Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 66175
How Do We Determine Volume?
Students are asked to determine how a unit cube can be used to measure the volume of a rectangular prism.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, volume, measure, cube
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_HowDoWeDeterimineVolume_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task should be implemented individually.
1. The teacher provides the student with the How Do We Determine Volume worksheet and says, “How could you use this cube (pointing to the smaller cube) to
determine the volume of this rectangular prism (pointing to the large rectangular prism)?”
2. If the student is able to explain that one could layer the smaller cubes in rows and columns with no gaps or overlaps to determine the volume, the teacher asks the
student, “If the dimensions of this cube are one by one by one, how can you describe the volume of the smaller cube?”
3. If the student states that the smaller cube has a volume of one cubic unit, the teacher should ask, “If it took 48 of these smaller cubes to completely fill the large
rectangular prism, what would the volume of the larger rectangular prism be?”
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the meaning of volume.
Examples of Student Work at this Level
The student says that you would place the smaller cubes around the edges of the large rectangular prism. The student cannot describe filling the large rectangular prism
even with prompting.
page 1 of 3 The student is only able to say that the volume could be determined by stacking the smaller cubes inside the larger cube and does not explain that the smaller cubes should
be stacked in rows and columns with no gaps or overlaps.
The student is not confident in his or her answer and needs prompting to offer a clear explanation.
Questions Eliciting Thinking
What does volume mean? How is volume measured?
Would we only stack the cubes around the edges of the box?
If I place cubes inside the box but there are gaps will I get an accurate measurement? How do you think we would stack the cubes?
Another student was determining the volume of this larger rectangular prism and she poured smaller cubes inside until it filled it up. However, the cubes were not stacked in
rows and columns. Do you think she will get the same volume as someone who filled it up in rows and columns with no gaps or overlaps?
Instructional Implications
Consider using the MFAS task How Do You Find the Volume (5.MD.3.3).
Explain that the unit of measure for volume is a cubic unit. Show the student examples of unit cubes such as a linking cube that can be used as a unit of measure for
volume. Use linking cubes to provide the student with examples and non-examples of how the volume of a rectangular prism can be measured. Explicitly express the volume
in terms of the unit cube (e.g., state that the volume is 120 cubic units reminding the student that a cubic unit is represented by one of the linking cubes).
Provide the student with an actual box and linking cubes. Have the student demonstrate how the volume of the box can be determined.
Making Progress
Misconception/Error
The student does not understand the unit used to determine volume.
Examples of Student Work at this Level
The student is able to explain that to measure the volume of the large rectangular prism one would need to stack the smaller cubes into rows and columns filling the entire
larger prism without any overlaps or gaps. However, the student is unable to explain the smaller unit represents one cubic unit and if 48 small cubes fit into the larger prism,
the volume would be 48 cubic units.
Questions Eliciting Thinking
How is volume measured? What is the unit of measure?
If each of these smaller cubes represents one cubic unit, how could you describe the volume of the large rectangular prism?
Instructional Implications
Explain that the unit of measure for volume is a cubic unit. Show the student examples of unit cubes such as a linking cube that can be used as a unit of measure for
volume. Show the student an example of a prism that was constructed with linking cubes. Ask the student to determine the volume of the prism. Guide the student to
express the volume in terms of the unit cube (e.g., state that the volume is 120 cubic units reminding the student that a cubic unit is represented by one of the linking
cubes).
Have the student build a rectangular prism with linking cubes and then determine the volume by counting the number of cubes (cubic units) that completely fill the
rectangular prism.
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 is able to explain that to measure the volume of the large rectangular prism one would need to stack the smaller cubes into rows and columns filling the entire
larger cube without any overlaps or gaps. Additionally, the student notes that the smaller cube has a volume of one cubic unit and that if 48 of those cubes were used to
completely fill the large rectangular prism, its volume would be 48 cubic units.
Questions Eliciting Thinking
How is surface area different from volume?
Instructional Implications
page 2 of 3 Explain to the student that every three-dimensional object has volume. Explain volume in terms of displacement as well as in terms of capacity. Demonstrate finding volumes
of a variety of solids by placing them in a known quantity of water in a measuring cup or graduated cylinder. Then measure the amount of water that has been displaced
and explain that the volume of the object is equal to the volume of displaced water. For this type of demonstration, it is convenient to use a cubic centimeter as the unit of
measure since one cubic centimeter equals one milliliter.
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 Determining Volume (5.MD.3.3) to encourage the student to use the bottom layer of cubic units to determine the volume of the entire
container.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
How Do We Determine the Volume worksheet (The same copy can be used for each student.)
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.3.3:
Description
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to
measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic
units.
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