Looking at models and scale

1. Understanding Size
Models and Scale

2. Enlargement
scale factor
Reduction
Scale
Proportions
Scale Diagram/Model

3. Model
• Representation of something else
• Usually too big or too small to analyze
easily

4. Enlargement
To make something bigger
so that one can
analyze/observe the
details.

5. Reduction
To make an object small so
that one
can observe/analyze the
details.

6. map distance
ground distance
• In math, scale shows
the relationship
between two things
as well.
• With maps, it is
usually between a
distance measured
on the map and the
actual distance on
the ground.
map scale

7. I Can Solve Problems Using Scale
Drawings!
• We know about
scales at the
supermarket. They
measure weight.
• They show the
relationship between
how much you are
buying and how
much you have to
pay.

8. I Can Solve Problems Using Scale Drawings!
• We also know about
the scales we stand
on. They measure
our weight.
• They help to show
the relationship
between our health
and Grandma’s
potato salad last
week!

9. • A scale drawing
represents something
that is too large or too
small to be drawn at
its actual size.
• Maps and blueprints
are examples of
scale drawings.

10. All scale drawings must have a scale written on
them. Scales are usually expressed as ratios.
Normally for maps and buildings the ratio:
Drawing length: Actual length
For maps the ratio is normally in the ratio:
Map distance: Actual Distance
Example: 1cm : 100cm
The ratio 1cm:100cm means that for every 1cm on the scale
drawing the length will be 100cm in real life
Example: 1:10000
The ratio 1:10000 means that the real distance is 10000
times the length of one unit on the map or drawing.

12. • Scale factor is the ratio of
change
• The number you multiply by
to relate the first shape to
the second is the scale
factor.

13. Scale factor = new measurement
old measurement
Old measurement x SF = new measurement
new
SF
old
- Scale factor more than 1 => shape gets bigger
(Enlargement)
- Scale factor less than 1 => shape gets smaller
(Reduction)
- Congruent shapes are similar shapes with SF = 1

14. • The scale can be written as a
scale factor, which is the ratio
of the length or size of the
drawing or model to the length
of the corresponding side or
part on the actual object.
• Scale Factor needs to be the
SAME UNITS!

15. 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
1
gauge model train is 87 .
1
This means that each dimension of the model is
87
of the corresponding dimension of the actual
train.

16. 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.

17. If you have ever seen Jurassic
Park, you saw how big the
dinosaurs were compared to the
people. Pretend that they made
a large Human to watch over the
animals. What would be the scale
factor if a 64 inch person was
made to be 160 feet?

18. The scale factor tells you
how many times bigger than
“normal” that person really is.
You must make all units of
measure the same….
64 inches 64 inches 64 inches
=
=
160 feet 160 x 12 1920 inches

19. Now take the:
64 inches
1920 inches
And simplify
1/30 inches
This means that the person
was created 30 times his
normal size.

20. 

21. Keep like
units in the
same
fraction.
Inches =
yards
Inches
yards

22. • There is more than
one way to set up a
proportion correctly!
• Cross Multiply!
• Use common
sense!

23. • Tom is drawing a blueprint for a
rectangular shed he wants to build.
The scale factor is 1 ft. to ¼ inch. If
the dimensions of the blueprint are 1 ¼
in. by 2 inches, what are the actual
dimensions of the shed going to be?

24. • If the length in inches is 2
¼ inch, what would the
actual length be in feet ?
¾ inch to 1 foot

26. Scale
Drawings
On
Maps
Vehicle
design
Footprints of
houses

27. 6cm
Scale 1 cm = 1 m
Length of units = 6 m
5

28. Scale 1 : 1 000 000

29. • The blueprint of the
pool shows each
square has a side
length of ¼ inch.
• If the scale is written
as ¼ in = 2 ft, what is
actual width of the
pool?
– (To figure this out, what
else do you need to
know?)

30. decking
pool
path
Scale 2 cm = 1 m
7

32. When objects are too small or too large to be
drawn or constructed at actual
size, people use a scale drawing or a model.
The scale drawing of this tree is 1:500
If the height of the tree on paper is 20
inches, what is the height of the tree in real
life?

33. The scale is the relationship between the
measurements of the drawing or model to
the measurements of the object.
In real-life, the length of this van may
measure 240 inches. However, the length
of a copy or print paper that you could use
to draw this van is a little bit less than 12
inches

34. • Map Scales (Legends) are
used to find distances on a
map.
• For example, if your map
legend tells you that ½ of an
inch represents 50 miles, how
could you find the mileage for
a 2 inch distance on the map?

35. Ratios and proportions can be used to
find distances using a scale.
Example:
1 inch = 15 miles
The distance from Jacksonville to Smithtown on a map
is 4 inches. How many miles are between these cities?
1 in. = 4 in
15 mi.
n
The distance between
1n = 60
n = 60
the two cities is
60 miles.

36. • Suppose the distance
between Coral
Springs and Fort
Lauderdale is about
4.1 centimeters on
the map.
• What is the actual
distance on the
ground if the scale is
1 cm = 4.5 km?
map distance
map scale
ground distance

37. • Use the scale as a
fraction.
• Use cross-products to
calculate.
1 centimeter
4.5 kilometers
Distance
Distance
4.1 cm
? km
1x ?
4.5 x 4.1
18.45 km

38. I Can Solve Problems Using Scale Drawings!
• Width of the pool on
the blueprint = 1.75
inches.
• How can you use
cross products to
figure out how wide
the pool really is?

39. I Can Solve Problems Using Scale Drawings!
1/4 inch
2 feet
1 3/4 inches
? feet
1/4 x ?
2 x 1 3/4
1/4 x ?
14/4
Width of pool
14 feet

40. I Can Solve Problems Using Scale Drawings!
(SOL 7.6)
• You can convert the
units in a scale to
simplify it.
• When you do that,
you end up with a
scale factor.
• It is a ratio written in
its simplest form.
1/4 inch
2 feet
1/4 inch
24 inches
4
1/4 inch
x
4
24 inches
Scale factor
1
96
1
or 1 : 96
96

41. I Can Solve Problems Using Scale Drawings!
• 1) Find the scale factor of the blueprint of
a school bus parking lot if the scale is
written as “1 inch = 8 feet”.
• 2) On a scale drawing of a new classroom,
the scale is 1 centimeter = 2.5 meters.
What is the scale factor?

42. I Can Solve Problems Using Scale Drawings!
• 1) Scale factor = 1/96. That means that
each measurement on the blueprint is
1/96th of the actual measurement of the
parking lot.
• 2) 1 centimeter / 2.5 meters:
= 1 cm / (2.5 m x 100) cm
= 1 cm / 250 cm
= 1/250

43. I Can Solve Problems Using Scale Drawings!
• If you know the actual length of an object
and you know the scale, you can build a
scale model.
• Scale models are used to represent
things that are too large or too small for an
actual-size model.
• Examples are cars, planes, trains, rockets,
computer chips, heart cells, bacteria.

44. I Can Solve Problems Using Scale Drawings!
• Designers are creating a larger model of a
computer memory board to use in design
work. The board measures 5 ¼ inches in
length.
• If they use a scale of 20 inches = 1 inch,
what is the length of the model?
20 inches
? inches
1
20 5
1 ?
1 inch
5 1/4 inches
4
Model length 105 inches

45. I Can Solve Problems Using Scale Drawings!
• Things to remember:
– When solving proportions, give your answer in
the correct unit of measurement.
– Scale factors do not have units.
– Equivalent scales have the same scale factor.
• For example 1 inch = 8 feet and ¼ inch = 2 feet both
equal 1/96 (or 1:96)
– Scale is the ratio between the drawing/model
measurement to the actual measurement.
• Not always the ratio of smaller to larger!