1. Aim: How do we calculate distance using a map scale?
June 2, Math 103
Objective: Students will determine what can be measured and how, using appropriate methods and formulas.
Aim: How do we calculate distance using a map scale?
NYS Mathematics Standards: 7.M.1
Prior Knowledge: Proportions. If Jarel pays $3.00 for six donuts, how much does it cost to buy three dozen donuts?

2. Mini-lesson: Scale drawings and scale models make it possible to show accurately that which cannot be drawn to correct size. A scale is a ratio – the ratio between the dimensions of the drawing and the actual dimensions of the object. A proportion is when two equivalent ratios are set equal to each other.

3. Example: On a map, Jonathan measured the straight-line distance between Rochester and Syracuse. The distance was 1.25 inches. Use the scale on the map to find the actual distance between the two cities.
Strategy: Make a proportion and solve it.
Step 1 – What is the scale on the map? inch = 50 mi.
Step 2 – Use the scale to set up a proportion.
.75 in./50 mi. = 1.25 in./? mi.
Step 3 – Solve by cross-multiplying
.75x = 50 * 1.25
x = miles
The distance between Rochester and Syracuse is about 47 miles.

4. Group Practice: Use your map to find the actual distance between New York City and Albany.
Strategy: Make a proportion and solve it.
Step 1 – What is the scale on the map? inch = 50 mi.
Step 2 – Use the scale to set up a proportion.
.75 in./50 mi. = in./? mi.
Step 3 – Solve by cross-multiplying
.75x = 50 * 1.625
x = miles
The distance between New York City and Albany is miles.

5. Independent Practice: You are going on a trip
Independent Practice: You are going on a trip. You begin in New York City and you drive to Kingston. Then you drive to Binghampton. Assuming the route to each city is a straight line, how many miles in all did you drive?

6. Solution:
Scale distance to Kingston = 1 inch
Scale distance to Binghampton = inches
Total inches =
Use a proportion:

7. Homework: How many miles do you drive if you go from Yonkers to Glens Falls, go over the mountains to Watertown, come down to Syracuse, and back to Yonkers?