Volume of
Rectangular Prisms
Objective To provide experiences with using a formula
ffor the volume of rectangular prisms.
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Key Concepts and Skills
Math Boxes 9 8
• Use formulas (l ∗ w ∗ h or B ∗ h) to
calculate the volumes of rectangular prisms. Math Journal 2, p. 323
Students practice and maintain skills
through Math Box problems.
[Measurement and Reference Frames Goal 2]
• Define the base and height of a rectangular
prism. [Geometry Goal 2]
Ongoing Assessment:
Recognizing Student Achievement
• Explore the properties of rectangular
prisms. [Geometry Goal 2]
Use Math Boxes, Problem 3. • Write number sentences with variables
to model volume problems. Study Link 9 8
[Patterns, Functions, and Algebra Goal 2]
Key Activities
Curriculum
Focal Points
[Number and Numeration Goal 5]
Math Masters, p. 279
Students practice and maintain skills
through Study Link activities.
Students discuss the difference between
volume and area. They define base and height
for a rectangular prism and develop a formula
for the volume of a rectangular prism. Students
use a formula to find volumes and to model a
rectangular prism with a given volume.
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Analyzing Prism Nets for Cubes
Math Masters, pp. 280 and 429
Students investigate solid geometry
concepts using cube diagrams.
ENRICHMENT
Finding the Volume of One Stick-On Note
Math Masters, p. 281
per partnership: one stick-on note, pad of
unused stick-on notes, centimeter cube
Students compare the volume of a
single stick-on note to the volume of a
centimeter cube.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, pp. 52 and 214
Students calculate the volumes of prisms.
Ongoing Assessment:
Informing Instruction See page 751.
Key Vocabulary
volume cubic unit rectangular prism face base (of a rectangular prism) height
(of a rectangular prism) Associative
Property of Multiplication
Materials
Math Journal 2, pp. 321, 322, and Activity
Sheet 8
Student Reference Book, pp. 195–197
Study Link 97
scissors transparent tape 36 centimeter
cubes slate
Advance Preparation
For Part 1, make models of the open boxes on Activity Sheet 8 to illustrate where to fold and where to
tape the patterns for Boxes A and B. Have students save the boxes for use in Project 9.
Teacher’s Reference Manual, Grades 4–6 pp. 187–189, 222–225
Lesson 9 8
747
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8
Content Standards
Getting Started
5.NBT.4, 5.NBT.7, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b
Mental Math and Reflexes
Math Message
Students practice rounding numbers. Have them write
their answers on their slates. Suggestions:
Write 2 questions that can be answered by reading
Student Reference Book, page 195.
Round 654 to the nearest hundred. 700
Round 4,654.97 to the nearest whole number. 4,655
Round 67.072 to the nearest tenth. 67.1
Round 3.452 to the nearest hundredth. 3.45
Round 67% of 100 to the nearest ten. 70
Round 8.006 to the nearest tenth. 8.0
Project Note
Study Link 9 7 Follow-Up
Ask volunteers to present the area formulas for a
triangle and for a parallelogram and the number
models they used to solve the Study Link Problems.
1 Teaching the Lesson
For more practice
finding the volume of
rectangular prisms, see
Project 9: Adding
Volumes of Solid
Figures.
▶ Math Message Follow-Up
(Student Reference Book, p. 195)
WHOLE-CLASS
DISCUSSION
ELL
Ask students to pose their questions for the class. Use the
questions and responses to discuss the difference between area
and volume. To support English language learners, write the key
ideas on the board. Emphasize the following points:
Shapes that are 2-dimensional are flat. The surfaces they
enclose take up a certain amount of area, but they do not have
any thickness, so they do not take up any space.
Shapes that are 3-dimensional have length, width, and
thickness, so they enclose a certain amount of space.
Student Page
Measurement
The amount of surface inside a 2-dimensional shape is the area
of the shape. Area is measured in square units, such as square
inches, square feet, square centimeters, and so on.
Volume and Capacity
The amount of space enclosed by a 3-dimensional shape is the
volume of the shape. Volume is measured in cubic units,
such as cubic inches, cubic feet, cubic centimeters, and so on.
Volume
The volume of a solid object such as a brick or a ball is a
measure of how much space the object takes up. The volume
of a container such as a freezer is a measure of how much
the container will hold.
Volume is measured in cubic units, such as cubic inches
(in.3), cubic feet (ft3), and cubic centimeters (cm3). It is easy
to find the volume of an object that is shaped like a cube or
other rectangular prism. For example, picture a container
in the shape of a 10-centimeter cube (that is, a cube that is
10 cm by 10 cm by 10 cm). It can be filled with exactly 1,000
centimeter cubes. Therefore, the volume of a 10-centimeter
cube is 1,000 cubic centimeters (1,000 cm3).
1 cm
Capacity
We often measure things that can be poured into or
out of containers such as liquids, grains, salt, and so
on. The volume of a container that is filled with a
liquid or a solid that can be poured is often called its
capacity.
Capacity is usually measured in units such as
gallons, quarts, pints, cups, fluid ounces, liters,
and milliliters.
The tables at the right compare different units of
capacity. These units of capacity are not cubic units,
but liters and milliliters are easily converted to
cubic units:
1 milliter = 1 cm3
1 liter = 1,000 cm3
1,000 cm
3
height
h
dt
To find the volume of a rectangular prism, all you need to
know are the length and width of its base and its height.
The length, width, and height are called the dimensions
of the prism.
You can also find the volume of another solid, such as a
triangular prism, pyramid, cone, or sphere, by measuring
its dimensions. It is even possible to find the volume of
an irregular object such as a rock or your own body.
3
length
wi
The dimensions of a
rectangular prism
U.S. Customary Units
1 gallon (gal) = 4 quarts (qt)
1 gallon = 2 half-gallons
1 half-gallon = 2 quarts
1 quart = 2 pints (pt)
1 pint = 2 cups (c)
1 cup = 8 fluid ounces (fl oz)
1 pint = 16 fluid ounces
1 quart = 32 fluid ounces
1 half-gallon = 64 fluid ounces
1 gallon = 128 fluid ounces
Metric Units
1 liter (L) = 1,000 milliliters (mL)
1
1 milliliter = _
1,000 liter
1 liter = 1,000 cubic centimeters
1 milliliter = 1 cubic centimeter
Student Reference Book, p. 195
182_214_EMCS_S_SRB_G5_MEA_576515.indd 195
748
Unit 9
3/8/11 5:00 PM
Coordinates, Area, Volume, and Capacity
The symbol used to indicate square units is the abbreviation of
the unit name with a superscript 2, for example, in2, ft2, cm2,
m2, and so on. For cubic units, the symbol is the abbreviation of
the unit name with a superscript 3, for example, in3, ft3, cm3,
m3, and so on. To support English language learners, discuss
the meanings of the word volume. Students might have
heard the word used in contexts involving sound level or a book.
Emphasize that volume is also used in the mathematical
context involving 3-dimensional shapes.
Student Page
▶ Defining Base and Height
WHOLE-CLASS
DISCUSSION
for Rectangular Prisms
ELL
Date
Time
LESSON
Rectangular Prisms
9 8
A rectangular prism is a geometric solid enclosed by six flat surfaces formed by
rectangles. If each of the six rectangles is also a square, then the prism is a cube. The
flat surfaces are called faces of the prism.
(Math Journal 2, p. 321)
Bricks, paperback books, and most boxes are rectangular prisms. Dice and sugar
cubes are examples of cubes.
Below are three different views of the same rectangular prism.
As a class, read the introduction on journal page 321. Have
students study the figures and then write their own definitions for
the base and height of a rectangular prism. Ask volunteers to
share their definitions with the class. Use their responses to
reinforce the following points:
A rectangular prism is formed by six flat surfaces, or faces,
that are rectangles. To support English language learners,
compare the common meaning and the mathematical meaning
of the word face.
height
height
12
height
base
6
12
3
base
6
1.
3
6
base
12
3
Study the figures above. Write your own definitions for base and height.
Sample answer: Any face of the
prism; usually the face the prism sits on
Height of a rectangular prism: Sample answer: The shortest
distance between the base and the opposite face
Base of a rectangular prism:
Examine the patterns on Activity Sheet 6. These patterns will be used to construct
open boxes—boxes that have no tops. Try to figure out how many centimeter cubes
are needed to fill each box to the top. Do not cut out the patterns yet.
Answers vary.
2.
I think that
centimeter cubes are needed to fill Box A to the top.
3.
I think that
centimeter cubes are needed to fill Box B to the top.
Any of the six faces of the prism can be a base, but the face
that the prism “sits on” is often chosen as a base.
The height (for a given base) is the shortest distance between
the base and the opposite face.
Math Journal 2, p. 321
292-332_EMCS_S_G5_MJ2_U09_576434.indd 321
2/22/11 5:18 PM
Links to the Future
The names and properties of prisms will be revisited in more detail in Unit 11.
There are two types of prisms, right and oblique. (See below.)
When the faces of a prism are all rectangles, it is a right
rectangular prism. When the faces are not all rectangles, it is an
oblique rectangular prism. Oblique prisms are not considered in
Fifth Grade Everyday Mathematics.
Right rectangular prism
NOTE You may want to remind students
that to be a prism, a polyhedron must have at
least one pair of parallel and congruent faces,
which can be called bases. Rectangular
prisms have 3 pairs of parallel congruent
faces. Therefore, when calculating the
volume of a rectangular prism, any face can
be chosen as the base.
Oblique rectangular prism
Adjusting the Activity
ELL
Have students identify objects in the classroom that have the shape of
rectangular prisms.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
▶ Developing a Formula
for Volume
V I S U A L
WHOLE-CLASS
ACTIVITY
PROBLEM
PR
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VI
VIN
ING
(Math Journal 2, pp. 321, 322, and Activity Sheet 8;
Student Reference Book, pp. 196 and 197)
Algebraic Thinking Give 24 centimeter cubes to each student.
Ask students to tear out Activity Sheet 8 from the back of their
journals and follow the directions on journal page 321 to answer
Problems 2 and 3.
Lesson 9 8
749
When students have completed the problems, display your
prepared models as guides for folding and taping the boxes. Direct
students to do the following:
1. Cut out the pattern for Box A, fold it on the dashed lines, and
tape it to make an open box.
2. Cover the bottom of Box A with one layer of centimeter cubes.
Ask: How many cubes are in this layer? 8
3. Put a second layer of cubes on top of the first layer. Ask: How
many cubes are in the box now? 16
4. Put a third layer on top of the second layer. Ask: How many
cubes are in the box now? 24 What is the volume of the box?
24 cm3
5. Cut out the pattern for Box B, fold it on the dashed lines, and
tape it to make an open box.
6. Cover the bottom of Box B with one layer of cubes. Ask: How
many cubes are in this layer? 9
Ask students to answer the following questions without putting
any more cubes in the box:
NOTE Traditionally, linear measures are
represented in formulas by lowercase letters,
and 2- and 3-dimensional measures are
represented by uppercase letters. For
example, b is used to represent the length of
the base of a rectangle, and B is used to
represent the area of the base of a prism.
Time
LESSON
Volume of Rectangular Prisms
9 8
Write the formulas for the volume of a rectangular prism.
V = B ∗ h or V = l ∗ w ∗ h
height
B is the area of the base (l ∗ w ).
base
h is the height from that base.
V is the volume of the prism.
Find the volume of each rectangular prism below.
1.
2.
5 in.
6 cm
4 in.
3 cm
4 in.
4 cm
3
80 in
V=
3.
72 cm3
V=
(unit)
(unit)
4.
4 in.
6 in.
7 cm
8 in.
7 cm
7 cm
V=
343 cm3
V=
(unit)
5.
192 in3
(unit)
6.
5 ft
5 cm
3 ft
4 cm
6 ft
V=
2.5 cm
3
90 ft
V=
(unit)
50 cm3
(unit)
Math Journal 2, p. 322
292-332_EMCS_S_MJ2_G5_U09_576434.indd 322
750
Unit 9
How many layers of cubes are needed to fill the box? 5
●
How many centimeter cubes in all are needed to fill the box? 45
How did you find the answer? Sample answer: By multiplying
the number of cubes in 1 layer by the number of layers.
●
What is the volume of the box? 45 cm3
Point out that the number of cubes in one layer is the same as the
number of square centimeters in the base (l ∗ w), and that the
number of layers is the same as the height in centimeters of the
box. Ask students how this information might be used in a formula
to find the volume of the box. Multiply the area of the base by the
height of the box.
Student Page
Date
●
3/22/11 12:42 PM
Coordinates, Area, Volume, and Capacity
This formula is written as V = B ∗ h, where V represents the
volume, B represents the area of the base, and h represents the
height from that base. Ask students to write this formula at the
top of journal page 322. Have students refer to pages 196 and 197
of the Student Reference Book as needed.
Student Page
of a Rectangular Prism
(Student Reference Book, pp. 196 and 197)
Measurement
Volume of a Geometric Solid
You can think of the volume of a geometric solid as the total
number of whole unit cubes and fractions of unit cubes needed
to fill the interior of the solid without any gaps or overlaps.
Prisms and Cylinders
In a prism or cylinder, the cubes can be arranged in layers that
each contain the same number of cubes or fractions of cubes.
Ask students to review pages 196 and 197 of the Student Reference
Book. Give each student 12 more centimeter cubes so each student
has 36 cubes.
Find the volume of the prism.
Note
Volume = 24 cubic units
The height of a prism or cylinder is the shortest distance
between its bases. The volume of a prism or cylinder is the
product of the area of the base (the number of cubes in one
layer) multiplied by its height (the number of layers).
base
base
base
Pyramids and Cones
The height of a pyramid or cone is the shortest distance
between its base and the vertex opposite its base.
height
If a prism and a pyramid have the same size base and height,
then the volume of the pyramid is one-third the volume of the
prism. If a cylinder and a cone have the same size base and
height, then the volume of the cone is one-third the volume
of the cylinder.
same base area
2. Build a second 4-by-3-by-1 rectangular prism. Place it on top of
the original rectangular prism.
Ask: How could you determine the volume of the new
rectangular prism? Sample answers: Multiply 4 ∗ 3 ∗ 2 to
obtain 24 cm3; multiply 12 ∗ 2 to get 24 cm3.
base
height
base
base
same height
1. Build a rectangular prism with a base that is 4 cubes long and
3 cubes wide, and that is 1 cube high.
Ask: Describe a way you could determine the volume of the
rectangular prism. Sample answer: Multiply 4 ∗ 3 ∗ 1 to obtain
12 cm3. What do the 4, 3, and 1 represent in the prism? The
length, width, and height
3 layers with 8 cubes in each layer makes a total of 24 cubes.
same height
Ask students to use the centimeter cubes to do the following:
For a right rectangular
prism with side lengths
l, w, and h units, the
volume V can be found
using the formula
V = l ∗ w ∗ h.
3 layers
8 cubes in 1 layer
NOTE If you do not have 36 centimeter cubes per student, ask students to build
the rectangular prisms in partnerships.
The area of the Pacific
Ocean is about 64 million
square miles. The
average depth of that
ocean is about 2.5 miles.
So, the volume of the
Pacific Ocean is about
64 million mi2 ∗ 2.5 mi,
or 160 million cubic
miles.
height
WHOLE-CLASS
ACTIVITY
height
▶ Another Formula for Volume
same base area
Student Reference Book, p. 196
182_214_EMCS_S_SRB_G5_MEA_576515.indd 196
4/4/11 5:01 PM
3. Build a third 4-by-3-by-1 layer. Place it on top of the existing
rectangular prism. Ask students to write a number model
using three factors to find the volume of the new prism.
4 ∗ 3 ∗ 3 = 36 cm3
Now ask the following question: Suppose you know the number of
cubes in the length, width, and height of a rectangular prism. How
could this information be used to write another formula for finding
the volume of a rectangular prism? Multiply: length ∗ width ∗ height
(l ∗ w ∗ h); V = l ∗ w ∗ h.
Volume of a Rectangular or Triangular Prism
Volume of a Prism
Area of a Rectangle
Area of a Triangle
V= B∗h
A = b∗h
V is the volume, B is the area
of the base, h is the height of
the prism.
A is the area, b is the length
of the base, h is the height of
the rectangle.
A=
1
_
2
∗ (b ∗ h)
A is the area, b is the length
of the base, h is the height of
the triangle.
Find the volume of the rectangular prism.
Step 1: Find the area of the base (B). Use the formula A = b ∗ h.
• length of the rectangular base (b) = 8 cm
• height of the rectangular base (h) = 5 cm
• area of base (B) = 8 cm ∗ 5 cm = 40 cm2
6 cm
Step 2: Multiply the area of the base by the height of the
5 cm
rectangular prism. Use the formula V = B ∗ h.
• area of base (B ) = 40 cm2
• height of prism (h) = 6 cm
• volume (V) = 40 cm2 ∗ 6 cm = 240 cm3
8 cm
The volume of the rectangular prism is 240 cm3.
Find the volume of the triangular prism.
Step 1: Find the area of the base (B ). Use the formula A =
• length of the triangular base (b) = 5 in.
• height of the triangular base (h) = 4 in.
• area of base (B ) = _12 ∗ (5 in. ∗ 4 in.) = 10 in.2
Step 2: Multiply the area of the base by the height of the
triangular prism. Use the formula V = B ∗ h.
• area of base (B) = 10 in.2
• height of prism (h) = 6 in.
• volume (V ) = 10 in.2 ∗ 6 in. = 60 in.3
1
_
2
(b ∗ h).
4 in.
6 in.
5 in.
The volume of the triangular prism is 60 in.3.
Find the volume of each prism. Include the unit in each answer.
1.
2.
3.
10 cm
7 yd
2 yd
3 yd
6 ft
10 cm
ft
Conclude by asking students to explain how they could use the new
formula to find the volume of a cube. Sample answers: Replace each
side-length letter in the formula with the length of a side of the
cube. You could rewrite the formula as V = s3, where s is the length
of a side of the cube.
Measurement
12
Have students write this formula at the top of journal page 322,
next to the first formula they derived for finding the volume of a
rectangular prism. Discuss why both formulas will result in the
same volume.
Student Page
10 cm
Check your answers on page 440.
8 ft
Student Reference Book, p. 197
182_214_EMCS_S_SRB_G5_MEA_576515.indd 197
3/8/11 5:00 PM
Lesson 9 8 750A
▶ Building a Rectangular
PARTNER
ACTIVITY
Prism with a Given Volume
Algebraic Thinking Ask students to use centimeter cubes to build
the shape of a rectangular prism with a volume of 24 cm3.
Ask: What are the possible areas for the base (B) and the length of the
height (h) from that base? B = 24 cm2, h = 1 cm; B = 12 cm2,
h = 2 cm; B = 8 cm2, h = 3 cm; B = 6 cm2, h = 4 cm; B = 4 cm2,
h = 6 cm; B = 3 cm2, h = 8 cm; B = 2 cm2, h = 12 cm; B = 1 cm2,
h = 24 cm
Ask students to use the cubes to make a rectangular prism that has
a length of 3 cm, a width of 2 cm (base of 6 cm2), and a height of 4 cm.
Explain that the volume can be found as follows:
V = (l ∗ w) ∗ h = (3 ∗ 2) ∗ 4
Now ask students to carefully rotate their rectangular prism so that
it now has a length of 4 cm, a width of 2 cm (base of 8 cm2), and a
height of 3 cm. Explain that the volume can be found as follows:
V = (l ∗ w) ∗ h = 3 ∗ (2 ∗ 4)
Ask: What do the two rectangular prisms have in common? Sample
answer: The dimensions of the prisms have the same three
measures, and each has a volume of 24 cm3.
Guide students to conclude that if the measures of the three
dimensions of two rectangular prisms are the same, the volumes are
the same. Then point out that this is an illustration of the
Associative Property of Multiplication, which means that
changing the grouping of factors does not change the product.
So, (3 º 2) º 4 = 3 º (2 º 4)
6º4
24
=
=
3º8
24
Have students repeat this activity by comparing the volumes of two
rectangular prisms that have dimensions of 2 cm, 3 cm, and 5 cm,
but different bases.
▶ Finding the Volumes of
INDEPENDENT
ACTIVITY
Rectangular Prisms
(Math Journal 2, p. 322)
Algebraic Thinking Have students complete journal page 322
by calculating the volume of six rectangular prisms from the
given dimensions.
750B Unit 9
Coordinates, Area, Volume, and Capacity
Student Page
Date
Time
LESSON
Math Boxes
9 8
1.
Watch for students who are not correctly matching the given dimensions to the
formula variables. Have them make and complete a table for the problems on
journal page 322, such as the following:
Solve.
b.
d.
18.95
– 6.07
V
80 in3
1
3
2
72 cm
3
3
343 cm
4
192 in
3
5
3
90 ft
3
6
50 cm
B
h
4∗4
5
4∗3
6
7∗7
7
8∗6
4
6∗3
5
2.5 ∗ 4
7
5
5.
21
16
24
15
3
5
b. _
8
4
and _
3
c. _
8
4
and _
2
d. _
5
2
and _
16
12
3
6
4 and _
_
16
12
f.
5
15
2
8
20
360
1,500
12
2,100
70
40
50
Elena received the following scores on
math tests: 80, 85, 76, 70, 87, 80, 90,
80, and 90.
4.
Find the following landmarks:
90
70
20
80
82
maximum:
minimum:
range:
48
_ and _ 120
e.
8
600
1,200
231 232
Find the least common denominator for
the fraction pairs.
2 and _
1
a. _
out
240
÷30
215.29
+ 38.75
34–36
3.
in
Rule
254.04
12.88
Problem
306.85
+ 216.96
523.81
42.82
c.
Complete the “What’s My Rule?” table,
and state the rule.
2.
128.07
– 85.25
a.
mode:
mean:
65
Use the graph to answer the questions.
a.
Which day had the
greatest attendance?
b.
What was the total
attendance for the five-day period?
Number of Tickets Sold
Ongoing Assessment: Informing Instruction
Friday
90
119
Movie Theater
Attendance
30
25
20
15
10
5
0
M
Tu
W
Th
F
Day of the Week
124
2 Ongoing Learning & Practice
▶ Math Boxes 9 8
Math Journal 2, p. 323
292-332_EMCS_S_G5_MJ2_U09_576434.indd 323
2/22/11 5:18 PM
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 323)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 9-10. The skills in Problems 2 and
5 preview Unit 10 content.
Writing/Reasoning Have students write a response to
the following: Explain the strategy you used to solve
Problem 1c and explain your reasoning. Answers vary.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 3
Study Link Master
Name
STUDY LINK
98
Use Math Boxes, Problem 3 to assess students’ abilities to find common
denominators. Students are making adequate progress if they correctly identify
the least common denominators.
Date
Time
Volumes of Cube Structures
The structures below are made up of centimeter cubes.
195–197
1.
2.
[Number and Numeration Goal 5]
1st layer
2nd layer
1st layer
Area of base =
15
Volume of first layer =
▶ Study Link 9 8
INDEPENDENT
ACTIVITY
Volume of entire
cube structure =
45
Area of base =
cm2
15
8
Volume of first layer =
cm3
Volume of entire
cube structure =
cm3
3.
16
cm2
8
cm3
cm3
4.
(Math Masters, p. 279)
1st layer
1st layer
Home Connection Students find the volume of
cube structures.
Area of base =
9
Volume of first layer =
Volume of entire
cube structure =
Practice
_3
5. 5
∗ _18 =
7. 960 ∗ 4 =
27
Area of base =
cm2
9
Volume of entire
cube structure =
cm3
3
_
40
3,840
6.
14
Volume of first layer =
cm3
56
cm2
14
cm3
cm3
960
, or _23
3,840 / 4 =
_4 _5
8. 5 ∗ 6 =
_4
6
Math Masters, p. 279
254-293_497_EMCS_B_MM_G5_U09_576973.indd 279
2/22/11 6:06 PM
Lesson 9 8
751
Teaching Master
Name
LESSON
98
Date
Time
3 Differentiation Options
Unfolding Prisms
If you could unfold a prism so that its faces are laid out as a set attached at their
edges, you would have a flat diagram for the shape. Imagine unfolding a cube.
There are many different ways that you could make diagrams, depending on how
you unfold the cube.
READINESS
▶ Analyzing Prism Nets
Which of the following are diagrams that could be folded to make a cube?
Write yes or no in the blank next to each diagram.
1.
PARTNER
ACTIVITY
5–15 Min
for Cubes
No
(Math Masters, pp. 280 and 429)
2.
No
To stimulate students’ ability to visualize, name, and
describe geometric solids, have students look at diagrams
to determine which shapes can and cannot be folded into
cubes. Read and discuss the introduction as a group. As students
choose which of the diagrams can be folded into a cube, provide
inch grid paper so students may check their work.
3.
Yes
4.
Yes
Discuss students’ solutions.
Math Masters, p. 280
ENRICHMENT
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2/22/11 6:06 PM
▶ Finding the Volume of
PARTNER
ACTIVITY
5–15 Min
One Stick-On Note
(Math Masters, p. 281)
To apply students’ understanding of how to find the
volume of a rectangular prism, have partners compare the
volume of a single stick-on note and that of a centimeter
cube. Give each partnership one stick-on note, one unused pad of
stick-on notes, and one centimeter cube. Ask students to estimate
how the volume of the single stick-on note compares with the
volume of the cube.
Have students record their strategies and solutions on Math
Masters, page 281. When partners have completed the page, ask
them to present their solutions.
Teaching Master
Name
LESSON
98
Date
Time
Comparing Volume
NOTE One approach to finding the volume of a single stick-on note would be to
What is the volume of one stick-on note? In other words, how much space is taken up
by a single stick-on note? How does the volume of a stick-on note compare to the
volume of a centimeter cube?
1.
An unused pad of stick-on notes is an example of what shape?
2.
Estimate the volume of one stick-on note.
3.
measure the dimensions and find the volume of the unused pad of stick-on notes.
A single stick-on note would represent a fraction of the pad.
Rectangular prism
Sample answer: About 0.75 cm3
Calculate the volume of one stick-on note. Volume = Answers vary.
EXTRA PRACTICE
Record your strategy.
4.
▶ 5-Minute Math
Use a formula to calculate the volume of one centimeter cube. Volume =
3
1 cm
Write the number sentence for this calculation.
Volume = (1 cm ∗ 1 cm) ∗ 1 cm = 1 cm3
5.
Explain how the volume of one stick-on note compares with the volume of one
centimeter cube.
Answers vary.
y
Math Masters, p. 281
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752
Unit 9
2/23/11 4:20 PM
Coordinates, Area, Volume, and Capacity
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with calculating the volumes
of prisms, see 5-Minute Math, pages 52 and 214.