Scale Factor and Scale Drawings

7th Grade: Introduction to Scale Factor

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​Identifying the Scale Factor between a figure and the scale drawing of that figure.

​​The Unit Rate as the Scale Factor

What is SCALE FACTOR?

• ​A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

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• The scale factor can be calculated from the ratio of any length in the scale drawing to its corresponding length in the actual figure. The scale factor corresponds to the unit rate and the constant of proportionality. Scaling by factors greater than 1 enlarges the segment, and scaling by factors less than 1 reduces the segment.

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​TYPES OF SCALE DRAWINGS

• If the scale drawing is LARGER than the original, then it is an enlargement.

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• If the scale drawing is SMALLER than the original, then it is a reduction.

​Steps to check for proportionality for scale drawing and original object or picture

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1. ​Create a table and record the lengths of the scale drawing on the table.

2. ​Record the corresponding lengths of the actual/original object or picture on the table.

3. ​Check for constant of proportionality by dividing scale drawing lengths by the original lengths.

Multiple Choice

If the scale factor is less than one, the new figure will be...

• an enlargement

• bigger

• a reduction

• a scale factor

Multiple Choice

If the scale factor is greater than one, the new figure will be...

• an enlargement

• a reduction

• a scale

• not proportional

Multiple Choice

Scale factor of 1/4 is ...

• enlargement

• reduction

Multiple Choice

Scale factor of 4 is ...

• enlargement

• reduction

Multiple Choice

What are corresponding parts?

• parts of a triangle

• another word for the perimeter of a shape

• parts of a square

• lines, points, and angles that are the same value or place on a shape

Multiple Choice

If you want to find the scale factor from one figure to another, which formula should you use?

• old/ new

• drawing / actual

• actual / model

Multiple Choice

What is the scale factor?

• 3

• 1/3

• 5

• 10

Multiple Choice

What is the scale factor from the large triangle to the small triangle?

• 1/2

• 2/3

• 3/4

• 2

Multiple Choice

Are the following similar? Why or why not?

• Yes, the sides are 2 times larger than the original

• No, one pair of corresponding sides are 2 times larger, but the other is the same length

• Yes, because the corresponding sides are the same length

• No, the numbers are even

Fill in the Blanks

Matching parts are called

parts.

Multiple Choice

On a map, the distance between Louisville, Kentucky, and Nashville, Tennessee, is 1 3/4 inches. The scale of the map is 1 in:100 mi. What is the actual distance between the two cities?

• 200 miles
• 175 miles
• 100 miles
• 125 miles

Multiple Choice

A model of a house was built using the scale 5 in:25 ft. If a window in the model is 1.5 in. wide, how wide is the actual window?

• 90 ft
• 7.5 ft 
• 4.5 ft
• 45 in

Multiple Choice

Maura is building a 2 ft. tall model of the Gateway Arch in St. Louis, Missouri.  The scale is 3 in : 78.75 ft.  Estimate the height of the actual arch.

• 630
• 600
• 400
• 200

Multiple Choice

From Denver to Chicago = 3 in. If the scale is 1 in = 300 miles, find the actual distance.

• 300 miles
• 1000 miles
• 900 miles
• 600 miles

Multiple Choice

This scale drawing shows a parking lot. What is the length of the longer side of the actual lot? 

• 63 m
• 235 m
• 315 m
• 630 m

Multiple Choice

Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?

• 14 in 
• 7 in
• 42 in
• 56 in

Multiple Choice

A model of a house was built using the scale 5 in:25 ft. If a window in the model is 1.5 in. wide, how wide is the actual window?

• 90 ft
• 7.5 ft 
• 4.5 ft
• 45 in

Multiple Choice

The __________ is the ratio of a length of the image to the corresponding length on the original figure.

• reduction
• enlargement
• scale factor
• center of dilation

Multiple Choice

The scale model of a building is 6.5 inches tall. How tall is the actual building if the scale used for the model is 1 inch = 150 feet?

• 650 feet
• 840 feet
• 900 feet
• 975 feet

Multiple Choice

A blueprint was using a scale of 3cm=4.5m. Find the actual length if it is 5cm on the drawing.

• 7.5
• 13.5
• 1.5
• 1.7

Multiple Choice

A scale drawing of a house shows 9cm ×10cm. If 6cm=12 ft, what are the actual dimensions?

• 9ft x 10ft
• 1ft x 2ft
• 12ft x 6ft
• 18ft x 20ft