Transcript 5.7 Scale Drawings and Models

5.7 Scale Drawings and Models
Standard: MG 1.3
Objective: Students use scales, ratios, and proportions
to solve scale drawing and model problems.
Key Concepts
• Scale drawing: a 2D drawing of an object
reduced to a proportion of the original
object.
• Scale model: a 3D model of an object
reduced to a proportion of the original
object.
• Scale: the ratio of the dimensions of the
large object to the reduced model.
Key Concept
• Maps, globes, Google maps, blueprints,
and model cars are all examples of scale
drawings and/or models.
• It makes it easier to
understand large objects.
Example 1: Find measurement
• Since the distance must be proportional to
the scale, write and solve a proportion to
find the missing value.
• Make sure units match when setting up
the proportion.
Practice 1
The scale on a map reads 1 cm : 200 m. Find the
actual distance if the distance measured on the
map is 7 cm.
map (cm)
actual (m)
1  7
200
x
x  1400
actual 
1400 m
Find the actual distance from LA to Houston.
Scale
0 1 in
0 300 mi
1 in : 300 mi
map (in.)
actual (mi.)
1
5

300 x
x  1500
actual 
1500 mi.
Example 2: Find scale
•
Just like in example 1, use a proportion to find the missing value.
Practice 2
• A blueprint shows a house that is 15 cm
long and the actual house is 75 m. The
scale is 1 cm : ? m. What is the scale?
Example 3: Find dimensions
1)
First change the scale to equal units (inches)
2)
Then write and solve the proportion
The scale of the house blueprint below is to be 1 in = 8 ft.
If the actual dimensions are 80 ft. by 30 ft., find the map
dimensions x and y.
y
Scale
1 in : 8 ft
x
Length
map (in.)
actual (ft.)
1  x
80
8
80  8x
Map Length  10 in.
Width
1  y
8
30
30  8y
Map Width  3.75 in.
Review
1) What is a scale model or drawing?
2) What is a scale?
3) How do you solve scale problems?
4) Give an example of when a scale is
used.