Name:_________________________________
M1L17H
Date:_________
Accordino-Math 7
Period:________
Lesson 17: The Unit Rate as the Scale Factor
Bellringer
1.
Steven has determined that there is a proportional relationship that exists between the amount of
time he works out each day to the amount of time he is able to focus on homework later on.
Time spent
exercising (in
minute), x
120
60
45
10
Time focusing
90
45
33.75
7.5
(in minutes), y
Identify the constant of proportionality that exists between time spent exercising and time spent
focusing.
Write an equation that would model this relationship.
If Steven exercises for 22 minutes how long can he focus on his homework for?
Name:_________________________________
M1L17H
Accordino-Math 7
Date:_________
Period:________
Lesson 17: The Unit Rate as the Scale Factor
Exit Ticket
1)
The drawing of a building, shown below, has a scale of 1 inch to 40 feet.
What is the actual height, in feet, of the building?
2)
a.
1.25 feet
b.
50 feet
c.
25 feet
d.
30 feet
Given the images below, what would be the scale factor of triangle GHI to triangle JKL?
a.
2
3
b.
2
c.
4
d.
1
1
2
Name:_________________________________
M1L17H
Date:_________
Accordino-Math 7
Period:________
Lesson 17: The Unit Rate as the Scale Factor
Notes
Review:
To calculate the constant of proportionality between two 2-D figures, define what is your original and what is your the
new (scaled) figure. Then compute the ratio
new of corresponding side lengths.
original
EXAMPLE 1:
Point 𝐴 to _________
Point 𝐵 to ____________
Point 𝐶 to ____________
Point 𝐷 to ____________
Length
AB
Length
CD
Original Drawing
New Drawing
Scale Factor:______________________
Calculate the length of
C'D' :
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 enlarge the segment, and scaling by factors less than 1, reduce the segment.
Calculate the length of
B'C' if BC= 6:
Name:_________________________________
M1L17H
Date:_________
Accordino-Math 7
Period:________
Example 2: Find the scale factor for each of the figures below using the ratio
new of corresponding side lengths to
original
determine your answer.
Actual Picture
Scale Drawing
Scale Factor: _________________________
Actual Picture
Scale Drawing
Scale Factor: _________________________
Actual Picture
24 cm
Scale Factor: _________________________
Scale Drawing
6 cm
Name:_________________________________
M1L17H
Date:_________
Accordino-Math 7
Period:________
EXAMPLE 3:
Use a Scale Factor of 3 to create a scale drawing of the picture below.
Picture of the flag of Colombia:
EXAMPLE 4:
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
portrait on your phone.
1
18
, what are the dimensions of the
Name:_________________________________
M1L17H
Accordino-Math 7
Date:_________
Period:________
EXAMPLE 5: 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.
Original Sketch:
Sticker:
Steps to check for proportionality for scale drawing and original object or picture:
1.
2.
3.
Name:_________________________________
M1L17H
Date:_________
Accordino-Math 7
Period:________
Homework:
1.
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
1
by 1 inches. What is the scale factor?
3
2.
Find the scale factor using the given scale drawings and measurements below.
Actual Picture
Scale Drawing
3 cm
5 cm
Scale Factor: _________________________
3.
Find the scale factor using the given scale drawings and measurements below.
Actual Picture
Scale Drawing
3 cm
5 cm
0.8 in.
1.5 in.
Scale Factor: _________________________
Name:_________________________________
M1L17H
Accordino-Math 7
4.
Date:_________
Period:________
Using the given scale factors and to create scale drawings from the actual picture below (in inches):
ACTUAL:
3in.
4
1in.
a.
Scale factor: 3
b. Scale factor:
Review:
What is the quotient of
7 and 4 ?
9 3
1
2