Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Write each fraction in the
simplest form.
4 48
9 135
2.
1.
Convert the following measurements.
3. 192 inches feet
16

4. 18.5 feet inches
222

5. 324 inches feet
27

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Problem of the Day A toy model of a 200 foot
dinosaur is 3 in. long. How many times as long as
the model is the dinosaur?
800
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• What are blueprints?
• What make maps and blueprints useful?

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Learn to understand ratios and proportions in
scale drawings. Learn to use ratios and
proportions with scale.
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Vocabulary
scale drawing scale factor scale model scale
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A scale drawing is a proportional two-dimensional
drawing of an object.
Its dimensions are related to the dimensions of
the actual object by a ratio called the scale
factor. For example, if a drawing of a building
has a scale factor of , this means that
each dimension of the drawing is of the
corresponding dimension of the actual building.

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A scale is the ratio between two sets of
measurements. Scales can use the same units or
different units. The photograph shows a scale
drawing of the model train.
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Additional Example 1 Finding a Scale Factor
Identify the scale factor.
blueprint length room length
Write a ratio using one of the dimensions.

1 8

Simplify.
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Check It Out Example 1
Identify the scale factor.
blueprint length aircraft length
2 12
Write a ratio using one of the dimensions.

1 6

Simplify.
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Additional Example 2 Using Scale Factors to Find
Unknown Lengths
A photograph was enlarged and made into a poster.
The poster is 20.5 inches by 36 inches. The
scale factor is . Find the size of the
photograph.
5 1
poster photo
5 1

Think
36 l
5 1
Write a proportion to find the length l.

5l 36
Find the cross products.
l 7.2
Divide.
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Additional Example 2 Continued
A photograph was enlarged and made into a poster.
The poster is 20.5 inches by 36 inches. The
scale factor is . Find the size of the
photograph.
5 1
poster photo
5 1

Think
20.5 w
5 1
Write a proportion to find the width w.

5w 20.5
Find the cross products.
w 4.1
Divide.
The photo is 7.2 in. long and 4.1 in. wide.
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Check It Out Example 2
Marys father made her a dollhouse which was
modeled after the blueprint of their home. The
blueprint is 24 inches by 45 inches. The scale
factor is . Find the size of the dollhouse.
1.5 1
dollhouse blueprint
1.5 1

Think
Write a proportion to find the length l.
Find the cross products.
l 45 1.5
l 67.5
Multiply.
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Check It Out Example 2 Continued
Marys father made her a dollhouse which was
modeled after the blueprint of their home. The
blueprint is 24 inches by 45 inches. The scale
factor is . Find the size of the dollhouse.
1.5 1
dollhouse blueprint
1.5 1

Think
w 24
Write a proportion to find the width w.
1.5 1

w 24 1.5
Find the cross products.
w 36
Multiply.
The dollhouse is 67.5 inches long and 36 inches
wide.
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Additional Example 3 Measurement Application
On a road map, the distance between Pittsburgh
and Philadelphia is 7.5 inches. What is the
actual distance between the cities if the map
scale is 1.5 inches 60 miles?
Let d be the actual distance between the cities.
1.5 60
7.5 d

Write a proportion.
1.5 d 60 7.5
Find the cross products.
1.5d 450
Multiply.
450 1.5
1.5d 1.5

Divide both sides by 1.5.
d 300
The distance between the cities is 300 miles.
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Check It Out Example 3
On a road map, the distance between Dallas and
Houston is 7 inches. What is the actual distance
between the cities if the map scale is 1 inch
50 kilometers?
Let d be the actual distance between the cities.
1 50
7 d

Write a proportion.
1 d 50 7
Find the cross products.
1d 350
Multiply.
d 350
The distance between the cities is 350 kilometers.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz Part I
Identify the scale factor.
1.
2.
144 inches, or 12 feet
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Lesson Quiz Part II
3.
On a road map, the distance from Green Bay
to Chicago is 11 cm. What is the actual distance
between the cities if the map scale is 3 cm 90
km?
330 km
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Lesson Quiz for Student Response Systems
1. Identify the scale factor. A. C. 10 B.
D. 20
Fish Model
Length (cm) 120 12
1 20
1 10
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Lesson Quiz for Student Response Systems
2. On a scale drawing, the height of a
building is 60 inches. The scale factor is .
What is the height of the actual building? A.
240 in., or 20 ft B. 300 in., or 25 ft C. 600
in., or 50 ft D. 900 in., or 75 ft
1 15
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Lesson Quiz for Student Response Systems
3. On a road map, the distance from Washington,
DC to New York is 15 cm. What is the actual
distance between the cities if the map scale is 3
cm 50 mi? A. 150 mi B. 200 mi C. 250 mi D. 300
mi