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 ID: 673094
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Slide1
Scale Factor &
Scale DrawingsSlide2
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 lengthFor maps the ratio is normally in the ratio:Map distance: Actual Distance
Example: 1cm : 100cmThe ratio 1cm:100cm means that for every 1cm on the scale drawing the length will be 100cm in real life
Example: 1:10000The ratio 1:10000 means that the real distance is 10000 times the length of one unit on the map or drawing.
Understanding ScalesSlide3
Scale FactorSlide4
When a figure is dilated, its size is changed by multiplying the length of each side by a
scale factor. All angles remain the same and so the new shape (or image) is similar to the original.Can be found by dividing a new side length by the original side length.
When going from a small shape to a larger shape the scale factor is greater than 1
. (Enlargement)
When going from a large shape to a smaller shape the scale factor is
less
than 1
. (Reduction)
Determine the corresponding side lengths.
Determine if you are making a larger shape or a smaller shape.Determine if the scale factor is greater than or less than 1.Write the correct ratio.
How to find Scale Factor
Slide5
Scale factor =
new measurement
old
measurement
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
Old measurement x SF = new measurement
SF
new
old
Scale
FactorSlide6
scale model
scale factorscale
scale drawing
VocabularySlide7
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!Slide8
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
87Slide9
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.Slide10
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?Slide11
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
160 feet
64 inches
160 x 12
64 inches
1920 inches
=
=Slide12
Now take the:
64 inches
1920 inches
And simplify
1/30 inches
This means that the person
was created 30 times his
normal size. Slide13
The scale factor of the pool is
1” to 20 yards.Or =
Scale FactorSlide14
Keep like
units in the same fraction.Inches = yardsInches yards
Setting up ProportionsSlide15
There is more than one way to set up a proportion correctly!
Cross Multiply!Use common sense!
Remember…Slide16
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?
Write a Proportion
Using
Scale FactorSlide17
¾ inch to 1 foot
If the length in inches is 2 ¼ inch, what would the actual length be in feet ?
Write a Proportion
Using a Scale FactorSlide18
Scale DrawingsSlide19
Scale Drawings
On Maps
Footprints of houses
Vehicle design
What are scale drawings?
Scale drawings are everywhere!
Can you think of any more? Slide20
Scale 1 cm = 1 m
6cm
Length of units = 6 m
5
Scale in everyday life: kitchen designSlide21
Scale 1 : 1 000 000
Scale in everyday life: mapsSlide22
Scale 2 cm = 1 m
pool
path
decking
7
Scale in everyday life: plansSlide23
Using
A
Scale DrawingSlide24
When
objects are too small or too large to be drawn or constructed at actualsize, people use a scale drawing or a model
.The scale drawing of this tree is 1:500If the height of the tree on paper is 20 inches, what is the height of the tree in real life?Slide25
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 inchesSlide26
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?
Map ScalesSlide27
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.
15 mi.
=
4 in
n
1n =
60
n = 60
The distance between the two cities is 60 miles.
Map Scales