1. Scale Drawings and Scale Models

2. Vocabulary
scale drawing: proportional two-dimensional drawing of an object (smaller or larger)
scale model: proportional three-dimensional model of an object (smaller or larger)
scale factor: a ratio of the model/drawing’s dimensions to the actual object’s dimensions in simplest form
scale: ratio between two sets of measurements

3. Examples of Scale Drawings
blueprints
maps

4. Examples of Scale Models
toy car
model of a house
toy airplane

5. Finding Scale Factor
model’s dimensions
actual object’s dimensions

6. Caution!!!
A scale factor is ALWAYS the ratio of the model’s dimensions to the actual object’s dimensions.

7. Caution!!
It’s alright to have a scale factor greater than 1. If the scale factor is greater than 1, this means that the new figure is bigger than the original (think about cells). If the scale factor is less than 1, then the new figure is smaller than the original (think about model airplanes).

8. Finding a Scale Factor MODEL LENGTH 20 Model Length (in.) 1,800 20
You can use the lengths or heights to find the scale factor.
MODEL LENGTH 20
Airplane
Model
Length (in.)
1,800 20
Height (in.)
756
8.4
AIRPLANE LENGTH
1,800
THEN SIMPLIFY! 20
÷ 20 1 =
1,800
÷ 20 90
SCALE FACTOR!

9. Finding a Scale Factor MODEL HEIGHT 8.4 Model Length (in.) 1,800 20
You can use the lengths or heights to find the scale factor.
MODEL HEIGHT
8.4
Airplane
Model
Length (in.)
1,800 20
Height (in.)
756
8.4
AIRPLANE HEIGHT
756
THEN SIMPLIFY!
8.4
÷ 8.4 1 =
756
÷ 8.4 90
SCALE FACTOR!

10. Finding a Scale Factor Model Height (in.) 35 10 MODEL HEIGHT 10 35
Great Dane
Model
Height (in.) 35 10
MODEL HEIGHT 10 35
GREAT DANE HEIGHT
THEN SIMPLIFY! 10
÷ 5 2 = 35
÷ 5 7
SCALE FACTOR!

11. The actual distance between these two cities is 420 miles.
Using Scale
On a road map with a scale of 1 cm: 120 mi., the distance between two cities measures 3.5 cm. What is the actual distance between these two cities?
MODEL
1 cm
3.5 cm =
ACTUAL
120 mi
x mi
420 ÷ 1 =
420
The actual distance between these two cities is 420 miles.

12. The length of his model car is 11 in.
Using Scale
Jeffery is making a model of a car. He uses the scale 1 in:12 in. If the length of the actual car is 132 in., what is the length of his model car?
MODEL
1 in
x in =
ACTUAL
12 in
132 in
132 ÷ 12 = 11
The length of his model car is 11 in.

13. Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth.
22 inches
x inches
x inches
38 inches

14. Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth.
Let’s find length first!
MODEL
6 in
38 in =
ACTUAL
1 in
x in 38 ÷ 6 =
6.3

15. Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth.
22 inches
x inches
6.3 inches
38 inches

16. Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth.
Now let’s find the width!
MODEL
6 in
22 in =
ACTUAL
1 in
x in 22 ÷ 6 =
3.6

17. Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth.
22 inches
3.6 inches
6.3 inches
38 inches

18. The original size of the photograph is 3.6 inches by 6.3 inches.
Now we know...
The original size of the photograph is 3.6 inches by 6.3 inches.
In this case, the scale factor was larger than one. This means, that the model is larger than the original.

19. Try This:
On a scale drawing of a horse, the scale is 1 mm: 10 mm. If the real horse is 1,500 mm tall, how tall is the horse on the scale drawing?