Lee B. Hotchkiss and Beverly Stern
Objectives
.
-
1. Given a map scale and map distance, determine the ground distance. Given a map scale and ground distance, determine map distance.
-
2. Using quadrangle maps of New Haven and Mount Carmel and a piece of string, determine the lengths of the Willow Brook and Mill River.
Materials
Connecticut quadrangle maps of New Haven and Mount Carmel, topographic maps of the 7.5-minute series. Scale 1:24 000. size 23 x 27 inches. Price $2.00 each. Available from same source as in Footnote 10.
String and rulers.
Background
A map scale expresses a comparison of ground distance and map distance. The map scale is the single most important map feature, and knowing it we can determine the ground measurement of an object if given the map measurement and determine the map measurement if given the ground measurement.
A ratio is a comparison of two numbers with the same unit of measure. Thus a map scale can be written as a ratio comparing the map distance to the ground distance using the same unit for both, for example 1 inch/63 630 inches.
13
If we invert the ratio, 63 360 inches/1 inch, we would still have a ratio or map scale, only now we would be comparing the ground distance to the map distance instead of the other way around. Consider the following:
(figure available in print form)
Notice that if you have, or are given, the map distance then the ratio you use would be the one with the map distance part in the denominator. If you have, or are given, the ground distance, the rate you use would be the one with the ground distance in the denominator.
14
Procedure
1. Explain meaning of map scale as a ratio comparing map and ground distances. Include explaining what the reciprocal ratios mean.
-
2.
(figure available in print form)
-
____
(1) On a New Haven Quadrangle Map the distance from Lee High School to the corner of Church and Chapel is 1 1/4 inches. The map scale is 1: 24 000. Find the distance in feet between the two places.
-
____
(2) If the distance between New Haven and Hartford is 36 miles, what is the map distance on a state map with a scale of 1: 125 000?
-
____
(3) Given a map scale of 1: 1 000 000, find the ground distance of a river whose map distance is 8 centimeters.
-
____
(4) Given a map scale of 1: 1 000, find the ground distance of a river whose map distance is 6.5 centimeters.
-
____
(5) Given a map scale of 1:1 000 000, find the map distance of a river whose ground length is 75 kilometers.
-
____
(6) Given a map scale of 1: 1 000 000, find the map distance of a river whose ground length is 429 kilometers.
-
3. Using the New Haven and Mount Carmel Quadrangle maps, do the following. Taping maps together to provide one continuous map would be helpful.
-
____
(1) State the map scale.
-
____
(2) Express the map scale as a ratio, that is using the same unit. Use inches.
-
____
(3) With a string, measure the length of Willow Brook. The part of string used = _____ inches.
-
____
(4) Using MD1 x GD/MD = GD1, determine length of Willow Brook.
-
4. With students working in pairs, have students repeat procedure in 3 for the Mill River.