Holt CA Course 1 5-8Scale Drawings and Scale Models NS1.3 Use proportions to solve problems (e.g.,...
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Holt CA Course 1 5-8 Scale Drawings and Scale Models NS1.3 Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross- multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. California Standards 4 7 N 21
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Transcript of Holt CA Course 1 5-8Scale Drawings and Scale Models NS1.3 Use proportions to solve problems (e.g.,...
Holt CA Course 1
5-8 Scale Drawings and Scale Models
NS1.3 Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.
California Standards
4 7
N 21
Holt CA Course 1
5-8 Scale Drawings and Scale Models
This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO
gauge model train is . 1
87
This means that each dimension of the model is of the corresponding dimension of the actual train.
187
Holt CA Course 1
5-8 Scale Drawings and Scale Models
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.
A scale drawing is a proportional two-dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Identify the scale factor.
Teacher Example 1: Finding a Scale Factor
Room Blueprint
Length (in.) 144 18
Width (in.) 108 13.5
blueprint lengthroom length
= 18
18The scale factor is .
Write a ratio. Then simplify.18144
=
You can use the lengths or widths to find the scale factor.
blueprint widthroom width
= 18 Write a ratio. Then simplify.
13.5108
=
Holt CA Course 1
5-8 Scale Drawings and Scale ModelsStudent Practice 1:
Identify the scale factor.
Model Aircraft Blueprint
Length (in.) 12 2
Wing span (in.) 18 3
blueprint length aircraft length
= 212
= 16
Write a ratio. Then simplify.
The scale factor is . 16
blueprint wing span aircraft wing span
= 318
= 16
Write a ratio. Then simplify.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
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 original photograph to the nearest tenth of an inch.
Teacher Example 2: Using Scale Factors to Find Unknown Lengths
51
Think: posterphoto
= 51
36 l
= 51
5l = 36
l = 7.2
Write a proportion to find the length l.
Find the cross products.
Divide.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
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.
Teacher Example 2 Continued:
51
Think: posterphoto
= 51
20.5 w
= 51
5w = 20.5
w = 4.1
Write a proportion to find the width w.
Find the cross products.
Divide.
The photo is 7.2 in. long and 4.1 in. wide.
Holt CA Course 1
5-8 Scale Drawings and Scale ModelsStudent Practice 2:
Mary’s 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. 1.51
Think: dollhouseblueprint
= 1.51
l = 45 · 1.5
l = 67.5
Write a proportion to find the length l.
Find the cross products.
Multiply.
l 45
= 1.51
Holt CA Course 1
5-8 Scale Drawings and Scale ModelsStudent Practice 2:
w 24
= 1.51
w = 24 · 1.5
w = 36
Write a proportion to find the width w.
Find the cross products.
Multiply.
The dollhouse is 67.5 inches long and 36 inches wide.
Think: dollhouseblueprint
= 1.51
Mary’s 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. 1.51
Holt CA Course 1
5-8 Scale Drawings and Scale Models
On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities?
Teacher Example 3: Measurement Application
Let d be the actual distance between the cities.
1.560
= 7.5d
1.5 · d = 60 · 7.5
1.5d = 4501.5d1.5
= 4501.5
d = 300The distance between the cities is 300 miles.
Write a proportion.
Find the cross product.
Multiply.
Divide both sides by 1.5.
Holt CA Course 1
5-8 Scale Drawings and Scale ModelsStudent Practice 3:
On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities?
Let d be the actual distance between the cities.1
50= 7
d
1 · d = 50 · 7
1d = 350
d = 350
The distance between the cities is 350 kilometers.
Write a proportion.
Find the cross products.
Multiply.
Holt CA Course 1
5-8 Scale Drawings and Scale ModelsLesson Quiz
Identify the scale factor.
Statue of Liberty Model
Height (in.)
1,824 8
1.
2.
144 inches, or 12 feet
1228
On a scale drawing, a kitchen wall is 6 inches long.
The scale factor is . What is the length of the
actual wall?
124
3. On a road map, the distance from Green Bay toChicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km?
330 km
