Engage NY Eureka Math 7th Grade Module 1 Lesson 22 Answer Key

Eureka Math Grade 7 Module 1 Lesson 22 Exploratory Challenge Answer Key

Using the new scale drawing of your dream room, list the similarities and differences between this drawing and the original drawing completed for Lesson 20.
Similarities
Differences
Similarities
– Same room shape
– Placement of furniture
– Space between furniture
– Drawing of the original room
– Proportional

Differences
– One is bigger than the other
– Different scale factors

Original Scale Factor: ___
$$\frac{1}{20}$$
New scale Factor: ___
$$\frac{1}{30}$$

What is the relationship between these scale factors?
$$\frac{1}{4}$$
Key Idea:
Two different scale drawings of the same top-view of a room are also scale drawings of each other. In other words, a scale drawing of a different scale can also be considered a scale drawing of the original scale drawing.

Example 1:
Building a Bench
To surprise her mother, Taylor helped her father build a bench for the front porch. Taylor’s father had the instructions with drawings, but Taylor wanted to have her own copy. She enlarged her copy to make it easier to read. Using the following diagram, fill in the missing information. To complete the first row of the table, write the scale factor of the bench to the bench, the bench to the original diagram, and the bench to Taylor’s diagram. Complete the remaining rows similarly.

The pictures below show the diagram of the bench shown on the original instructions and the diagram of the bench shown on Taylor’s enlarged copy of the instruction.

Exercise 1.
Carmen and Jackie were driving separately to a concert. Jackie printed a map of the directions on a piece of paper before the drive, and Carmen took a picture of Jackie’s map on her phone. Carmen’s map had a scale factor of $$\frac{1}{563,270}$$. Using the pictures, what is the scale of Carmen’s map to Jackie’s map? What was the scale factor of Jackie’s printed map to the actual distance?

Exercise 2.
Ronald received a special toy train set for his birthday. In the picture of the train on the package, the boxcar has the following dimensions: length is 4$$\frac{5}{16}$$ inches; width is 1$$\frac{1}{8}$$ inches; height is 1$$\frac{5}{8}$$ inches. The toy boxcar that Ronald received has dimensions l is 17.25 inches; w is 4.5 inches; h is 6.5 inches. If the actual boxcar is 50 feet long:
a. Find the scale factor of the picture on the package to the toy set.

b. Find the scale factor of the picture on the package to the actual boxcar.

c. Use these two scale factors to find the scale factor between the toy set and the actual boxcar.

d. What is the width and height of the actual boxcar?

Eureka Math Grade 7 Module 1 Lesson 22 Problem Set Answer Key

Question 1.
For the scale drawing, the actual lengths are labeled onto the scale drawing. Measure the lengths, in centimeters, of the scale drawing with a ruler, and draw a new scale drawing with a scale factor (SD2 to SD1) of $$\frac{1}{2}$$.

Question 2.
Compute the scale factor of the new scale drawing (SD2) to the first scale drawing (SD1) using the information from the given scale drawings.
a.
$$\frac{1}{48}$$

b.
$$\frac{5}{4}$$