Map is Not Drawn to Scale
NAME_________________________
The New York City Subway map is not drawn to scale, but how off scale is it? Have the Tour
Guide draw a triangle on the New York City Subway map using the following locations as
vertices:
• 81 St-Museum of Natural History
• 59 St-Columbus Circle
• 66 St-Lincoln Center
Measure the segment lengths and record them in the table below. Round your measurements to
the nearest tenth of a centimeter.
SEGMENT
DISTANCE
(KM)
SUBWAY MAP
SEGMENT
LENGTHS (CM)
MAP SCALE
81 St-Museum of Natural History
to
59 St-Columbus Circle
1.8 km
[5.1 cm]
[0.4 km:1 cm]
59 St-Columbus Circle
to
66 St-Lincoln Center
0.7 km
[2.2 cm]
[0.3 km:1 cm]
66 St-Lincoln Center
to
81 St-Museum of Natural History
1.3 km
[3.4 cm]
[0.4 km:1 cm]
1. Is this portion of the map drawn to scale? If not, what adjustments could be made so that the
map would be drawn to scale?
This portion of the map is not drawn to scale. There should be a distance of
approximately 1.8cm between 59 St-Columbus Circle and 66 St-Lincoln Center.
2. Draw and label a sketch of the triangle from the subway map.
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3. Is your triangle from Question 2 similar to the triangle below? Explain how you know.
No. The sides are not proportional.
4. If not, what adjustments could be made so that the triangles would be similar?
The length of the side between 59 St-Columbus Circle
and 66 St-Lincoln Center should be 1.8 cm.
5. How do your responses to Question 1 and Question 4 compare?
They are the same because similar figures involve solving proportions in the same way
that map scale does.
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Let the Grand Prize Winner choose three more places to visit. Each place should be on a
different subway line. Draw a triangle on the subway map and compare those distances to the
Google Earth map, which is drawn to scale.
SEGMENT
SUBWAY MAP
SEGMENT LENGTHS
GOOGLE EARTH
SEGMENT LENGTH
LENGTH RATIO OF
SUBWAY MAP TO
GOOGLE EARTH
6. Does it appear that this portion of the map is drawn to scale? Explain.
Answers will vary, but very few sections of the map are drawn to scale.
7. According to the subway map, what is the actual distance between these stops? Use the
adjusted scale from Question 1 for these calculations.
Answers will depend on which points are chosen.
8. The Google Earth map has a scale of 1 cm = 0.2 km. According to the Google Earth map,
what is the actual distance between these stops?
Answers will depend on which points are chosen.
9. How accurate is this portion of the map?
Answers will vary.
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10. The Tour Guide has planned for the Grand Prize Winner to get to the airport using the
subway. The Grand Prize Winner will go from Times Square to Grand Central Station before
leaving for JFK Airport. Have the Tour Guide mark and measure the segment lengths
between these three vertices.
SEGMENT
Times Square to
Grand Central
Station
Grand Central
Station to JFK
Airport
JFK Airport to
Times Square
SUBWAY MAP SEGMENT
LENGTHS (CM)
DISTANCE (KM)
SCALE (KM:CM)
[6.3 cm]
1 km
[0.16 km : 1 cm]
[53.2 cm]
16.1 km
[0.30 km : 1 cm]
[47.9 cm]
17 km
[0.35 km : 1 cm]
11. Adjust the measurements on the subway map so that the distances between these three stops
would be drawn to scale.
One possibility is shown below.
SEGMENT
Times Square to
Grand Central
Station
Grand Central
Station to JFK
Airport
JFK Airport to
Times Square
SUBWAY MAP SEGMENT
LENGTHS (CM)
DISTANCE (KM)
SCALE (KM:CM)
[3.3 cm]
1 km
[0.30 km : 1 cm]
[53.2 cm]
16.1 km
[0.30 km : 1 cm]
[56.7 cm]
17 km
[0.30 km : 1 cm]
12. Do you think the subway map should be changed so that the distances between stops are
drawn to scale? Why or why not?
Answers will vary, but the main point of discussion is whether making the map more
difficult to read and less user-friendly would be superior to misleading people who use
the map to estimate the distance and time they are traveling.
Resources for Teaching Math
© 2010 National Council of Teachers of Mathematics
http://illuminations.nctm.org