Scale Factors
Terminal Objective
Given the volume of a prism in which the
dimensions have been multiplied by a scale
factor, students will be able to accurately
determine the new volume without using
a formula.
Content Standard Reference:
Grade 7
Measurement & Geometry
2.3
Compute the length of the
perimeter, the surface area of the
faces, and the volume of a threedimensional object built from
rectangular solids. Understand
that when the lengths of all
dimensions are multiplied by a
scale factor, the surface area is
multiplied by the square of the
scale factor and the volume is
multiplied by the cube of the scale
factor.
Materials
1. Centimeter cubes
2. Box
3. Scale Factors PowerPoint
Time Required
1 class
scale factors
| 23
Scale Factors Lesson 3
Lesson three
Introduction of Lesson
Anticipatory Set:
Students will be asked to find the volume of a
triangular prism and rectangular prism.
Student Objective:
Scale Factors Lesson 3
Given a prism with its dimensions multiplied by a
scale factor, you will find the new volume without
using a formula.
Purpose:
• Architects and engineers need to know the effect
of scale factors on volume when they make scale
models of buildings.
• Shippers who come through the Port of Long
Beach may need to know the effect of scale factors
on volume when they load cargo ships.
Lesson
Keyword
1. Scale
factor - A number that
multiplies a quantity.
Input
Describe a scale factor. A scale factor is a number
that multiplies a quantity.
Modeling
Fill a box with centimeter cubes and show the
students what a scale factor is. Ask students to
predict the number of cubes that would be needed
if the dimensions of the box were doubled. Use the
cubes to find the volume of the new box.
24 | scale factors
Lesson cont’d
Check for Understanding
Ask the students to write a description of a scale
factor in their own words. Students will share
their descriptions with their partner and the
teacher will randomly call on members of each
pair to share with the class.
Input
Scale Factors Lesson 3
Students will use a table to explore the effects of
scale factors on rectangular prisms.
Modeling
We know that the volume of a 40 foot container is
2,752 ft3. What do you suppose would happen to
the volume if we multiplied the length, width and
height by a scale factor of 2? Or by a scale factor of
3? Or by a scale factor of 4?
Complete the table when multiplying the
dimensions by a scale factor of 2.
hx2
lx2
wx2
Original
x2
x3
x4
x5
Length Width Height
Volume
40
80
2,752 ft3
22,016 ft3
8
16
8.6
17.2
Volume compared
to original
Same
23 or 8 times
larger
scale factors
| 25
Lesson cont’d
Scale Factors Lesson 3
Now, multiply the original dimensions by a scale
factor of 3 and complete the table.
Length
Width Height Volume Volume
compared
to
original
Original
x2
40
80
8
16
8.6
17.2
2,752 ft3
22,016
ft 3
Same
x3
120
24
25.8
74,304
ft3
33 or 27
times
x4
x5
23 or 8
times
larger
Let’s complete the entire table.
Length
Width Height Volume Volume
compared
to
original
Original
x2
40
80
8
16
8.6
17.2
2,752 ft3
22,016
ft3
Same
x3
120
24
25.8
74,304
ft3
x4
160
32
34.4
176,128
ft3
33 or 27
times
x5
200
40
43
344,000 53 or 125
ft3
times
larger
Check for Understanding
23 or 8
times
larger
43 or 64
times
larger
Display five true/false questions. Students will
answer by giving a “thumbs up” if the statement is
true and a “thumbs down” if the statement is false.
1. Whenever the length, width, and height are
multiplied by a scale factor of 2, the original volume is multiplied by 23.
26 | scale factors
Answer: True
Lesson cont’d
2. Whenever the length, width, and height
are multiplied by a scale factor of 3, the
original volume is multiplied by 34.
Answer: False
Scale Factors Lesson 3
3. Whenever the length, width, and height
are multiplied by a scale factor of 23, the
original volume is multiplied by 232.
Answer: False.
4. Whenever the length, width, and height
are multiplied by a scale factor of 54, the
original volume is multiplied by 543.
Answer: True.
5. Whenever the length, width, and height
are multiplied by a scale factor of x, the
original volume is multiplied by x3.
Answer: True.
Input
Students will use a table to explore the effects
of scale factors on triangular prisms.
5f
4f
5f
14f
6f
scale factors
| 27
Lesson cont’d
Modeling
Show how to complete the table when multiplying
the dimensions by a scale factor of 2.
Scale Factors Lesson 3
Base
Height Height Volume Volume
of the
of the
of the
compared
triangle triangle prism
to
original
Original
x2
6
12
4
8
14
28
168 ft3
1,344 ft3
x3
x4
x5
Same
23 or 8
times
larger
Show how to complete the table when multiplying
the dimensions by a scale factor of 2, 3, 4 and 5.
Base
Height Height Volume Volume
of the
of the
of the
compared
triangle triangle prism
to
original
Original
x2
6
12
4
8
14
28
168 ft3
1,344 ft3
x3
18
12
42
x4
24
16
56
x5
30
20
70
4,536 ft3 33 or 27
times
larger
10,752
43 or 64
ft3
times
larger
21,000
53 or 125
ft3
times
larger
Check for Understanding
Same
23 or 8
times
larger
Display five true/false questions. Students will
answer by giving a “thumbs up” if the statement is
true and a “thumbs down” if the statement is false.
28 | scale factors
Lesson cont’d
1. The volume of a triangular prism is 100m3. If
the dimensions are multiplied by a scale factor
of 2, the new volume will be 800m3.
Answer: True.
Scale Factors Lesson 3
2. The volume of a triangular prism is 310 ft3. If
the dimensions are multiplied by a scale factor
of 2, the new volume will be 620 ft3.
Answer: False.
3. The volume of a rectangular prism is 10 km3. If
the dimensions are multiplied by a scale factor
of 4, the new volume will be 270 km3.
Answer: False
4. Th
e volume of a rectangular prism is 21 yd3. If
the dimensions are multiplied by a scale factor
of 3, the new volume will be 567 yd3.
Answer: True
5. The volume of a rectangular prism is 50 m3. If
the dimensions are multiplied by a scale factor
of x, the new volume will be 50x3 m3.
Answer: True
Guided Practice
Display the following problems:
1. Suppose the volume of a rectangular prism is 40
ft3. Find the new volume, if the dimensions are
multiplied by a scale factor of 3.
Answer: 1,080 ft3
scale factors
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Lesson cont’d
2. Suppose the dimensions of a triangular prism
are multiplied by a scale factor of 2 and the new
volume is 432 cm3. What was the original volume?
Answer: 54 cm3
Scale Factors Lesson 3
3. Suppose the original volume of a triangular
prism is 120 m3 and the new volume is 3,240 m3.
What scale factor were the dimensions multiplied by?
Answer: 3
Partners will be asked to check each other’s work.
Closure
Students will be asked to write a brief explanation
of what would happen to the volume of a triangular
prism if the dimensions were multiplied by a scale
factor. Students will share their responses with
their partner and several students will be selected
to share with the class.
30 | scale factors
Worksheet
Lesson three
Scale Factors
Scale Factors Lesson 3
Solve
Using scale factors for rectangular prisms.
Base
Height Height Volume Volume
of the
of the
of the
compared
triangle triangle prism
to
original
Original
x2
x3
x4
x5
40
8
8.6
2,752 ft3
Same
Using scale factors for triangular prisms.
Base
Height Height Volume Volume
of the
of the
of the
compared
triangle triangle prism
to
original
Original
x2
x3
x4
x5
6
4
14
168 ft3
Same
scale factors
| 31