Lesson 11
Scales without Units
Let’s explore a different way to express scales.
Problem 1
A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. Explain your reasoning. (There are about 1.1 yards in a meter, and 2.54 cm in an inch.)

1 in to 1 ft

1 in to 1 m

1 in to 1 yd
Problem 2
Which scales are equivalent to 1 inch to 1 foot? Select all that apply.
1 to 12
\(\frac{1}{12}\text{ to }1\)
100 to 0.12
5 to 60
36 to 3
9 to 108
Problem 3
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?
Problem 4
Quadrilateral A has side lengths 3, 6, 6, and 9. Quadrilateral B is a scaled copy of A with a shortest side length equal to 2. Jada says, “Since the side lengths go down by 1 in this scaling, the perimeter goes down by 4 in total.” Do you agree with Jada? Explain your reasoning.
Problem 5
Polygon B is a scaled copy of Polygon A using a scale factor of 5. Polygon A’s area is what fraction of Polygon B’s area?
Problem 6
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 factors for each of the following:
 From T to S
 From S to R
 From R to T
 From T to R