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In some scale drawings, the scale specifies one unit for the distances on the drawing and a different unit for the actual distances represented. For example, a drawing could have a scale of 1 cm to 10 km.

In other scale drawings, the scale does not specify any units at all. For example, a map may simply say the scale is 1 to 1,000. In this case, the units for the scaled measurements and actual measurements can be any unit, so long as the same unit is being used for both. So if a map of a park has a scale 1 to 1,000, then 1 inch on the map represents 1,000 inches in the park, and 12 centimeters on the map represent 12,000 centimeters in the park. In other words, 1,000 is the scale factor that relates distances on the drawing to actual distances, and (1/1,000) is the scale factor that relates an actual distance to its corresponding distance on the drawing.

A scale with units can be expressed as a scale without units by converting one measurement in the scale into the same unit as the other (usually the unit used in the drawing). For example, these scales are equivalent:

• 1 inch to 200 feet

• 1 inch to 2,400 inches (because there are 12 inches in 1 foot, and 200 ⋅ 12 = 2,400)

• 1 to 2,400

This scale tells us that all actual distances are 2,400 times their corresponding distances on the drawing, and distances on the drawing are (1/2,400) times the actual distances they represent.

Neil Armstrong and Buzz Aldrin were the first people to walk on the surface of the moon. The Apollo Lunar Module was the spacecraft they used when they landed on the moon in 1969. The landing module was one part of a larger spacecraft that was launched from Earth.

Is it possible to express the 1 to 50 scale of the Lunar Module as a scale with units? What units would you use? In your next activity, you will explore how a scale without units and one with units could express the same relationship between scaled lengths and actual lengths!

Complete this activity on the back of the Lunar Module Activity.

A rectangular parking lot is 120 feet long and 75 feet wide.

• • Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches.

  • Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches.

1. Explain or show how each scale would produce an 8 inch by 5 inch drawing.

2. Make another scale drawing of the same parking lot at a scale of 1 inch to 20 feet. Be prepared to explain your reasoning.

3. Express the scale of 1 inch to 20 feet as a scale without units. Explain your reasoning.

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