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A Tale of Three Cities –
The Pythagorean Theorem
The following project is a multidisciplinary lesson
designed for high school students, teachers and
home schooling parents. It is an engaging project
that integrates multiple types of instructional content
so that students are able to use and explore a
variety of sensory learning experiences and skills.
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A Tale of Three Cities –
The Pythagorean Theorem
This lesson requires that students have access to a
computer and the internet and that they have an
intermediate understanding of computer operations
and software applications such as word processors,
spreadsheets and presentation software.
A Tale of Three Cities –
The Pythagorean Theorem
Every attempt is made in lessons like this one to
integrate core instructional content in subjects
such as Math, Science, English, and Social
Studies with web-based applications and mediabased applications such as graphics, photography,
animation, music, video, search engines and
Google Maps.
Math
Science
Media
English
Social Studies
Web / Internet
A Tale of Three Cities –
The Pythagorean Theorem
Through this integration, students are challenged to
apply mastery of core content subject matter
through applications that are fun, engaging and
based on 21st Century web-based tools that high
school students are now accustomed to using in
everyday life. Through this integration we believe
that the learning experience is dramatically
enhanced.
A Tale of Three Cities –
The Pythagorean Theorem
You will notice that even in the initial presentation
and lesson plans, graphics related to the topic
and final work product are used to frame the
lesson. Throughout the lesson students are
required to choose their own photos and clip art,
add their own animation and music, and create
unique titles that reflect their own personalities
and uniqueness.
A Tale of Three Cities –
The Pythagorean Theorem
Free lesson plans and the associated rubrics are
available to students, teachers and home schooling
parents.
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AND NOW…..
A Tale of Three Cities –
The Pythagorean Theorem
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Pythagoras lived in the 500's BC,
and was one of the first Greek mathematical
thinkers. He had a group of followers known as the
Pythagoreans who followed him around and
taught other people what he had taught them.
Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
Pythagoreans were interested in philosophy, but
especially in music and mathematics, two ways
of making order out of chaos. Music is noise that
makes sense, and mathematics is rules for
how the world works.
Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
Pythagoras himself is best known for proving
that the Pythagorean Theorem was true.
Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
The Pythagorean Theorem says that in a right triangle,
the sum of the squares of the two right-angle sides will
always be the same as the square of the hypotenuse
(the long side). A2 + B2 = C2.
Source: http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
A Tale of Three Cities –
The Pythagorean Theorem
Step-by-Step Instructions
1. Using Google Maps, find three cities that form a right triangle. Left-click and hold the mouse to move the map to
any location on the planet. Zoom in and out until the three cities fill the map window.
2. Print the map to a printer or print to a PDF creator program. Many of these programs are available for free. If you
are using the PDF method, instead of saving the map as a PDF, use the PDF creator software to save the map as a
JPEG (photo). Save it into a specific folder. Next, in that folder right-click on the map photo, choose copy and then
open a new Presentation document where you will paste the map onto a slide.
3. On the printed map, use a straight edge to draw a right triangle between the three cities. If you are using the
PDF/JPEG method, use your Presentation software to open and paste a right triangle on top of the JPEG map. You
can edit the triangle using the Format Shape function (remove the fill, the thicken the line, change the line color,
etc.)
4. On a separate slide, insert a Right Triangle, then add labels for the three sides and the three City Names.
5. On another slide, write out the definition for the Pythagorean Theorem (see example).
6. On the same slide, use a “Distance Finder” website to find the actual distance between the cities on side a. and
the cities on side b. of the Right Triangle (see example).
7. Use the Pythagorean Theorem to solve for the distance of side c (see example).
8. On this same slide, give the name of side c.
9. Next, solve the following problem. Traveling at an average rate of 50 miles per hour, calculate how long it will take
to make a round trip journey to all three cities, including an 8-hour sight-seeing tour in each city. Show this on a
separate slide.
10. Using Custom Animation in Microsoft Powerpoint, create a presentation in which you move a vehicle around to
each city on your map. Choose a vehicle using Clip Art or a photo.
11. As your vehicle reaches each city, stop and present 10 facts about that city (see list provided). Show these facts on
a separate slide for each city.
A Tale of Three Cities –
The Pythagorean Theorem
The first step is to go to Google Maps and use
the Zoom tool to zoom in and out until you find
three cities that form a right triangle.
City 1
City 2
City 3
A Tale of Three Cities –
The Pythagorean Theorem
A Right Triangle placed on top
of a JPEG photo of a Google Map.
Students may print the
Google map to a printer
and use a ruler to draw a
right triangle on the map
or print the map to a PDF
creator program and save
it as a JPEG photo. If the
PDF method is used,
students can copy the
map into the presentation
software and then insert a
right triangle on top of the
map as shown here using
the Insert > Basic Shapes
command.
A Tale of Three Cities –
The Pythagorean Theorem
City Name 1
Students must draw a
right triangle in the
presentation software
with labels for the cities
and the sides of the
triangle.
c
a
City Name 2
b
City Name 3
A Tale of Three Cities –
The Pythagorean Theorem
San Angelo
a
Dallas
Example
c
b
Galveston
A Tale of Three Cities –
The Pythagorean Theorem
The equation for the Pythagorean Theorem is _____________________
Use a Distance Finder website to find:
Example
232
The distance between City 1 and City 2 (Side a.) = ___________
miles.
269
The distance between City 2 and City 3 (Side b.) = ___________
miles.
Using the equation for the Pythagorean Theorem, solve for the distance between City 1
and City 3 (Side c.).
232 miles2 + 269 miles 2 = c2
c2 = c
53,824 + 72,361 = c2
126,185 = c
126,185 = c2
355 miles
c = _______
355
The distance between City 1 and City 3 = ____________
miles.
Side c is called the _______________________
A Tale of Three Cities –
The Pythagorean Theorem
In our example, the total distance is
232 miles + 269 miles + 355 miles = 856 miles
A nice little getaway.
A Tale of Three Cities –
The Pythagorean Theorem
Solve this problem.
You will make a round trip journey to all three cities
traveling at an average rate of 50 miles per hour.
Additionally, you will stay 8 hours in each city on
sightseeing tours. How long will the trip take?
_________ hours.
If we know the distance (miles) and the
rate (miles per hour), we can find the
time (hours) based on the following formula:
Distance = Rate x Time
d=rxt
856 miles = 50 miles per hour x t
856 miles
50 miles per hr
=
50 miles per hour x t
50 miles per hr
t = 17 hours, then add 24 hours = 41 hours
A Tale of Three Cities –
The Pythagorean Theorem
Using clip art or a photo, insert a vehicle
onto your map. Move it around to all three
cities using Custom Animation. Stop the
animation after each leg of your trip, and
go to the facts for that city.
A Tale of Three Cities –
The Pythagorean Theorem
Find these 10 facts on each city.
FACT SHEET
City Name
1. State
2. Year Founded
3. Current Population
4. Longitude and Latitude
5. Weather Fact
6. Current Mayor
7. Form of Government
8. Largest Employer
9. Two Colleges
10. A fun activity that you
would do if you were there.
Click your mouse or hit the space
bar to move the car along its trip.
San Angelo
1. Texas
2. 1867
3. 88,439
4. 31°27′11″N / 100°27′9″W
5. San Angelo averages 251 days of sunshine a year
6. Alvin New
7. Council-manager
8. Shannon Medical Center
9. Angelo State University and Howard College
10. 10 miles of river frontage on the Concho River
winding through downtown and beyond.
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Dallas
1.
2.
3.
4.
5.
Texas
1841
1,279,910
32°47′0″N / 96°48′0″W
Winters in Dallas are generally mild, with
normal daytime highs ranging from
55 °F (13 °C) to 70 °F (21 °C)
6. Tom Leppert
7. Council-manager
8. American Airlines (22,077 employees)
9. Southern Methodist University (SMU) and Texas Woman’s
University
10. Dallas Cowboys in the new Cowboys Stadium
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bar to advance through the slides.
Galveston
1. Texas
2. The first permanent European
settlements on the island were
constructed around 1816 by the
pirate Louis-Michel Aury
3. 57,466
4. 29°18′04″N / 94°47′51″W
5. In 1900, the island was struck by a devastating hurricane. It
holds the record as the United States' deadliest natural
disaster killing 6,000 to 8,000 people on the island
6. Lyda Ann Thomas
7. Council-manager
8. University of Texas Medical Brach at Galveston
9. Galveston College and Texas A&M University at Galveston
10. Mardi Gras, Moody Gardens
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Wow, that was
a fun trip.
A Tale of Three Cities –
The Pythagorean Theorem
Additional Integration: Writing
To add further integration, students may add a writing component to
the lesson. Here are two examples:
1. Write an essay about Pythagoras and how he established his
theorem. Include facts about the time period, the cities he lived
in and some of his contemporaries. Also describe how you think
Pythagoras impacted the world.
2. Write an essay about people you might have met on your trip to
the three cities. Include one person from each city. Describe
how and where you met them. Describe each person in detail
and include an interested story or fact that each person told you.
A Tale of Three Cities –
The Pythagorean Theorem
Additional Integration: Math with Spreadsheets
To add further integration, students may create
a spreadsheet in which they input data showing
how long it would take (hours) to make a round
trip journey to all three cities if they travelled at
different rates of speed.
The End.
I hope you
enjoyed this
lesson.