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Map distance
Task
On the map below, $\frac14$ inch represents one mile. Candler, Canton, and Oteen are three cities on the map.

If the distance between the real towns of Candler and Canton is 9 miles, how far apart are Candler and Canton on the map?
If Candler and Oteen are $3\frac12$ inches apart on the map, what is the actual distance between Candler and Oteen in miles?
IM Commentary
The purpose of this task is for students to translate between information provided on a map that is drawn to scale and the distance between two cities represented on the map. This task is a very straightforward application of the mathematics described in 7.G.A.1. This task would be appropriate for assessment.
Solution

A distance of nine miles means 9 quarter inches on the map. This is $$9\times\frac14 = \frac94$$ or $2\frac14$ inches between Candler and Canton on the map.

How many $\frac14$ inches are in $3\frac12$ inches? To find this, we divide: $$3\frac12 \div \frac14 = \frac72 \times \frac41 = 14$$ So it is 14 miles between Chandler and Oteen.
Map distance
On the map below, $\frac14$ inch represents one mile. Candler, Canton, and Oteen are three cities on the map.

If the distance between the real towns of Candler and Canton is 9 miles, how far apart are Candler and Canton on the map?
If Candler and Oteen are $3\frac12$ inches apart on the map, what is the actual distance between Candler and Oteen in miles?
Comments
Log in to commentIndustry Mathematician says:
over 3 yearsI'm not sure how the picture helps at all in this example. In fact, I think that the path drawn in the picture connecting various towns is confusing since students might not be sure which "distance" is being referred to: the distance along the path or the distance in the plane.