Scales without Units

Warmup

Activity #1

Determine Scale By Measurement.

Here is the Apollo Lunar Module. It is drawn at a scale of 1 to 50. The “legs” of the spacecraft are its landing gear.

• Study the diagram carefully and answer the questions that follow.

(1.) Use the applet above to estimate the actual length of each leg on the sides. Write your answer to the nearest 10 centimeters.

(2.) Explain how you estimated the actual length of each leg.

(3). Use the drawing to estimate the actual height of the Apollo Lunar Module to the nearest 10 centimeters. Show your reasoning or explain below.

(4.) Explain how you estimated the actual height of the Apollo Lunar Module.

(5.) 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.

(6.) Explain how you determined Neil Armstrong’s height in the drawing.

(7.) 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.

Activity #2

Determine Scale Factor From Scaled Copies.

Figures R, S, and T are all scaled copies of one another. Figure S is a scaled copy of R using a scale factor of 3. Figure T is a scaled copy of S using a scale factor of 2.

• Find the scale factor for the following:

(1.) From T to S

(2.) From S to R

(3.) From R to T

(4.) From T to R

Activity #3

Create a Scaled Model.

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

• Study the table carefully and answer the questions that follow.

(1.) If you wanted to create a scale model of the solar system that could fit somewhere in your school, what scale would you use?

(2.) The diameter of Earth is approximately 8,000 miles. What would the diameter of Earth be in your scale model?

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.

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

Challenge #1

Use this information to answer the question. (There are about 1.1 yards in a meter, and 2.54 cm in an inch.) A scale drawing of a car is presented in the following three scales.

Challenge #2

A model airplane is built at a scale of 1 to 72. If the model plane is 8 inches long, how many feet long is the actual airplane?

Challenge #3

Which scales are equivalent to 1 inch to 1 foot?

Quiz Time