Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Title of Lesson: How Much Do They Hold?
UFTeach Students’ Names: Meghan Wilder
Teaching Date and Time: Monday, April 7, 2014; 9:15 AM
Length of Lesson: 50 minutes
Grade / Topic: 6th – Advanced/Volume of Rectangular Prisms
Source of the Lesson: http://illuminations.nctm.org/Lesson.aspx?id=2927
http://www.mathsisfun.com/definitions/rectangular-prism.html
Appropriateness for Middle School Students: In this lesson, students will be working in pairs. Having students
working in pairs will allow them to develop vital communication and cooperation skills necessary for molding
them into productive members of society. Group work will also allow the students to learn how to collaborate
with their peers and exchange thoughts and ideas freely. Additionally, this lesson will allow the students to be
hands-on; the students will be constructing models of rectangular prisms, which will help them visualize the
connection between the volumes of the prisms and their dimensions.
Concepts: A prism is a three-dimensional figure with two congruent parallel bases and rectangular faces for
sides. The different parts that contribute to a prism are vertices, edges, bases, and faces. This threedimensional figure is named by the polygon that makes up its base; therefore, there are multiple types of
prisms, including hexagonal, rectangular, and triangular. These prisms can be found everywhere, ranging from
a cereal box to all the way to the Pyramids in Egypt. This lesson will focus on the rectangular prism, more
specifically on the volume of rectangular prisms. Volume is the measure of how much space a threedimensional object can take up or the amount it can hold. When measuring the volume, cubic units are used
because three dimensions, the base, width, and height, are multiplied together. Another way to find the
volume is to consider how many unit cubes it can contain. A unit cube is a simple cube used to measure one
inch, one centimeter, or whatever the units of measurement being used are on all sides. In this lesson,
students will discover the meaning of the equation of volume for the rectangular prism. Mastering this
concept will help the students to determine the volume of other prisms, such as the triangular prism; this will
in turn prepare students for future mathematics courses and other physical sciences. Additionally, developing
an understanding of the volume of rectangular prisms will help students recognize the amount of material a
prism, such as a pool, can hold or the amount of material is needed to make a rectangular prism in everyday
life.
Sources: http://content.blackgold.ca/courses/math_4/Unit%2034/Unit%2034%20SLG/MA4_SLG_U3L6.pdf
http://www.ck12.org/geometry/Volume-of-Rectangular-Prisms/lesson/Volume-of-RectangularPrisms/r9/
Florida State Standards (NGSSS) with Cognitive Complexity:
Benchmark Number Benchmark Description
MA.6.G.4.3
Determine a missing dimension of a plane figure or
prism, given its area or volume and some of the
dimensions, or determine the area or volume given the
dimensions.
Cognitive Complexity
Moderate (Level 2)
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Performance Objectives: Students will be able to:
 Calculate a missing dimension of a rectangular prism using its volume and some of the dimensions.
 Show how to find the volume, given the dimensions of a rectangular prism.
Materials List and Student Handouts
 Lesson PowerPoint
 Pre-Evaluation – one per student
 Post-Evaluation – one per student
 How Much Do They Hold? worksheet packet – one per student
 Now You Try It! worksheet – one per student
 Thinking Further worksheet – one per student
 2.125 in. X 2.125 in. X 11 in. sample popcorn container – one for teacher
 2.75 in. X 2.75 in. X 8.5 in. sample popcorn container – one for teacher
 Green 2.125 in. X 2.125 in. X 11 in. prism for “How Much Do They Hold?” activity – one for each pair of
students
 Blue 2.75 in. X 2.75 in. X 8.5 in. prism for “How Much Do They Hold?” activity – one for each pair of
students
 Bag of Fruit Loops cereal – one bag containing 3.25 cups of cereal for every pair of students
 Calculator – one per student
 Ruler – one for every pair of students
 Paper plates – one for every pair of students
 8 oz. cup – one cup for every pair of students
Advance Preparations
 Create lesson PowerPoint.
 Xerox evaluations and worksheets.
 Create one 2.125 in. X 2.125 in. X 11 in. and one 2.75 in. X 2.75 in. X 8.5 in. sample popcorn container.
 Construct enough green 2.125 in. X 2.125 in. X 11 in. prisms and blue 2.75 in. X 2.75 in. X 8.5 in. prisms
for each pair of students for “How Much Do They Hold?” activity.
 Portion out cereal for each group into bags.
Safety
 Students are not to eat the cereal.
 Students are not to throw the cereal.
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
5E Lesson:
Engagement
Time: 8 minutes
What the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible
(What Teacher Says)
Misconceptions
Have slide 1 on the board Good morning, class! It’s great to see you
and give introductions.
all again.
Today, you will be learning about
rectangular prisms and how to find their
volumes.
First, you need to show what you already
know about this.
Pull up slide 2.
Everyone will have 5 minutes to complete
Pass out Pre-Evaluations. this pre-evaluation by yourself. Be sure to
put your name at the top of your paper.
Don’t worry about getting everything
right; just try your best! When you’re
finished, raise your hand, and your papers
will be collected.
What questions do you have?
No student should raise
his/her hand. If they do,
address each question.
Great. You may begin!
After 5 minutes collect
Okay, time’s up! If your pre-evaluation has
Pre-Evaluations.
not yet been collected, please raise your
hand.
Display slide 3.
By a show of hands, who likes watching
Students who like watching
movies?
movies raise their hands.
Display slide 4.
More specifically, who all enjoys going to
Students who enjoy going to
the movies?
the movies raise their hands.
Great! Going to the movies is one of my
favorite pastimes, and every time I go, I
am so tempted to get some snacks from
the concession stand.
Display slide 5.
What kinds of snacks do you like to get
when you go to the movies?
Call on multiple students. Yes, ____________?
[Popcorn, candy, ICEEs,
nachos] responses can vary
Those are some good ones. When I go to
the movies, I really enjoy getting popcorn,
and since it can be kind of expensive, it’s
nice to get the most for my money.
Show two different sized
Suppose you go to the movies and want to
popcorn containers to
buy some popcorn. The concession stand
class.
is selling two different sized popcorn
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Display slide 6.
containers, or rectangular prisms, for the
same price.
Which prism is the best deal?
Call on student.
Yes, ________?
Call on multiple students.
Display slide 7.
[The blue prism] the green
prism
Answers can vary.
Well, in today’s lesson, we are going
determine which prism is the best deal by
figuring out which prism has a greater
volume!
Exploration
Time: 22 minutes
What the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible
(What Teacher Says)
Misconceptions
Display slide 8.
For this activity, everyone will be working
Divide students into
with his or her shoulder partner. You and
groups of two.
your partner are going to receive a “How
Pass out “How Much Do
Much Do They Hold?” worksheet packet, a
They Hold?” worksheet
bag of cereal, a blue rectangular prism, a
packet, rulers, calculators, green rectangular prism, and some other
green rectangular prisms, supplies to help you complete the activity,
blue rectangular prisms,
but don’t start until you are told to do so.
bags of cereal, paper
plates, and cups.
Together, you and your partner will follow
the directions on your “How Much Do
They Hold?” worksheet packet to
determine which prism holds more using
cereal.
Use the two prisms given to you to start
answering the questions in your packet.
After you finished the first three problems,
raise your hand, and your work will be
checked. Do not eat the cereal.
You will then finish answering the
questions in the packet. Be sure to discuss
your answers with your partner as you go.
You will have 10 minutes to answer all of
the questions. We will announce when
only 5 minutes remain.
What questions do you have?
No student should raise
his/her hand. If they do,
address each question.
You may begin!
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Walk around to each
group asking probing
questions and make sure
students stay on task.
Halfway through the
activity, tell students to
finish the activity and
Which side of the ruler are you going to
use to measure your prisms?
[The inch side] the
centimeter side, I don’t
know, I’m not sure what you
mean
Are you going to record your
[Decimals] fractions, I’m not
measurements as fractions or as decimals? sure what you mean
Do you think the prisms will hold the same [One will hold more than the
amount of cereal, or do you think one will other because it has a
hold more than the other? Why?
greater volume] they will
hold the same amount
because one is short and fat
and the other is tall and
skinny, they will hold the
same amount because they
have the same volume, I
don’t know
How are you going to determine which
[By placing Prism A inside of
prism holds more cereal?
Prism B, filling Prism A with
cereal, and removing Prism
A to let the cereal fall into
Prism B] by pouring the
same amount of cereal into
each of the prisms
separately and seeing which
one is fuller, I’m not sure
What did you discover when you placed
[That Prism B has a greater
Prism A into Prism B, filled Prism A with
volume than Prism A] the
cereal, and then removed Prism A?
cereal spilled over
How are you going to mathematically
[I will find the volume of
prove that Prism B has a greater volume
Prism A and the volume of
than Prism A?
Prism B using V=bwh] I’m
not sure how to prove it
mathematically
How will you calculate the height Prism B
[I will solve V=bwh for h by
needs to be in order to make the volumes plugging the volume of
of the two prisms equal?
Prism A in for V, the length
of Prism B’s base in for b,
and the length of Prism B’s
width in for w.] I’m not sure
how to, I’m not sure what
the question means
Only five minutes remain. If you haven’t
finished the activity, you need to be
finishing it up and starting to work on
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
begin working on the
questions.
Continue to walk around
asking probing questions.
Pick up any scrap
materials.
Collect the students’
cereal once they have
completed the activity.
Gather students’
attention after 10
minutes.
Call on student.
answering the questions.
Give me three, two, one.
Thank you.
So what happened when you placed Prism
A inside of Prism B, filled Prism A with
cereal, and then removed Prism A?
Yes, ___________?
Call on student.
Right. Was Prism B full, not full, or
overflowing with cereal?
Yes, ____________?
Since Prism B was not full, what does this
tell us about the volumes of the two
prisms?
Yes, _________?
Call on student.
Exactly. Since you’ve visually proven that
Prism B has a greater volume than Prism
A, you can prove this mathematically.
Now, who can tell me what the
dimensions are for Prism A and for Prism
B?
Yes, __________?
Call on student.
Display slide 9.
That’s correct, ___________.
Since you know the dimensions of the two
Students become silent and
listen to teacher.
[All of the cereal in Prism A
fell into Prism B] the cereal
filled up Prism B
[Not full] full, overflowing
[Prism B has a greater
volume than Prism A] Prism
A has a greater volume than
Prism B, Prism A and B have
the same volume
[Prism A has a base of 2.125
in., width of 2.125 in., and
height of 11 in.; Prism B has
a base of 2.75 in., width of
2.75 in., and height of 8.5
in.]
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Call on student.
Display slide 10.
Call on student.
Call on student.
prisms, how can you calculate their
volumes?
Yes, __________?
Right. Will you come up to the board and
show how to do this for Prism A?
Thank you, ___________.
Who can tell me the units for this volume?
Very good. And who can tell me why the
units are cubed?
Yes, ___________?
[Plug the values of the base,
width, and height into
V=bwh]
Student will come to the
board and substitute the
values of b, w, and h for
Prism A into the equation for
the volume of a rectangular
prism.
[in3] in2, in
[Because you’re multiplying
three lengths together]
because the units are always
cubed for volume, I don’t
know
Precisely!
Display slide 11.
Call on student.
Display slide 12.
Call on student.
Call on student.
Who will come up to the board and show
how to find the volume of Prism B?
Yes, ___________?
Thank you.
Now, who can tell me how to find what
the height of Prism B needs to be in order
to make the volumes of the two prisms
equal?
Yes, ____________?
Exactly! __________, will you come to the
board and show how to do this?
Student will come to the
board and substitute the
values of b, w, and h for
Prism B into the equation for
the volume of a rectangular
prism.
[Solve V=bwh for h by
plugging the volume of
Prism A in for V, the length
of Prism B’s base in for b,
and the length of Prism B’s
width in for w.] I’m not sure
what you mean, I don’t
know
Student will come to the
board, substitute the volume
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
of Prism A in for V, the
length of Prism B’s base in
for b, and the length of Prism
B’s width in for w into the
equation for the volume of a
rectangular prism, and solve
for h.
Pass out Now You Try It!
Worksheets.
Display slide 13.
Walk around to make
sure students stay on
task.
Ask probing questions.
Great job!
Now, you’re going to get some practice
finding the volumes of rectangular prisms
given certain dimensions and also using
the volumes of rectangular prisms to find a
missing dimension.
You are now going to get another
worksheet.
Using the equation for the volume of a
rectangular prism, solve the four given
problems. Be sure to show all of your
work.
Once you have solved all four problems,
discuss your answers with your shoulder
partner. The time will be announced when
only one minute remains.
What questions do you have?
No student should raise
his/her hand. If they do,
address each question.
Great. You may begin!
What equation are you using to solve
[V=bwh] I’m not sure
these problems?
What are you given in the first problem,
and what are you solving for?
How would you solve the second
problem?
What are your final units in the third
problem? Why?
What are you solving for in the fourth
problem?
[The measure of the base,
width, and height; solving
for the volume]
[Plug 216 in3 in for V, 6 in. in
for b, and 12 in. in for h;
multiply b and h together
and divide V by this value to
find w]
[ft; because I am finding the
length of just one side] ft3, I
don’t know
[The base]
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Explanation
What the Teacher Will Do Teacher Directions and Probing Questions
(What Teacher Says)
Gather students’
Give me three, two, one.
attention.
Display slide 14.
Thank you. So who can tell me what you
are solving for in the first problem?
Call on student.
Yes, __________?
Have student come up to Right. Now, who can come up to the board
the board.
and show how you solved this problem?
Call on student.
Call on student.
Thank you, _______. Who can explain
what _________ did to solve for the
volume?
Yes, ________?
Exactly. _______, what units did he/she
need to include in his/her final answer?
And why are these units cubed?
Great. What questions do you have?
Display slide 15.
Call on student.
Awesome. For the second problem, what
information are you given?
Call on student.
Right. What are you looking for?
Call on student.
So who can come show how you solved
this problem?
____________, come up to the board and
show what you did.
Thank you. Can you explain to the class
what you did?
Call on student.
Great. Now, ________, can you tell me
Time: 10 minutes
Student Responses/Possible
Misconceptions
Students become silent and
listen to teacher.
[The volume]
Student will come to the
board and write out the
steps he/she took to find the
answer.
[Plugged 6 m in for h, 4 m in
for w, and 9 m in for b and
multiplied them together]
[m3] I’m not sure, none
[Because we multiplied
three dimensions together,
so the units get cubed] I’m
not sure
No student should raise
his/her hand. If they do,
address each question.
[That the volume is 216 in3,
the base is 6 in., and the
height is 12 in.]
[The width] the length, I
don’t know
Student will come to the
board and write out the
steps he/she took to find the
answer.
[Plugged 216 in3 in for V, 6
in. in for b, and 12 in. in for
h; then multiplied b and h
together and divided V by
this value]
[in.] in3, I’m not sure what
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Call on student.
Display slide 16.
Call on student.
Call on student.
Call on student.
Call on student.
Display slide 17.
Call on student.
Call on student.
Call on student.
what the final units are for this problem?
you mean
Correct. And why are the final units inches, [Because we divided in3 by
_________?
two other lengths, which
only leaves one length]
because we only have one
length, I don’t know
Exactly! What questions do you have so
No student should raise
far?
his/her hand. If they do,
address each question.
Okay. Who can tell me what you are trying
to find in this third problem?
Yes, ________?
[The height] the volume, the
base, the width
And what are you given?
[That the base is 11 ft, the
width is 2 ft, and the volume
of 154 ft3]
Thank you, __________. Who can tell me
how to solve this problem?
Yes, ________. Come on up to the board.
Student will come to the
board and write out the
steps he/she took to find the
answer.
Thank you. Can you explain to the class
[Plugged 154 ft3 in for V, 2 ft
the steps you took to find the height?
in for w, and 11 ft in for b;
then multiplied w and h
together and divided V by
this value]
Great. Now, __________, what are the
[ft], ft3
units for this volume?
Awesome. What questions do you have?
No student should raise
his/her hand. If they do,
address each question.
For this last problem, what information
[That the volume is 240 cm3,
are you given?
the width is 4 cm, and the
height is 15 cm]
Right. And what are you looking for?
[The base] the bottom, I
don’t know
Exactly. Who can show how they solved
Student will come to the
this problem?
board and write out the
steps he/she took to find the
answer.
Thank you, ________.
Now, __________, can you explain how
[Plugged 240 cm3 in for V, 4
___________ solved this problem?
cm in for w, and 15 cm in for
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
And what were the final units for this
problem?
Thank you, ____________.
What questions do you have?
h; then multiplied w and h
together and divided V by
this value]
[cm]
No student should raise
his/her hand. If they do,
address each question.
Elaboration
Time: 5 minutes
What the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible
(What Teacher Says)
Misconceptions
Display slide 18.
Now that you’ve had some practice using
the equation for the volume of a
rectangular prism, you are going to apply
it to some real world situations.
Pass out Thinking Further Each of you will be receiving a “Thinking
worksheets.
Further” worksheet.
You will have 5 minutes to answer both
questions. Be sure to show all of your
work and include the correct units. You
may work with your shoulder partner.
What questions do you have?
No student should raise
his/her hand. If they do,
address each question.
You may begin.
Walk around asking
What are you given in the first problem?
[That the case has a volume
probing questions.
of 264 ft3, a width of 3 ft,
and a height of 8 ft]
What are you looking for in the first
[The length of the base]
problem?
What are you solving for in the second
[The volume of the pool]
problem?
how much water his pool
would hold
How would you solve for the volume in
[Plug 32 ft in for b, 16 ft in
the second problem?
for w, and 5 ft in for h, and
then multiply them
together] I’m not sure
After 5 minutes gather
Give me three, two, one.
Students become silent and
the students’ attention.
listen to teacher.
Thank you. If you haven’t finished your
Students complete
worksheet, that’s okay. Complete your
worksheet for homework.
worksheet for homework tonight, and
bring it back to class tomorrow.
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Evaluation
Time: 5 minutes
What the Teacher Will Do Teacher Directions and Probing Questions Student Responses/Possible
(What Teacher Says)
Misconceptions
Display slide 19.
The post-evaluation is now going to be
Pass out Post-Evaluations. passed out. Be sure to put your name at
the top of the page. Complete the
evaluation to the best of your ability.
Please work by yourself, and when you’re
finished, raise your hand. Remain quietly
seated until all of the papers have been
collected and you have been dismissed.
What questions do you have?
No student should raise
his/her hand. If they do,
address each question.
Great. You may begin!
After 5 minutes collect
All right, time’s up! If your paper has not
Students who still have their
Post-Evaluations.
been collected yet, please raise your hand. post-evaluations raise their
hands.
Pass out cereal to any
Thank you all for your attention! If you
Students who want cereal
students who want some. would like some cereal, raise your hand.
raise their hands.
Dismiss the class.
Have a great day!
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:______________________________
How Much Do They Hold?
For this activity, you and your shoulder partner will be comparing the volume of
two rectangular prisms to determine which can hold more cereal. To do this, you
and your shoulder partner will receive two rectangular prisms made out
of the same size sheet of paper and calculate their volumes by measuring the
dimensions of the containers.
Materials:
 Green prism
 Blue prism
 Paper plate
 Bag of cereal



Cup
Ruler
Calculator
Take the green prism, and measure the length,
width, and height of each dimension using the
inches side of your ruler. Make sure to measure
each length to the nearest eighth of an inch.
Record your data below as a decimal.
Label it Prism A.
Take the blue prism, and measure the length,
width, and height of each dimension using the
inches side of your ruler. Make sure to measure
each length to the nearest eighth of an inch.
Record your data below as a decimal.
Label it Prism B.
1.
Dimension
Base (in.)
Width (in.)
Height (in.)
Prism A
Prism B
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
2. Do you think the two prisms will hold the same amount, or do you think one will hold more than the
other? Which one? Explain your answer.
3. Place Prism B on the paper plate with Prism A inside of it. Use your cup to pour cereal into Prism A
until it is full. Carefully, lift Prism A so that the cereal falls into Prism B. Describe what happened. Is
Prism B not full, full, or overflowing?
Raise your hand once you complete problems 1-3. Do not proceed until your work has been checked.
____________________________________________________________________________________
Answer the following questions. Be sure to discuss your answers with your shoulder partner as you go.
Show all of your work when needed.
4. a) Was your prediction correct? How do you know?
b) If your prediction was incorrect, describe what actually happened.
Knowing that the formula for the volume of rectangular prism is V = bwh, answer the following
questions.
5. a) Calculate the volume of Prism A. Label the dimensions in the figure.
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
b) Calculate the volume of Prism B. Label the dimensions in the figure.
c) Explain why the prisms do not hold the same amount. Use the formula for the volume of a prism
to guide your explanation.
6. What would the height of Prism B need to be in order to make the volumes of the two prisms equal?
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:____________KEY_______________
How Much Do They Hold?
For this activity, you and your shoulder partner will be comparing the volume of
two rectangular prisms to determine which can hold more cereal. To do this, you
and your shoulder partner will receive two rectangular prisms made out
of the same size sheet of paper and calculate their volumes by measuring the
dimensions of the containers.
Materials:
 Green prism
 Blue prism
 Paper plate
 Bag of cereal



Cup
Ruler
Calculator
Take the green prism, and measure the length,
width, and height of each dimension using the
inches side of your ruler. Make sure to measure
each length to the nearest eighth of an inch.
Record your data below as a decimal.
Label it Prism A.
Take the blue prism, and measure the length,
width, and height of each dimension using the
inches side of your ruler. Make sure to measure
each length to the nearest eighth of an inch.
Record your data below as a decimal.
Label it Prism B.
1.
Dimension
Prism A
Prism B
Base (in.)
2.125 in.
2.75 in.
Width (in.)
2.125 in.
2.75 in.
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Height (in.)
11 in.
8.5 in.
2. Do you think the two prisms will hold the same amount, or do you think one will hold more than the
other? Which one? Explain your answer.
Answers will vary.
3. Place Prism B on the paper plate with Prism A inside of it. Use your cup to pour cereal into Prism A
until it is full. Carefully, lift Prism A so that the cereal falls into Prism B. Describe what happened. Is
Prism B not full, full, or overflowing?
Prism B is not full. There is still room for more cereal in the prism.
Raise your hand once you complete problems 1-3. Do not proceed until your work has been checked.
____________________________________________________________________________________
Answer the following questions. Be sure to discuss your answers with your shoulder partner as you go.
Show all of your work when needed.
4. a) Was your prediction correct? How do you know?
Answers will vary.
b) If your prediction was incorrect, describe what actually happened.
Prism B has a greater volume than Prism A.
Knowing that the formula for the volume of rectangular prism is V = bwh, answer the following
questions.
5. a) Calculate the volume of Prism A. Label the dimensions in the figure.
V = bwh
= (2.125 in.)(2.125 in.)(11 in.)
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
= 49.7 in3
b) Calculate the volume of Prism B. Label the dimensions in the figure.
V = bwh
= (2.75 in.)(2.75 in.)(8.5 in.)
= 64.3 in3
c) Explain why the prisms do not hold the same amount. Use the formula for the volume of a prism
to guide your explanation.
The prisms have different dimensions, so the volumes are different.
6. What would the height of Prism B need to be in order to make the volumes of the two prisms equal?
Prism A: V = 49.7 in3
PrismB: V = bwh
(49.7 in3) = (2.75 in.)(2.75 in.)(h)
h = 6.6 in.
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:______________________________
Now You Try It!
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. Find the volume of a rectangular prism
with a height of 6 m, width of 4 m, and
base of 9 m.
2. Find the width of a rectangular
prism when its volume is 216 in3
and has a base of 6 in. and height
of 12 in.
V = _______________
w = _______________
3. Find the height of a rectangular
prism with a volume of 154 ft3,
width of 2 ft, and base of 11 ft.
4. Find the base of a rectangular
prism when its volume is 240 cm3
and has a width of 4 cm and height
of 15 cm.
h = _______________
b = _______________
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:_________KEY__________________
Now You Try It!
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. Find the volume of a rectangular prism
with a height of 6 m, width of 4 m, and
base of 9 m.
2. Find the width of a rectangular
prism when its volume is 216 in3
and has a base of 6 in. and height
of 12 in.
V = bwh
V = (9 m)(4 m)(6 m)
V = 216 m3
V = bwh
216 in3 = (6 in.)w(12 in.)
216 in3 = (72 in2)w
w = 3 in.
V = ____216 m3_____
w = _____3 in._____
3. Find the height of a rectangular
prism with a volume of 154 ft3,
width of 2 ft, and base of 11 ft.
4. Find the base of a rectangular
prism when its volume is 240 cm3
and has a width of 4 cm and height
of 15 cm.
V = bwh
154 ft3 = (11 ft)(2 ft)h
154 ft3 = (22 ft2)h
h = 7 ft
V = bwh
240 cm3 = b(4 cm)(15 cm)
240 cm3 = (60 cm2)b
b = 4 cm
h = ____7 ft_____
b = _____4 cm______
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:______________________________
Thinking Further
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. Taylor is building a glass case for a reptile display. The interior of the case is in the
shape of a rectangular prism as shown in the diagram.
The interior of the case has a width of 3 feet, a height of 8 feet, and a total volume of
264 cubic feet. What is the value of b?
2. Summer is approaching, and John wants to build a pool in his backyard. He has
enough room for a base of 32 feet and a width of 16 feet. If John wants his pool to be
5 feet deep, how much water would his pool hold?
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:___________KEY________________
Thinking Further
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. Taylor is building a glass case for a reptile display. The interior of the case is in the
shape of a rectangular prism as shown in the diagram.
The interior of the case has a width of 3 feet, a height of 8 feet, and a total volume of
264 cubic feet. What is the value of b?
V = bwh
264 ft3 = b(3 ft)(8 ft)
264 ft3 = b(24 ft2)
b = 11 ft
2. Summer is approaching, and John wants to build a pool in his backyard. He has
enough room for a base of 32 feet and a width of 16 feet. If John wants his pool to be
5 feet deep, how much water would his pool hold?
V = bwh
V = (32 ft)(16 ft)(5 ft)
V = 2560 ft3
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:______________________________
Pre-Evaluation
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. What is the volume of a rectangular prism with a base of 3 in., width of 6 in., and
height of 7 in.? Show all of the steps you took to find this volume.
2. Find the volume of a rectangular prism with a base of 4 ft, height of 8 ft, and width of
2 ft.
3. The volume of a rectangular prism is 150 cm3. The prism has a height of 10 cm and a
width of 3 cm. Show how to calculate the length of the prism’s base. Write your
answer in the space below.
Base = ______________________
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:_________KEY__________________
Pre-Evaluation
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. What is the volume of a rectangular prism with a base of 3 in., width of 6 in., and
height of 7 in.? Show all of the steps you took to find this volume.
V = bwh
V = (3 in.)(6 in.)(7 in.)
V = 126 in3
2. Find the volume of a rectangular prism with a base of 4 ft, height of 8 ft, and width of
2 ft.
V = bwh
V = (4 ft)(8 ft)(2 ft)
V = 64 ft3
3. The volume of a rectangular prism is 150 cm3. The prism has a height of 10 cm and a
width of 3 cm. Show how to calculate the length of the prism’s base. Write your
answer in the space below.
V = bwh
150 cm3 = b(3 cm)(10 cm)
150 cm3 = (30 cm2)b
b = 5 cm
Base = _________5 cm_________
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:______________________________
Post-Evaluation
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. What is the volume of a rectangular prism with a base of 11 m, width of 1 m, and
height of 8 m? Show all of the steps you took to find this volume.
2. Find the volume of a rectangular prism with a base of 3 ft, height of 5 ft, and width of
9 ft.
3. The volume of a rectangular prism is 210 cm3. The prism has a base of 7 cm and a
width of 5 cm. Show how to calculate the length of the prism’s height. Write your
answer in the space below.
Height = ______________________
Step 1/2: Explorations in Teaching Secondary Mathematics and Science
Name:_________KEY__________________
Post-Evaluation
Using the equation for the volume of a rectangular prism, solve the following problems.
Be sure to show all of your work and include appropriate labels in your answers.
1. What is the volume of a rectangular prism with a base of 11 m, width of 1 m, and
height of 8 m? Show all of the steps you took to find this volume.
V = bwh
V = (11 m)(1 m)(8 m)
V = 88 m3
2. Find the volume of a rectangular prism with a base of 3 ft, height of 5 ft, and width of
9 ft.
V = bwh
V = (3 ft)(9 ft)(5 ft)
V = 135 ft3
3. The volume of a rectangular prism is 210 cm3. The prism has a base of 7 cm and a
width of 5 cm. Show how to calculate the length of the prism’s height. Write your
answer in the space below.
V = bwh
210 cm3 = (7 cm)(5 cm)h
210 cm3 = (35 cm2)h
h = 6 cm
Height = _________6 cm_________