Introduction to Scale Factor

What is a scale drawing?
Scale Drawing
• A drawing that shows a real object with
accurate sizes except they have all been
reduced or enlarged by a certain amount
(called the scale).
The scale is shown as the length in the
drawing, then a colon (":"), then the
matching length on the real thing.
Example: this drawing has a scale of "1:10", so
anything drawn with the size of "1" would have a
size of "10" in the real world, so a measurement of
150mm on the drawing would be 1500mm on the real
Investigating Scale
Click on the Butterfly Below…
• The scale indicates how many units of length
of the actual object are represented by each
unit of length in the drawing.
• A scale of 1:1 implies that the drawing of the
grasshopper is the same as the actual object.
• The scale 1:2 implies that the drawing is
smaller (half the size) than the actual object
(in other words, the dimensions are multiplied
by a scale factor of 0.5).
• The scale 2:1 suggests that the drawing is
larger than the actual grasshopper -- twice as
long and twice as high (we say the dimensions
are multiplied by a scale factor of 2).
• If no units are listed in the scale, then you can
assume that the drawing and the object are
measured using the same units. For example,
the scale 1:2 might represent 1 cm:2 cm or 1
in.:2 in.
Teacher’s Domain videos
Island of the Little (48 s)
Island of the Giants (3min 33s)
• Scale drawing/scale model: is used
to represent an object that is too
large or too small to be drawn or built
at actual sizes
• Scale: gives the relationship between
the measurements on the drawing or
model and the measurements of the
real object
• Scale factor: the ratio of a length on a
scale drawing or model to the
corresponding length on the real
• Rates are often written with a slash
rather than the word per:
– such as mi/h for miles per hour
– $2/dozen for $2 per dozen
– a car traveling 30 miles per hour
– making a long-distance telephone call that
costs 20¢ per minute
– skating at an ice rink that costs $10 for 2
A statement that shows two ratios are
• A proportion is often used when one
ratio is known and only part of a second
ratio is known, such as:
“The ratio of girls to boys in a class is 6:8
and there are 12 boys in the class.” A
proportion can be set up and solved to
find how many girls there are in the
• Set up the proportion.
Solving Proportions
_6_ = _X_
cross multiply:
6 x 12 = 8 x X
72 = 8x
isolate the variable:
72 = 8x
8 8
X = 9 girls
By using proportions, you can find
lengths needed to make a scale drawing
or can find the actual lengths of an
object based on a given scale drawing.
map scales
• If 1 cm on a map represents a distance
of 250 km, what is the approximate
distance of a length represented by 2.7
cm? We can set up a proportion to show:
1 cm = 2.7cm
250 km
• Solving the equation for x, we get
x = 250 • 2.7 = 675 km.
3 ways scale can be expressed
1. 1 cm = 1 km
2. ______ = 1 km
3. 1: 50,000
Practice Problem
• A student has a map on which
the scale is 2 cm = 5 km. Having
measured the distance between
two points on the map to be
7.5 cm how do you calculate the
real world distance from this
Scale Factor
Example: Suppose a scale model has a scale of
2 inches = 16 inches. The scale factor is
2 or 1
The lengths and widths of objects of a scale
drawing or model are proportional to the
lengths and widths of the actual object.
Your Turn, Again!
In an illustration of a honey bee, the length of the
bee is 4.8 cm. The actual size of the honeybee is
1.2 cm. What is the scale of the drawing?
4.8 cm = 1cm
1.2 cm x cm
4.8x = 1.2
x = .25
The scale of the drawing is 1 cm = .25cm
Example 1: Find Actual Measurements
A set of landscape plans shows a flower bed that is
6.5 inches wide. The scale on the plans is 1 inch =
4 feet.
What is the width of the actual flower bed?
Let x represent the actual width of the flower bed.
Write and solve a proportion.
Plan width----> 1 inch = 6.5 inches<---plan width
Actual width--> 4 feet x feet <-----actual width
1x = 46.5 cross products
x= 26 The actual flower bed width is
26 feet.
From the last example, what is the
scale factor?
To find the scale factor, write the ratio of 1 inch
to 4 feet in simplest form.
1inch = 1 inch
Convert 4 feet
4 feet 48 inches to inches
The scale factor is 1 . That is , each
measurement on the plan is 1 the actual
Example 2: Determine the Scale
In a scale model of a roller coaster, the highest hill
has a height of 6 inches. If the actual height of
the hill is 210 feet, what is the scale of the model?
Model height---> 6 inches = 1 inch <--model height
Actual height--->210 feet x feet <--actual height
6x = 210
6x = 210 x= 35
6 So, the scale is 1” =
35 feet
Your Turn!
On a set of architectural drawings for an office building,
the scale is 1/2” = 3 feet. Find the actual length of
each room.
.5” = 2”
Lobby: 2 inches
3ft x ft
.5x = 6
x = 12
The actual length
of the lobby is 12 ft
Cafeteria: 8.25 inches
.5” = 8,25”
3ft x ft
.5x = 24.75
x = 49.5
The actual length of the
cafeteria is 49.5 feet
Practice Problem
A mural of a dog was painted on a wall. The
enlarged dog was 45 ft. tall. If the average
height for this breed of dog is 3 ft., what is the
scale factor of this enlargement? Can you
express this scale in more than one way?
• The scale factor is 45:3. This can be simplified
to 15:1 or expressed in other ways, such as
Make a scale map of your desk
Place three or four objects on their desk.
Orient the objects parallel to the edges of the desk.
Use a 1:10 scale, with 1 cm on the map representing 10 cm of the desk
To help students appreciate what the scale is doing and how the
numbers are used in calculating, the teacher may give students a
10 cm × 25 cm rectangle of paper to be one of the objects on the
desk. This gives students one object for which it is easy to work out
what the scaled version is; they may be able to generalize this to
their other objects with more awkward dimensions. A second map
using a different scale could then be produced, perhaps 2 cm = 5 cm
(which is 1:2.5).
Graph paper may help students in drawing their maps.

similar documents