## Engage NY Eureka Math 7th Grade Module 1 Lesson 17 Answer Key

### Eureka Math Grade 7 Module 1 Lesson 17 Example Answer Key

Example 1.
Jake’s Icon
Jake created a simple game on his computer and shared it with his friends to play. They were instantly hooked, and the popularity of his game spread so quickly that Jake wanted to create a distinctive icon so that players could easily identify his game. He drew a simple sketch. From the sketch, he created stickers to promote his game, but Jake wasn’t quite sure if the stickers were proportional to his original sketch.

Steps to check for proportionality for scale drawing and original object or picture:
1. Record the lengths of the scale drawing on the table.
2. Record the corresponding lengths on the actual object or picture on the table.
3. Check for the constant of proportionality.

Key Idea:
The scale factor can be calculated from the ratio of any length in the scale drawing to its corresponding length in the actual picture. The scale factor corresponds to the unit rate and the constant of proportionality.
Scaling by factors greater than 1 enlarges the segment, and scaling by factors less than 1 reduces the segment.

→ What relationship do you see between the measurements?
→ The corresponding lengths are proportional.
→ Is the sticker proportional to the original sketch?
→ Yes, the sticker lengths are twice as long as the lengths in the original sketch.
→ How do you know?
→ The unit rate, 2, is the same for the corresponding measurements.
→ What is this called?
→ Constant of proportionality
→ Introduce the term scale factor and review the key idea box with students.
→ Is the new figure larger or smaller than the original?
→ Larger
→ What is the scale factor for the sticker? How do you know?
→ The scale factor is two because the scale factor is the same as the constant of proportionality. It is the ratio of a length in the scale drawing to the corresponding length in the actual picture, which is 2 to 1. The enlargement is represented by a number greater than 1.
→ Each of the corresponding lengths is how many times larger?
→ Two times
→ What can you predict about an image that has a scale factor of 3?
→ The lengths of the scaled image will be three times as long as the lengths of the original image.

Example 2.
Use a scale factor of 3 to create a scale drawing of the picture below.
Picture of the flag of Colombia:

A. 1$$\frac{1}{2}$$in. × 3 = 4$$\frac{1}{2}$$in.
B. $$\frac{1}{2}$$in. × 3 = 1$$\frac{1}{2}$$in.
C. $$\frac{1}{4}$$in. × 3 = $$\frac{3}{4}$$in.
D. $$\frac{1}{4}$$in. × 3 = $$\frac{3}{4}$$in.

Example 3.
Your family recently had a family portrait taken. Your aunt asks you to take a picture of the portrait using your phone and send it to her. If the original portrait is 3 feet by 3 feet, and the scale factor is $$\frac{1}{18}$$, draw the scale drawing that would be the size of the portrait on your phone.
Sketch and notes:
Sketch and notes:
3 × 12in. = 36in.
36in. × $$\frac{1}{18}$$ = 2in.

### Eureka Math Grade 7 Module 1 Lesson 17 Exercise Answer Key

Exercise 1.
App Icon

Exercise 2.
Use a Scale factor of 3 to create a scale drawing of the picture below.
Picture of the flag of Colombia:

Scale Factor = $$\frac{1}{2}$$
Sketch and notes:
A. 1 $$\frac{1}{2}$$ in.×$$\frac{1}{2}$$ = $$\frac{3}{4}$$ in.
B. $$\frac{1}{2}$$ in.×$$\frac{1}{2}$$ = $$\frac{1}{4}$$ in.
C. $$\frac{1}{4}$$ in.×$$\frac{1}{2}$$ = $$\frac{1}{8}$$ in.
D. $$\frac{1}{4}$$ in.×$$\frac{1}{2}$$ =$$\frac{1}{8}$$ in.

Exercise 3
John is building his daughter a doll house that is a miniature model of their house. The front of their house has a circular window with a diameter of 5 feet. If the scale factor for the model house is $$\frac{1}{30}$$, make a sketch of the circular doll house window.
5 × 12 in. = 60 in.
60 in. × $$\frac{1}{30}$$ = 2 in.

### Eureka Math Grade 7 Module 1 Lesson 17 Problem Set Answer Key

Question 1.
Giovanni went to Los Angeles, California, for the summer to visit his cousins. He used a map of bus routes to get from the airport to his cousin’s house. The distance from the airport to his cousin’s house is 56 km. On his map, the distance was 4 cm. What is the scale factor?
The scale factor is $$\frac{1}{1,400,000}$$ . I had to change kilometers to centimeters or centimeters to kilometers or both to meters in order to determine the scale factor.

Question 2.
Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked the poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by 1$$\frac{1}{3}$$ inches. What is the scale factor?
The scale factor is $$\frac{2}{3}$$.

Question 3.
Find the scale factor using the given scale drawings and measurements below.
Scale factor: ___

Scale Factor: $$\frac{5}{3}$$

Question 4.
Find the scale factor using the given scale drawings and measurements below.
Scale Factor: ___

Scale Factor: $$\frac{1}{2}$$

Question 5.
Using the given scale factor, create a scale drawing from the actual pictures in centimeters:
a. Scale factor: 3

Small Picture : 1 in.
Large Picture: 3 in.

b. Scale factor: $$\frac{3}{4}$$

Hayden likes building radio-controlled sailboats with her father. One of the sails, shaped like a right triangle, has side lengths measuring 6 inches, 8 inches, and 10 inches. To log her activity, Hayden creates and collects drawings of all the boats she and her father built together. Using the scale factor of $$\frac{1}{4}$$ , create a scale drawing of the sail.
A rectangular pool in your friend’s yard is 150 ft. × 400 ft. Create a scale drawing with a scale factor of $$\frac{1}{600}$$ . Use a table or an equation to show how you computed the scale drawing lengths.