Transcript Unit 6: Scale Factor and Measurement

Unit 6: Scale Factor and
Measurement
How will you measure up?
6x = 84
y = 25
5
What am I Learning Today?
Scale Factor and Scale Drawing
How will I show that I learned it?
Demonstrate the relationship between similar
plane figures
Read and use map scales
Interpret and sketch simple scale drawings
Solve problems involving scale drawings
What do these things have in
common?
Vocabulary
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Scale: The ratio of a set of measurements
Scale factor: The number by which each
side of the original object is multiplied to
find the corresponding side of the model.
Scale drawing: A drawing of a real object
that is proportionally smaller or larger
than the real object
Visualizing Vocabulary
The map shown is a scale
drawing. A scale drawing is a
drawing of a real object that is
proportionally smaller or larger
than the real object. In other
words, measurements on a
scale drawing are in proportion
to the measurements of the
real object.
A scale is a ratio between two sets of measurements.
In the map above, the scale is 1 in:100 mi. This ratio
means that 1 inch on the map represents 100 miles.
Scale Factor
The scale factor for Hot
Wheels®
cars is 64:1.
The scale factor is 4.
Questions
Answers
What is scale
factor?
The number used to proportionately enlarge or
reduce an object based on the ratio of the length of
one pair of corresponding sides.
How do I use
scale factor?
1) Write a proportion: One ratio should represent
the scale and the other should represent the
actual measurements.
2) Solve for the missing piece of information
http://www.thefutureschannel.com/dockets/hands-on_math/designing_toy_cars/
The scale on a map is 4 in: 1 mi. On the
map, the distance between two towns
is 20 in. What is the actual distance?
4 in. _____
20 in.
____
1 mi = x mi
1 • 20 = 4 • x
20 = 4x
20 =
___
4
5=
4x
___
4
x
5 miles
Write a proportion using the scale.
Let x be the actual number of
miles between the two towns.
The cross products are equal.
x is multiplied by 4.
Divide both sides by 4 to undo
multiplication.
HINT: Think “4 inches is 1 mile, so 20 inches
is how many miles?” This approach will help
you set up proportions in similar problems.
Now Try This!!
On a map of the Great Lakes, 2 cm = 45 km.
Find the actual distance of the following,
given their distances on the map.
1. Detroit to Cleveland = 12 cm
270 km
2. Duluth to Nipigon = 20 cm
450 km
3. Buffalo to Syracuse = 10 cm
225 km
4. Sault Ste. Marie to Toronto = 33 cm 742.5 km
Is the Statue of Liberty’s nose too long?
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Can we assume that the
Statue of Liberty is
similar in scale to an
average person?
Would it be true that the
lengths of corresponding
body parts should have
the same ratio?
Typically your nose is 1/8
the length of your arm,
which is the scale factor.
Is the Statue of Liberty’s nose too long?
Using a proportion, determine
the length of the Statue of
Liberty’s nose if her arm is 42
feet long.
nose = Lady Liberty’s nose
arm
Lady Liberty’s arm
 Lady Liberty’s nose, if
proportionate, should be 5 1/4
feet long.
 How long is it?
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4 1/2 feet long
Practice
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Page 378
Use the floor plan of the house to find the
dimensions of the following rooms. Give length
and width of each room in feet:
Living Room
Bedroom #1
Bedroom #2
Bathroom
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Hall
Kitchen
Length of house
Width of house