Scale Drawings Math 7 McGraw Hill 5.7

Scale Drawings

Some text here about the topic of discussion

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Scale Drawings

Content Objective
Students will solve problems involving scale
drawings.

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Scale Drawings

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Warm Up

Solve each problem

1. Heath ran a 5-kilometer race. How many meters did he run?

2. Beckett is 48 inches tall. How many feet tall is she?

3. Two towns are 3 miles apart. How many feet apart are the towns?

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Scale Drawings

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Warm Up

Solve each problem

1. Heath ran a 5-kilometer race. How many meters did he run?

2. Beckett is 48 inches tall. How many feet tall is she?

3. Two towns are 3 miles apart. How many feet apart are the towns?

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Scale Drawings

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Scale drawings are models, maps, or diagrams that are
used to represent objects that are too large or too small to
be drawn or built at actual size.

The scale on a scale drawing gives the ratio that compares
the measurements of the drawing or model to the
measurements of the real object. The measurements on a
drawing or model are proportional to the measurements on
the object.

Learn
Scale Drawings

​p. 328

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Scale Drawings

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A scale written as a ratio without units in simplest form is called the
scale factor. The scale factor is the constant of proportionality
between the corresponding parts in the scale drawing and the
actual object. The scale factor is represented by the variable k.

To find the measurements in the scaled object, multiply the
corresponding part in the original object by k.

Learn
Scale Factor

​The numerator and denominator of the scale factor must be in the same units of measure so you may have to convert one of them.

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Scale Drawings

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Example 2
Use Length to Find the Scale Factor

Talk About It!

If the scale factor is 6, how many times larger is
the perimeter of the projection than the perimeter
of the paper?

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Scale Drawings

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Example 2
Use Length to Find the Scale Factor

Check

A scale model of a plane has a length of 20 centimeters. The
plane has an actual length of 85 meters. Find the scale factor.

​p. 329

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Scale Drawings

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Example 2
Use Length to Find the Scale Factor

Check

A scale model of a plane has a length of 20 centimeters. The
plane has an actual length of 85 meters. Find the scale factor.

​p. 330

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Scale Drawings

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Example 3
Use Scale Factor to Find Length

Check

An artist is drawing an illustration of a giraffe for a science book. His
illustration uses a scale factor of

1

24. If the actual height of the giraffe

is 17 feet, how many inches tall will the giraffe be in the book?

8.5 inches

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Scale Drawings

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Check

A model ship uses a scale factor of

1

200.

If the model is 1.8 inches long, what is the length of the actual ship in feet?

Example 4
Use Scale Factor to Find Length

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Scale Drawings

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Check

A model ship uses a scale factor of

1

200.

If the model is 1.8 inches long, what is the length of the actual ship in feet?

30 feet

Example 4
Use Scale Factor to Find Length

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Scale Drawings

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Example 5
Use Scale Factor to Find Area

Check

A volleyball court is 18 meters long by 9 meters wide. The coach’s
clipboard is a scale drawing of the court with a scale factor of

1

45.

What is the area of the coach’s clipboard in square centimeters?

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Scale Drawings

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Example 5
Use Scale Factor to Find Area

Check

A volleyball court is 18 meters long by 9 meters wide. The coach’s
clipboard is a scale drawing of the court with a scale factor of

1

45.

What is the area of the coach’s clipboard in square centimeters?

800 cm2

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Scale Drawings

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Apply
Construction

William is laying new flooring in a
storage shed. The blueprint of the floor
shown uses a scale of 1 inch = 3 feet. If
the building material costs $1.09 per
square foot, how much will it cost for the
new flooring? Round to the nearest cent
if necessary.

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Scale Drawings

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Apply
Construction

Talk About It!

What do you need to determine before you calculate the cost
of the flooring?

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Scale Drawings

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Apply
Construction

Talk About It!

What do you need to determine before you calculate the cost
of the flooring?

1. ​Change each measurement in the drawing to feet using the scale 1 in = 3ft.

2. Multiply the length times the width to find the area (square feet).

3. Multiply the square footage by the cost per foot($1.09/ft).

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Scale Drawings

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Apply
Construction

Check

Chantele is buying wallpaper for one wall of her
living room. The blueprint of the wall uses a scale
of 1 inch = 4 feet. If the wallpaper costs $1.79 per
square foot, how much will it cost to buy wallpaper
for the actual wall of the living room? Round to the
nearest cent if necessary.

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Scale Drawings

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Apply
Construction

Check

Chantele is buying wallpaper for one wall of her
living room. The blueprint of the wall uses a scale
of 1 inch = 4 feet. If the wallpaper costs $1.79 per
square foot, how much will it cost to buy wallpaper
for the actual wall of the living room? Round to the
nearest cent if necessary.

$225.54

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Scale Drawings

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Pause and Reflect

Compare what you learned about scale factors and
scale drawings in this lesson to concepts you learned
in an earlier module or grade. How did knowing those
concepts help you in this lesson?

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Scale Drawings

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Exit Ticket

When designing a new structure, architects make detailed drawings of
rooms, buildings, and even landscapes, called blueprints. Blueprints
are examples of scale drawings. The scale drawing helps the builder
determine placement of elements such as electrical outlets, windows,
doors, and trees. The blueprint shows that the height of the building is
22 feet. If the scale for the drawing is 1 centimeter = 2 feet, how tall is
the building represented in the blueprint? Write a mathematical
argument that can be used to defend your solution.

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Scale Drawings

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Exit Ticket

When designing a new structure, architects make detailed drawings of
rooms, buildings, and even landscapes, called blueprints. Blueprints
are examples of scale drawings. The scale drawing helps the builder
determine placement of elements such as electrical outlets, windows,
doors, and trees. The blueprint shows that the height of the building is
22 feet. If the scale for the drawing is 1 centimeter = 2 feet, how tall is
the building represented in the blueprint? Write a mathematical
argument that can be used to defend your solution.

11 cm; Sample answer: Write an equation:

1 cm

2ft=

𝑥 cm

22 ft. Solve the

equation to find that x = 11.