1. Scale Drawings and Scale Models
Course 2
5-9
Scale Drawings and Scale Models
Do Now
Convert the following measurements.
inches = feet 16
feet = inches
222
inches = feet 27
Hmwk: Wbk p 50

2. Scale Drawings and Scale Models
Course 2
5-9
Scale Drawings and Scale Models
EQ: How do I use ratios and proportions in scale drawings?
M7G3.b Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures

3. Insert Lesson Title Here
Course 2
5-9
Scale Drawings and Scale Models
Insert Lesson Title Here
Vocabulary
scale model
scale factor
scale
scale drawing

4. Scale Models and Scale Drawings
Course 2
5-9
Scale Models and Scale Drawings
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. 1 87

5. Scale Models and Scale Drawings
Course 2
5-9
Scale Models and Scale Drawings
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 drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

6. 1 unit on the drawing is 20 units.
Scale
Interpretation
1:20
1 unit on the drawing is 20 units.
1 cm:1 m
1 cm on the drawing is 1 m.
in. = 1 ft
in. on the drawing is 1 ft.
1 4
1 4

7. Additional Example 1: Finding a Scale Factor
Course 2
5-9
Scale Drawings and Scale Models
Additional Example 1: Finding a Scale Factor
Identify the scale factor.
Room
Blueprint
Length (in.)
144 18
Width (in.)
108
13.5
blueprint length
room length 18
144
Write a ratio using one of the
dimensions. = 1 8 =
A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.
Caution! 1 8
The scale factor is .

8. Additional Example 1: Using Proportions to Find Unknown Scales or Lengths
A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale?
1 cm
x m
2 cm
8 m
Set up proportion using
scale length .
actual length =
4 = x
The scale is 1 cm:4 m.

9. The scale a:b is read “a to b
The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.”
Reading Math

10. The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale?
4 cm
12 m
Set up proportion using
scale length .
actual length
1 cm
x m =
3 = x
The scale is 1 cm:3 m.

11. Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length?
scale length
actual length
1000 1 =
8 mm
x mm
x = 0.008
The actual length of the amoeba is mm.

12. Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length?
scale length
actual length
10,000 1 =
1 mm
x mm
x =
The actual length of the fiber is mm.

13. Insert Lesson Title Here
Course 2
5-9
Scale Drawings and Scale Models
Insert Lesson Title Here
Identify the scale factor.
Model Aircraft
Blueprint
Length (in.) 12 2
Wing span (in.) 18 3
blueprint length
aircraft length 2 12 = 1 6 =
The scale factor is . 1 6

14. Scale Drawings and Scale Models
Course 2
5-9
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. 5 1 5 1
poster
photo =
Write a proportion to find the length l. 36 l 5 1 =
l = 7.2

15. Scale Drawings and Scale Models
Course 2
5-9
Scale Drawings and Scale Models
poster
photo 5 1 =
20.5 w
Write a proportion to find the width w. 5 1 =
w = 4.1
The photo is 7.2 in. long and 4.1 in. wide.

16. Scale Drawings and Scale Models
Course 2
5-9
Scale Drawings and Scale Models
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.
1.5 1
dollhouse
blueprint
1.5 1 =
Write a proportion to find the length l. l 45 =
1.5 1
l = 67.5
Multiply.

17. Scale Drawings and Scale Models
Course 2
5-9
Scale Drawings and Scale Models
dollhouse
blueprint
1.5 1 = w 24
1.5 1
Write a proportion to find the width w. =
w = 36
Multiply.
The dollhouse is 67.5 inches long and 36 inches wide.

18. Scale Drawings and Scale Models
Course 2
5-9
Scale Drawings and Scale Models
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?
1.5 60
7.5 d =
d = 300
The distance between the cities is 300 miles.

19. Insert Lesson Title Here
Course 2
5-9
Scale Drawings and Scale Models
Insert Lesson Title Here
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? 1 50 7 d =
d = 350
The distance between the cities is 350 kilometers.

20. A model of a 27 ft tall house was made using a scale of 2 in. :3 ft
A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model?
18 = h
The height of the model is 18 in.

21. A model of a 24 ft tall bridge was made using a scale of 4 in. :2 ft
A model of a 24 ft tall bridge was made using a scale of 4 in.:2 ft. What is the height of the model?
48 = h
The height of the model is 48 in.

22. A model was built using the scale 2 cm:0. 01 mm
A model was built using the scale 2 cm:0.01 mm. If the model is 30 cm long, what is the length of the actual object?
x = 0.15mm

23. Scale Drawings and Scale Models Insert Lesson Title Here
Course 2
5-9
Scale Drawings and Scale Models
Insert Lesson Title Here
Lesson Quiz: Part I
Identify the scale factor. 1.
Statue of Liberty
Model
Height (in.)
1,824 8 1
228 2.
On a scale drawing, a kitchen wall is 6 inches long.
The scale factor is What is the length of the
actual wall? 1 24
144 inches, or 12 feet

24. Scale Drawings and Scale Models Insert Lesson Title Here
Course 2
5-9
Scale Drawings and Scale Models
Insert Lesson Title Here
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

25. Lesson Quiz
1. What is the scale of a drawing in which a 9 ft wall is 6 cm long?
2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be?
3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person?
1 cm = 1.5 ft 1 4
5.5 in.
72 in.