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. 1 in to 1 ft

  2. 1 in to 1 m

  3. 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.

(From Unit 1, Lesson 3.)

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?

(From Unit 1, Lesson 6.)

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:

  1. From T to S
  2. From S to R
  3. From R to T
  4. From T to R
(From Unit 1, Lesson 5.)