Handouts for NCTM session #1025, 9-10 a.m., Saturday, April 15, 327 Navy Pier,
“Map Reading and Graphing Ordered Pairs Using Street Address Numbers”
Thomas N. Canright, The Latin School of Chicago
 
 

Plotting Points in Chicago

Presentation for NCTM Annual meeting in Chicago: April 15, 2000
By: Tom Canright, middle school math teacher, The Latin School of Chicago
tcanright@latinschool.org

This a presentation of a series of lessons which introduce coordinate graphing. In addition to this, students get practice with map reading skills. Finally the work is entered and displayed on students’ graphing calculators. Students get practice using graphing calculators and they are introduced to both connected graphs and scatter plots. Computers may be used instead of graphing calculators.

Activity 1:
For Chicago, Madison Street and State Street correspond with the x-axis and y-axis respectively. A location’s street number corresponds to the x-value of an ordered pair if the location is on an east-west street, and the street number corresponds to the y-value of an ordered pair if the location is on a north-south street. East and north go with positive numbers, and west and south go with negative numbers. After the street number is used to find half of an ordered pair, then street maps are used to estimate the other half of the ordered pair. For example, Wrigley Field is located at 1060 West Addison Street. The x-value of the ordered pair for Wrigley Field, then, is -1060. A glance at a street map shows that Addison Street is runs east and west at 3600 north. The y-value for the ordered pair is 3600. The ordered pair which represents Wrigley Field is (-1060, 3600). The origin, (0, 0), is the intersection of State and Madison Streets.

Use a street map to find ordered pairs to represent the following locations:
 
x        
y            
Field Museum     
Art Institute     
Lincoln Park Zoo     
Museum of Science and Industry     
Frank Lloyd Wright Studio     
Second City     
Pullman     
Chinatown     
Sears Tower     
Navy Pier     
Comiskey Park     
United Center     
Midway Airport     
O'Hare Airport     

Activity 2:
Graph the ordered pairs from Activity 1 and graph the ordered pairs below which represent Chicago’s lakefront. Students need to decide what the increments for the graph should be. Also they need to decide where to locate the x-axis and the y-axis.
Activity 3:
Type or use a graph link cable to enter the ordered pairs for Chicago’s lakefront into your graphing calculator. Use List 1 and List 2. Type the ordered pairs found in Activity 1 into your graphing calculator using List 3 and List 4. Use the state plot feature to make a connected graph for the lakefront and a scatter plot for the notable locations. Students should be able to understand why a connected graph makes sense for the points which represent the lakefront, and a scatter plot works well for graphing the chosen locations.
 

Possible extensions:
A poster size grid could be made to plot points for display in the classroom. Students could be asked to determined how many street numbers it takes to make a mile. In this example, they will find that it is 800. The distance formula could be introduced here, or for younger students right triangles could be formed and the Pythagorean theorem used to determine the distance between locations. Students not quite ready for the distance formula could be given it and ask to substitute values for pairs of points. Answers would need to be divided by 800 to find out the distance in miles. Students could be asked to chose another city to see if they could do the activity using the new city’s street numbering system. Finally, I discovered that about 400 street numbers are apparently skipped just south of downtown. This, of course, means that our graph is not perfect. Perhaps a student would like to track down just where this is and why.
 
 
 
 
 
 
 
 

Solutions for Activity 1:
 
x
y
Field Museum 
400
-1,200
Art Institute 
100
-200
Lincoln Park Zoo 
-200
2,100
Museum of Science and Industry 
1,800
-5,600
Frank Lloyd Wright Studio 
-7,000
800
Second City 
-200
1,660
Pullman 
600
-11,100
Chinatown 
-300
-2,200
Sears Tower 
-300
-300
Navy Pier
600
500
Comiskey Park 
-333
-3,500
United Center 
-1,901
0
Midway Airport 
-4,800
-5,700
O'Hare Airport 
-10,500
5,600

 
 
 
 
 
 
 
 
 
 
 
 
 
 

Solutions for Activity 2:

Solutions and set up screens for Activity 3:

The window may be set up just like the maximums and minimums for Activity 2.  After this is done, the screen must be "squared up" so the proportions are correct.  On a TI-83 this is done by pressing "Zoom", followed by a "5" (Zsquare).  The calculator will then automatically adjust the window so that it is proportional and fits into the screen.

For the TI-83, set up the stat plots as shown above.

Window 1              Window 2                  Window 3              Window 4
 

Window 1:
Here is the calculator window which shows the lakefront and the locations with the axes hidden.

Window 2:
Here is the calculator window which shows the lakefront and the locations using a different mark for the locations.

Window 3:
Here is the lakefront only with the axes on, which represent State and Madison Streets.

Window 4:
Here is the lakefront only.