his travels, and find the
missing length using the Pythagorean Theorem.
If he spent $3.95 in gas per mile, how much did he spend in gas for her entire trip?
If he has $1,000 to spend in gas, will he have enough money to complete his trip?
Hey there! My name is Selena Gomez. You may
recognize me from my role on Wizards of Waverly
Place, or from singing the hit song Naturally, or as Justin
Bieber’s ex girlfriend. I am currently enrolled in Cyber
School. This month in history class, we were learning
about Abraham Lincoln. We learned that he was buried
in Illinois with three of his four sons. I thought this was
really cool, so after I finished performing in Minnesota I
decided to travel 615 miles east to Illinois and visit his
tomb. After my visit to Illinois I traveled directly 260
miles to Iowa to perform once again. I love performing
in front of my fans. While I was visiting Abraham
Lincoln’s tomb, and performing in Iowa, my mom stayed
in Minnesota because she wanted to skii. Once I was
done performing I headed directly north to Minnesota
for a few days of relaxation and skiing with my family.
*
Where did Selena travel? Draw a right triangle that approximately marks her travels, and find the
missing length using the Pythagorean Theorem.
If she spent $3.95 in gas per mile, how much did she spend in gas for her entire trip?
If she has $1,000 to spend in gas, will she have enough money to complete his trip?
Instructions: 1. Read your scenario
2. Distinguish where your celebrity traveled
3. Draw points in each state your celebrity traveled
4. Connect lines to form a right triangle
5. Use the Pythagorean Theorem to determine the distance not and find the total your
celebrity traveled
6. If extra time allots, determine how much money your celebrity spent on gas, if he/she
spent $3.95 per mile and if they have enough money for their trip
7. If extra time, complete the Pythagorean Theorem problem worksheet
Scenario Answer Key
Assigned Groups
Here is a list I was given prior to teaching my lesson. For confidentiality reasons I only
put the first letter of their first name. However, if you would like a detailed list one can be
provided. This list was used when I choose the partners for each student. This class is the lowest
level class out of the four classes my mentor teaches. This class is comprised of students with
504 Plans and student who have IEPs, for those students who are not in these two categories they
then are considered below basic in mathematics. The learning support teacher helped me in
choosing the students partnerships to maximize the learning outcomes.
Higher Lower 1. M 13. G
2. A 14. A
3. A 15. J
4. C 16. B
5. D 17. K
6. S 18. N
7. K 19. D
8. T 20. E
9. A 21. L
10. P 22. A
11. J 23. K
12. P 24. J
25. P
Since there was not a perfect match higher to lower we decided to look at students who
were lower but still above in their own specific way. Therefore, we were able to move them over
and with that everyone had a partner and we only had one group of three. After speaking with
both the Learning Support Teacher and my mentor teacher we decided to group them according
to their ability and with who worked best together. We did not decide to have one higher with
one lower, if fact my teacher felt that if we grouped them that way the higher student would do
all the work and the lower level students wouldn’t even try.
Here are the Groups:
1 & 2 13 & 23
3 & 4 14 &21
5 & 9 16 & 17
8 & 12 15 & 22
6 & 10 18 & 19 & 20
7 & 11
