RATIO AND PROPORTION

Scale Drawings
(Teacher Copy)

### Activity  9:  Road and City Maps

Students use state and city maps as scale drawings to estimate distances.  Also use page S9.

To understand how ratios are used in scale drawings.

Introduction:

Have you ever wanted to take a trip?  Find lost treasure?  Rearrange your room?  Build a scale model of a car, airplane, or space ship?  All of these activities can involve the use of scale drawings.  Have students locate the legend on each map and determine the scale.

Part A

5 miles » 0.385 inches
1 inches = 13 miles
Scottsburg to Memphis »  1 1/8 (1.125) inches
Scottsburg to Memphis »  14.6 miles
Perimeter of Bedford-Uniontown-Henryville-Paoli rectangle »  9 inches direct distance (answers will vary if distances are determined by following various roadways, but they should be equal to or greater than the direct-distance figure)

Bedford to Uniontown »  36.5 miles

Entire trip »  117 miles direct distance (estimates and actual distances will vary according to the roadways followed, although these distances should exceed the direct-distance figure)

Closing Discussion

Why are map scales ratios?  Would it be possible to provide a table instead of the map scale?  What would such a table look like?  Map scales are ratios because distance is a ratio of inches to miles.  It would be possible to provide a table on a map instead of a scale (a table is provided on some maps), but a scale is always provided because it is a single, simple ratio that applies to the entire scale drawing.  A table on a map that did not also have a scale would have to have a row for distance in inches and a row for distance in miles; some city names might be included in the table.

When you read the mileage table on a road map, the distance shown between cities is often a little different from the distance you get by measuring.  Why is this the case?  The distance shown on maps is based on the route most likely to be traveled, but only an approximate measure can be made using a ruler (which is straight).

All of the scales we have used in this lesson are ratios that have different units.   Is it possible to have a map drawn using a same-units ratio?  Explain.  It would be possible but impractical to have a map drawn using a same-units ratio.  For example, a 5-miles-per-inch scale is also a 316,800-inch-to-1-inch scale, and people are interested in distances between cities in miles, not inches.

Further Exploration

Find a blueprint of a house or small building.  Discuss the scale used and exactly how large a building constructed from your blueprint would be.  Using tape, outline the actual size of one of the rooms on your classroom floor.