Scale, Scale Factors, and Scale Drawings

​5.1 Scales, scale factors, and scale drawings

Pay Attention, asks questions, participate!!!​

​Scale Factors

​A scale is a ratio that compares two measures. When you multiply a measure by a scale to produce a reduced or enlarged measure, the scale is called scale factor.​

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​Scale Factors

​To create an enlarged figure the scale factor has to be greater than 1.

To create a reduced figure the scale factor has to be less than 1.​

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​original

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​Enlarged Figure

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by a scale factor of 2.​

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Reduced

Figure by a scale factor

of .5

​scale factor:

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​Triangle A’s side

lengths are 200%

of Triangle B’s side

lengths. But they are

100% larger.

​SF= NEW

OLD​

​SF: NEW

OLD​

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Fill in the Blank

What scale factor is used to produce:

Triangle C’s lengths, given Triangle B’s lengths?

Fill in the Blank

What scale factor is used to produce:

Triangle B’s lengths, given Triangle C’s lengths?

Fill in the Blank

What scale factor is used to produce:

Triangle C’s lengths, given Triangle A’s lengths?

​Scale Drawing:

A scale drawing is a representation of a real object or place that is in

proportion to the real object or place it represents. The purpose of a

scale drawing is to represent either a very large or very small object.

The scales on scale drawings often use different units of measure.​

Subject | Subject

Fill in the Blank

Study the Worked Example. What scale factor is used

to produce:

a. the drawing length given the actual length?

Fill in the Blank

Study the Worked Example. What scale factor is used

to produce:

b. the map distance given the actual distance?

Subject | Subject

​6. Write a sentence to describe the meaning of each.

a. A scale on a map is 1 in. : 2 mi.

Subject | Subject

​6. Write a sentence to describe the meaning of each.

a. A scale on a map is 1 in. : 2 mi.

​For every 1 inch on the map there are 2 miles of actual distance.

Subject | Subject

​6. Write a sentence to describe the meaning of each.

b. A scale on a drawing is 1 cm : 4 cm.

Subject | Subject

​6. Write a sentence to describe the meaning of each.

b. A scale on a drawing is 1 cm : 4 cm.

​For every 1 centimeter of length on the drawing there are 4 centimeters of length on the actual object.

Open Ended

6. Write a sentence to describe the meaning of each.

c. A scale on a drawing is 2 in. : 1 in.

Open Ended

6. Write a sentence to describe the meaning of each.

d. A scale on a drawing is 1 cm : 1 cm.

Multiple Choice

The scale factor for a model car is 1:24. What does this mean?

• The model car is 24/1 the size of an actual car. An actual car is 1 time the size of the model car.

• The model car is 1/ 24 the size of an actual car. An actual car is 24 times the size of the model car

Multiple Choice

8. The scale factor for a model train is 1 : 87. What does this mean?

• The model car is 87/1 the size of an actual car. An actual car is 1 time the size of the model car.

• The model train is 1 /87 the size of an actual train. An actual train is 87 times the size of the model train.

​5.2 Similar Figures

Figures that are proportional in size, or that have proportional dimensions, are called similar figures.​

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When Timmons Photo Company prints photo packages, they include several sizes of photos that are all mathematically similar. The largest size is 12 in. 3 16 in. This is read as “12 inches by 16 inches.” The first measure is the width of the photo, and the second measure is the height of the photo.

Fran and Joe determined the width of a mathematically similar photo that has a height of 8 inches.

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​Similar Figures:

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​1. What is similar about the two solution methods? What is

different about the two solution methods?

​Scale Drawing:

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​​Given ▲EFG is similar to ▲JKL What is the measurement for JK?

Multiple Choice

Given ▲TOP is similar to ▲MAN. What is the measurement for TP?

• 7.11 inches

• 4.25 inches

• 17 inches

• 514.25 inches

​Scale Drawing:

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​​Given ▲MAP is similar to ▲MRS What is the measurement for MA?

Multiple Choice

Given ▲MAP is similar to ▲MRS What is the measurement for MA?

• 10 cm

• 6.4 Centimeters

• 22.5 Centimeters

Open Ended

Closing Question:

How do you find scale factor?