Map distance

Task

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

1. If the distance between the real towns of Candler and Canton is 9 miles, how far apart are Candler and Canton on the map?

2. 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

1. 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.
   

2. 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.