Lesson 7Units in Scale Drawings

Learning Goal

Let’s explore a different way to express scales.

Learning Targets

I can use scales without units to find scaled distances or actual distances.

Lesson Terms

scale
scale drawing

Warm Up: One to One Hundred

A map of a park says its scale is 1 to 100.

What do you think that means?
Give an example of how this scale could tell us about measurements in the park.

Activity 1: Apollo Lunar Module

Your teacher will give you a drawing of the Apollo Lunar Module. It is drawn at a scale of 1 to 50.

The “legs” of the spacecraft are its landing gear. Use the drawing to estimate the actual length of each leg on the sides. Write your answer to the nearest 10 centimeters. Explain or show your reasoning.
Use the drawing to estimate the actual height of the Apollo Lunar Module to the nearest 10 centimeters. Explain or show your reasoning.
Neil Armstrong was 71 inches tall when he went to the surface of the Moon in the Apollo Lunar Module. How tall would he be in the drawing if he were drawn with his height to scale? Show your reasoning.
Sketch a stick figure to represent yourself standing next to the Apollo Lunar Module. Make sure the height of your stick figure is to scale. Show how you determined your height on the drawing.

Are you ready for more?

The table shows the distance between the sun and 8 planets in our solar system.

planet	average distance (millions of miles)
Mercury	$35$
Venus	$67$
Earth	$93$
Mars	$142$
Jupiter	$484$
Saturn	$887$
Uranus	$1, 784$
Neptune	$2, 795$

If you wanted to create a scale model of the solar system that could fit somewhere in your school, what scale would you use?
The diameter of the Earth is approximately 8,000 miles. What would the diameter of the Earth be in your scale model?

Activity 2: The World’s Largest Flag

As of 2016, Tunisia holds the world record for the largest version of a national flag. It was almost as long as four soccer fields. The flag has a circle in the center, a crescent moon inside the circle, and a star inside the crescent moon.

Problem 1

Complete the table. Explain or show your reasoning.

	flag length	flag height	height of crescent moon
actual	$396 m$		$99 m$
at 1 to 2,000 scale		$13.2 cm$

Problem 2

Complete each scale with the value that makes it equivalent to the scale of 1 to 2,000. Explain or show your reasoning.

1 cm to cm
1 cm to m
1 cm to km
2 m to m
5 cm to m
cm to 1,000 m
mm to 20 m

Problem 3

What is the area of the large flag?
What is the area of the smaller flag?
The area of the large flag is how many times the area of the smaller flag?

Lesson Summary

Sometimes scales come with units, and sometimes they don’t. For example, a map of Nebraska may have a scale of 1 mm to 1 km. This means that each millimeter of distance on the map represents 1 kilometer of distance in Nebraska. Notice that there are 1,000 millimeters in 1 meter and 1,000 meters in 1 kilometer. This means there are $1, 000 \cdot 1, 000$ or 1,000,000 millimeters in 1 kilometer. So, the same scale without units is 1 to 1,000,000, which means that each unit of distance on the map represents 1,000,000 units of distance in Nebraska. This is true for any choice of unit to express the scale of this map.

Sometimes when a scale comes with units, it is useful to rewrite it without units. For example, let’s say we have a different map of Rhode Island, and we want to use the two maps to compare the size of Nebraska and Rhode Island. It is important to know if the maps are at the same scale. The scale of the map of Rhode Island is 1 inch to 10 miles. There are 5,280 feet in 1 mile, and 12 inches in 1 foot, so there are 63,360 inches in 1 mile (because $5, 280 \cdot 12 = 63, 360$ ). Therefore, there are 633,600 inches in 10 miles. The scale of the map of Rhode Island without units is 1 to 633,600. The two maps are not at the same scale, so we should not use these maps to compare the size of Nebraska to the size of Rhode Island.

Here is some information about equal lengths that you may find useful.

Customary Units

1 foot (ft) = 12 inches (in)
1 yard (yd) = 36 inches
1 yard = 3 feet
1 mile = 5,280 feet

Equal Lengths in Different Systems

1 inch = 2.54 centimeters
1 foot $\approx$ 0.30 meter
1 mile $\approx$ 1.61 kilometers

Metric Units

1 meter (m) = 1,000 millimeters (mm)
1 meter = 100 centimeters
1 kilometer (km) = 1,000 meters

1 centimeter $\approx$ 0.39 inch
1 meter $\approx$ 39.37 inches
1 kilometer $\approx$ 0.62 mile