Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Teacher Background Information:
The student will need to not only use the formula, but understand the formula for finding volumes of right rectangular prisms.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Resources:
o Mini Unit 6, Lesson 1:
o Mini Unit 6, Lesson 2:

https://www.engageny.org/resource/grade-5-mathematics-module-5topic-b-lesson-4 Use multiplication to calculate volume.

https://www.engageny.org/resource/grade-5-mathematics-module-5topic-b-lesson-5 Use multiplication to connect volume as packing with
volume as filling.

http://www.cpalms.org/Public/PreviewResource/Preview/30402 This
lesson provides a hands-on approach to develop the formula for finding
the volume of a right rectangular prism. Students will apply the formula.
Students will determine the volume of figures composed of two right
rectangular-prism solids.

http://www.cpalms.org/Public/PreviewResource/Preview/35911 This is
the second part of a two-part volume lesson. In the first Building
Rectangular Prisms (attached) lesson, foundational volume concepts are
taught and students count cubes to find volume. In this lesson, students
will discover the volume formulas length x width x height and base x
height as they build rectangular prisms. They will use the formulas to find
volume in real world situations.
Indianapolis Public Schools

https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5thmeasurement-topic Khan Academy: Volume

https://learnzillion.com/student/lessons/1485 Learnzillion videos

https://learnzillion.com/student/lessons/1264-find-volume-bycounting-cubes Find volume by counting cubes

http://www.mathplayground.com/cube_perspective.html Count the
cubes game.

http://illuminations.nctm.org/Activity.aspx?id=4095 Online
interactive
Curriculum & Instruction
Mathematics Pacing Resource Document

http://www.cpalms.org/Public/PreviewResource/Preview/46110 Students
will use situational stories to help them apply the formulas V = l × w × h
and V = B × h to find the volumes of right rectangular prisms with wholenumber edge lengths.

http://www.cpalms.org/Public/PreviewResource/Preview/49093 In this
MEA, students will use problem-solving strategies to rank different
parking garages based on given factors. Students will need to apply their
knowledge of volume to find the total volume of each parking garage and
correctly calculate these values.

http://www.k-5mathteachingresources.com/supportfiles/designingatoybox.pdf Design a Toy Box Activity Sheet

http://www.k-5mathteachingresources.com/supportfiles/designingacerealboxx.pdf Designing a Cereal Box Activity Sheet

http://www.k-5mathteachingresources.com/support-files/create-asculpture.pdf Create a Sculpture Activity

http://www.k-5mathteachingresources.com/support-files/find-thevolume.pdf Find the Volume Activity Sheet

http://www.k-5mathteachingresources.com/support-files/joesbuildings.pdf Joe's Building: Word Problems Sheet

http://www.k-5mathteachingresources.com/support-files/comparingvolumes-of-cereal-boxes-project-and-rubric.pdf Comparing Volumes of
Cereal Boxes Activity Sheet

http://illuminations.nctm.org/Lesson.aspx?id=2927 Popcorn Anyone?

http://illuminations.nctm.org/Lesson.aspx?id=2863 Hay Bale Farmer
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Kelsey has a fish tank in the shape of a rectangular prism. A diagram of her fish tank is shown below.
What is the volume, in cubic feet, of Kelsey’s fish tank?
Martin has two fish tanks, each in the shape of a rectangular prism. The total volume of his two fish tanks is equal to the volume of Kelsey’s fish tank. The first of
Martin’s fish tanks has a length of 3 feet, a width of 1 foot, and a height of 2 feet, as shown in the diagram below.
List two unique sets of dimensions that could represent the dimensions of Martin’s second fish tank.
Pia also has a fish tank. The volume of her tank is greater than that of Martin’s second fish tank but less than that of Kelsey’s fish tank. The area of the bottom of
Pia’s fish tank is 7 square feet. What is one possible height, in feet, of Pia’s fish tank?
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Mr. Elkins plans to buy a refrigerator. He can choose from five different refrigerators whose interior dimensions, in inches, are given below. Which refrigerator has
the greatest capacity (volume)?
A. 42 x 34 x 30
B. 42 x 30 x 32
C. 42 x 28 x 32
D. 40 x 34 x 30
E. 40 x 30 x 28
[NAEP 2007]
It takes 64 identical cubes to half fill a rectangular box. If each cube has a volume of 8 cubic centimeters, what is the volume of the box in cubic centimeters?
A. 1,024
B. 512
C. 128
D. 16
E. 8
[NAEP 1992]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
The volume of a rectangular prism is 72 cubic units. If the length of the prism is 6 units, what might the width and height be? How many solutions are there? Use
what you know about volume to explain your answer.
[Howard County Public Schools, Maryland]
The volume of a juice box is about 24 cubic inches. A juice box company wants to design a new juice box. What are some of the possible dimensions for a juice
box? Use pictures, numbers and/or words to show some possibilities.
[Howard County Public Schools, Maryland]
Carter’s Candy Company is selling a new type of chocolate. They have decided to sell the candy in packages of 24. You are leading a team in charge of
developing a box for the candy.
A. Use unit cubes to build all of the possible boxes for the package of candy. How many possibilities are there? Record the dimensions and volume of each
box. What do you notice about all of the volumes?
B. After determining all of the possible boxes, you must make a recommendation to the president of the company about which box should be used. Write
a paragraph explaining which box would be best. Make sure to explain your reasons for choosing this box.
C. Two of your team members get in an argument about the boxes. Cathy says that a 1x24 box is the same as a 24x1 box. Curtis says that these
dimensions would lead to two different boxes. Who do you agree with? Why?
[North Carolina Dept. of Public Instruction]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Cut out a 10x10 square from your centimeter grid paper. From each corner of the square, cut out a 1x1 square.
Fold up each flap and tape them together so that you have an open box.
Use centimeter cubes to measure the volume of your box.
How would your volume change if you cut out a 2x2 square from each corner instead of a 1x1 square? How would your volume change if you started with a
20x20 square instead of a 10x10 square?
[North Carolina Dept. of Public Instruction]
Bennett and Seth are having an argument about the formula for finding the volume of a rectangular prism. Bennett says that to find volume you have to know
the length, height, and width of the figure. Seth says that you only need to know the base and height of the figure.
Which student do you agree with? Why? Write an expression that shows each boy’s formula for finding volume.
Draw a rectangular prism and label it with dimensions. How would Bennett find the volume of this prism? How would Seth find its volume?
[North Carolina Dept. of Public Instruction]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Ms. Webb is switching schools and needs to pack up her classroom. She has decided to rent a moving truck so that she can move her boxes in one trip. All of
the trucks are 5 feet wide and 6 feet tall, but the trucks have different lengths. The choices of lengths are 10 feet, 14 feet, 17 feet, 20 feet, 24 feet, and 26 feet.
Find the volume of each truck to determine how much it can hold.
Ms. Webb stacked all of her boxes into a pile that is 12 feet wide, 7 feet long, and 3 feet high. Which truck should she rent?
Ms. Bradley is also switching schools. She and Ms. Webb are thinking about renting a truck together. If Ms. Bradley’s stack of boxes is 9 feet wide, 11 feet long,
and 4 feet high, which truck would the two teachers have to rent in order to hold all their boxes?
[North Carolina Dept. of Public Instruction]
PNC Plaza is the tallest and largest skyscraper in Raleigh. It is 538 feet high. Cassie’s Construction Company wants to build a skyscraper that is even taller. The
spot they have to build the building on is 200 square feet. What are some possible dimensions for the base of the building? If they build the skyscraper to be
550 feet high, what will its volume be?
[North Carolina Dept. of Public Instruction]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
A rectangular container that has a length of 30 cm, a width of 20 cm, and a height of 24 cm is filled with water to a depth of 15 cm. When an additional 6.5 liters
of water is poured into the container, some water overflows. How many liters of water overflow the container? Use words, pictures, and numbers to explain
your answer. (Remember 1 cm3 = 1 mL.)
[www.engagyny.org]
Miguel and Jacqui built towers out of craft sticks. Miguel’s tower had a 4-inch square base. Jacqui’s tower had a 6-inch square base. If Miguel’s tower had a
volume of 128 cubic inches and Jacqui’s had a volume of 288 cubic inches, whose tower was taller? Explain your reasoning.
[engagyny.org]
Jack found the volume of the prism pictured to the right by multiplying 5 × 8 and then adding 40 + 40 + 40 = 120. He says the volume
is 120 cubic inches.

8 in
Jill says he did it wrong. He should have multiplied the bottom first (3 × 5) and then multiplied by the height. Explain to Jill
why Jack’s method works and is equivalent to her method.
5 in

Use Jack’s method to find the volume of this right rectangular prism.
3 in
5 ft
[www.engagyny.org]
Indianapolis Public Schools
2 ft
3 ft
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
5.M.5
Standard: 5.M.5: Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge
lengths to solve real-world problems and other mathematical problems.
Item Bank:
Indianapolis Public Schools
Curriculum & Instruction