Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 66732
Volume in Cubic Units
Students are asked to determine the volume of a rectangular prism in cubic units.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, volume, right rectangular prism, unit of measure, unit, cubic units
Resource Collection: MFAS Formative Assessments
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task should be implemented individually.
1. The teacher should build a 3 x 4 x 6 rectangular prism with linking cubes prior to giving the task.
2. The teacher shows the student the rectangular prism and asks, “What is the volume of this rectangular prism in cubic units?”
3. Have a piece of paper and a pencil available for the student to use, if needed.
4. If the student’s response does not include “cubic units” the teacher should ask, “What is the unit of measurement?”
5. If the student uses a formula (either l x w x h or B x h) to determine the volume the teacher should ask, “If you counted all of the cubes would you get the same
answer?”
TASK RUBRIC
Getting Started
Misconception/Error
The student does not completely understand the concept of volume.
Examples of Student Work at this Level
The student is unable to determine the volume of the prism and believes the answer will not be the same if the cubes are counted. The student may:
Determine the number of cubes in one face.
Multiply 3 x 4 = 12 and double that to determine a volume of 24 inches.
page 1 of 4 Multiply base by height and base by width and add the products.
Questions Eliciting Thinking
What is volume? What kinds of units are used to describe volume?
How is volume different from area? How is volume different from surface area?
Are there some cubes that cannot be seen? How can you be sure that you have counted all of the cubes?
I see you are trying to use a volume formula. How can you determine the length, width, and height of the prism?
Instructional Implications
Remind the student that volume is determined by the number of cubic units that completely fill a given shape. Guide the student in counting cubes in a systematic way. For
example, assist the student in determining how many cubes comprise the bottom layer of the prism (which is numerically the area of the base) and the number of layers (or
the height) of the prism. Guide the student to multiply the number of cubes in the bottom layer by the number of layers needed to fill the prism. Allow the student to use
linking cubes to model both the layers and the entire prism.
Consider using the MFAS task How Do You Find Volume? (5.MD.3.3) to assess the student’s understanding of volume.
Provide additional opportunities to calculate volume using unit cubes.
Moving Forward
Misconception/Error
The student uses a formula to find the volume but is unable to relate the formula to finding volume by counting unit cubes.
Examples of Student Work at this Level
The student is able to apply the formula for volume but cannot relate it to counting the unit cubes. The student has difficulty distinguishing linear and cubic units.
Questions Eliciting Thinking
If you did not know the formula for volume, how could you count to determine the volume of this rectangular prism?
How many cubes are on the bottom layer of this prism? How can you use that to help you determine the volume?
What dimensions do we need to consider when determining volume? How many dimensions is that?
Instructional Implications
page 2 of 4 Acknowledge that one can find the volume of a rectangular prism by multiplying the length by the width by the height. Clarify that in doing so, the unit of measure is one
cube. Explain that the question is asking the student to find the volume of the prism using the cube as the unit of measure. Have the student build the prism with linking
cubes. Guide the student to observe that the product of the length and width determines the number of cubes in each layer. The height is the number of layers in the
prism, so multiplying length by width by height determines the number of cubes in the prism (e.g., the volume).
Provide opportunities for the student to use various unit cubes to build a rectangular prism with a partner and then to determine the volume of each prism.
Almost There
Misconception/Error
The student makes a minor counting error.
Examples of Student Work at this Level
The student understands the process of determining the number of cubes needed to fill the prism but counts the number of cubes incorrectly.
Questions Eliciting Thinking
Good mathematicians check their work. Can you look at what you counted and double check it?
How many cubes are in one layer of this prism? Can that help you determine the total number of cubes in the prism?
Instructional Implications
Provide feedback concerning the error and ask the student to revise his or her work. Guide the student to be systematic in counting the number of cubes (e.g., suggest
determining the number of cubes that will fill each layer and then multiplying this number by the number of layers).
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly determines the volume of the prism is 72 cubic units. The student:
Counts the cubes to find the volume.
Applies one of the rectangular prism volume formulas (l x w x h or B x h) and is able to relate the formula to counting the number of cubes.
Questions Eliciting Thinking
How are volume and area different?
How can you determine the volume if you cannot see the cubes in the middle?
What can you do to find the volume of an object that cannot be taken apart? What if you didn’t have the cube in front of you to manipulate?
Instructional Implications
Provide numerous opportunities for the student to determine volume with and without manipulatives. Provide the student with images of rectangular prisms and have the
student determine the volume.
If the student does not know the formula for finding volume of rectangular prisms, encourage the student to use the concept of modeling a solid with unit cubes to derive
a formula for the volume of a rectangular prism. Guide the student to write the formula as either V = l x w x h or B = B x h where B is the area of the base.
Consider using the MFAS task Find The Volume (5.MD.3.4) to assess the student’s understanding of finding volume without manipulatives.
Consider using the MFAS task Volume With Improvised Units (5.MD.3.4) to assess the student’s understanding of determining volume without manipulatives and with
improvised units.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
3 x 4 x 6 rectangular prism made with linking cubes
page 3 of 4 Blank sheet of paper
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.MD.3.4:
Description
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
page 4 of 4