Unit 1, Lesson 8
Scale Drawings and Maps
Grade 7
8.2
Activity
A cyclist rides at a constant speed of 15 miles per hour. At this speed, about how long would it take the cyclist to ride from Garden City to Dodge City, Kansas?
Map with a line, trending downward and right. Endpoints are Garden City and Dodge City. Scale with line segment labeled 4 miles. The distance between the endpoints is about 12 and one half of the scale line segments.
8.3
Activity
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A driver is traveling at a constant speed on Interstate 90 outside Chicago. If she traveled from Point A to Point B in 10 minutes, at what speed was she driving? Explain your reasoning.
- A helicopter flew directly from Point A to Point B in 9 minutes. Did the helicopter travel faster or slower than the driver? Explain or show your reasoning.
Student Lesson Summary
Maps with scales are useful for making calculations involving speed, time, and distance. Here is a map of part of Alabama.
A map of a part of Alabama. Three points indicate three different cities on the map. The bottom point is labeled Montgomery, the middle point is labeled Centreville, and the top point is labeled Birmingham. A scale on the map shows 1 inch equals 20 miles. The distance between Birmingham and Montgomery is approximately 4 point 5 inches on the map.
Suppose it takes a car 1 hour and 30 minutes to travel at constant speed from Birmingham to Montgomery. How fast is the car traveling?
To make an estimate, we need to know about how far it is from Birmingham to Montgomery. The scale of the map represents 20 mi, so we can estimate that the distance between these cities is about 90 mi.
Table with arrows. Time, hours. Data, from top to bottom, 1.5, 3, 1. Distance, miles. Data from top to bottom, 90, 180, 60. On the left and right of the table, two downward arrows labeled times 2 and times one third.
Since 90 miles in 1.5 hours is the same speed as 180 mi in 3 hours, the car is traveling about 60 mi per hour.
Suppose a car is traveling at a constant speed of 60 miles per hour from Montgomery to Centreville. How long will it take the car to make the trip? Using the scale, we can estimate that it is about 70 mi. Since 60 miles per hour is the same as 1 mile per minute, it will take the car about 70 minutes (or 1 hour and 10 minutes) to make this trip.
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