IV-p3 distance
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INTRODUCTION TO SCALE

"Hey Lulu, I got a map! How about my trotting over from Louberg to visit you in Luluville?! How long will it take me?"
"Love you to, Lou! But I can't tell you how long it'll take! For one thing, there's nothing on the map to tell me how far it is between Louberg and Luluville. Or between any other two places! Your map needs a scale!"
"What's a scale?"
"A scale is something that tells you how the distance on the map compares to the distance on the ground. Take a look at my copy of your map! It has three different ways of giving the scale!"

 

THREE WAYS OF EXPRESSING THE SAME SCALE
TYPE EXAMPLE EXPLANATION
REPRESENTATIVE FRACTION (R.F.) 1/500,000
commonly written as
1:500,000		 One unit of length on the map represents 500,000 of that same unit on the ground. For example, 1 inch on the map = 500,000 inches on the ground. One cm on the map represents 500,000 cms on the ground. And so on.
STATEMENT OF EQUIVALENCY One inch = 7.9 miles It may be useful to know how many miles on the ground one inch on the map represents. For this map, the R.F. is 1/500,000, so 1 inch on the map = 500,000 inches on the ground. To find out how many miles 500,000 inches equals, divide 500,000 inches by 63,360 inches per mile. The answer is 7.89 miles (or approximately 7.9 miles). So, one inch on the map = about 7.9 miles on the ground.
Similarly, to find out how many kilometers on the ground 1 cm on the map represents, divide 500,000 cms by 100,000 cm per km. The answer is 1 cm on the map = 5 km on the ground.
BAR SCALE A bar scale is a graphic representation of distance. It shows, visually, what distance on the map represents a unit of distance on the ground. In this case, the distances on the map that represent miles and kilometers are shown.

USING MAP SCALES

 
"How do I use scales, Lulu!? How can I determine the shortest distance from Louberg to Luluville?"
"I'll tell you how! Let's deal with one type of scale at a time!"

 

STATEMENT OF EQUIVALENCY

 
"Take a look at this map! It gives a statement of equivalency: One inch = four miles. The shortest distance between the two towns is a straight line (along Bo Ring Way)! First, place a ruler marked in inches on the map and measure how many inches separate the two towns on the map! The two towns are about 2.5 inches apart! (They may not be 2.5 inches apart on your computer monitor because the image size varies according to your screen settings.) The rest is duck soup! Since each inch on the map represents about 4 miles on the ground, Louberg and Luluville are about 2.5 inches times 4 miles per inch = 10 miles apart on the ground!"

 

BAR SCALE

 
"On this map there's a bar scale! All you have to do is take a piece of paper, mark off miles from the bar scale onto the edge of the paper, and then hold the edge of the paper so that it lies along Bo Ring Way from Louberg to Luluville. If Louberg is at the zero miles mark (red arrow), then you can see that Luluville is about 10 miles away (other red arrow!)"
"But suppose I want a more exciting route than Bo Ring Way? Suppose I want to go along Dingle Road?"

"That's more difficult because the road is curved! You need some way to estimate distance along the curves of Dingle Way from Louberg to Luluville. There is a simple gadget called a MAP MEASURER that can do the job for you! It has a little wheel on one end and a dial on the other. You roll the wheel end along the curves and the dial keeps a record of how far you've gone!

But if you don't have a map measurer, you can use a piece of string! Take the string and lay it out along the route. Then, straighten the string out and hold it against the bar scale or a ruler!

If you don't have a piece of string, you can just mark off the units of distance as best as you can along the curves! That's what I've done on this map! I've marked off miles (taken from the bar scale) in red. It's not very accurate, but there are about 16 to 17 miles along Dingle Way between Louberg and Luluville!"
"Cool!!"

 

REPRESENTATIVE FRACTION

 
"On this map the scale is given as a representative fraction (1/253,440) and also as a ratio (1:253,440). The fraction and the ratio mean the same thing: that one unit of distance on the map represents 253,440 of the same units on the ground!"

"Let's say we want to know how far it is from Louberg to Luluville along Bo Ring Way! This is how to solve the problem!!:"
bulletFirst measure the distance on the map between the two towns - the answer is 2.5 inches.
bulletNow we need to know the distance on the ground that that distance on the map represents.
bulletThe rep. fraction tells us that 2.5 inches on the map represents 253,440 times 2.5 inches on the ground. Multiplying 253,440 times 2.5 inches gives us 633,600 inches on the ground.
bulletBut we're not used to thinking of large distances in terms of inches. We prefer miles. So we need to convert 633,600 inches into miles.
bulletSince there are 12 inches in a foot, if we divide 633,600 by twelve we get the number of feet: 633,600/12 = 52,800 feet.
bulletThen, since there are 5,280 feet in a mile, if we divide 52,800 by 5,280 we get the number of miles: 52,800/5,280 = 10 miles. That's our answer!

 

 
"Check out your understanding of distance, Lou, by doing some exercises!"

 

DIRECTIONS:
(READ ALL THE DIRECTIONS BEFORE YOU CLICK ON ANY BUTTONS!)
  1. Click on the pink button to print out instructions on how to use the "Distance and Directions on Maps: Exercises."
  2. Click on the top blue button to go to the Exercises.
  3. There you will find exercises with maps that use a
    bulletBar Scale (Lower Manhattan)
    bulletStatement of Equivalency (Northeast US)
    bulletRepresentative Fraction (Western US)
  4. For each map, answer the questions about distance. Questions about direction and azimuth may be ignored until you have studied 'Direction'. Make sure to use the 'answer-checking' device.
  5. Do as many of the exercises as are needed for you to feel confident that you understand the material.
  6. Check your understanding by doing the "Additional Exercises" (click on the bottom blue button).
PRINT INSTRUCTIONS FOR EXERCISES
LINK TO EXERCISES
LINK TO ADDITIONAL EXERCISES

Our thanks to Professor of Geology, David Leveson at Brooklyn College , CUNY
for his kind permission to use this copyrighted material

http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/maptop.html

 

 

 

 

 

 

© 2000
David J. Leveson