Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 65192
Cube Volume and Surface Area
Students are asked to calculate the volume and surface area of a cube.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, surface area, volume, area, edge, face, cube
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_CubeVolumeAndSurfaceArea_Worksheet.docx
MFAS_CubeVolumeAndSurfaceArea_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Cube Volume and Surface Area worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not demonstrate an understanding of surface area and volume.
Examples of Student Work at this Level
The student:
Uses an incorrect formula/strategy.
Multiplies edge length by six (rather than the area of a side by six) for a surface area of 49.2.
Multiplies edge length by three (rather than exponent of three) for a volume of 25.6.
page 1 of 5 Multiplies edge length by two (rather than squaring the edge length), then that product by six, for a surface area of 98.4.
Multiplies the perimeter of one face by six (rather than the area of the face), for a surface area of 196.8.
Multiplies edge length by number of edges (12) for a product of 98.4 (without specifying surface area or volume).
Multiplies volume by six for a total volume (after correctly multiplying the area of one face by six for surface area).
Finds the area and/or perimeter of a single face.
Calculates only the surface area or volume, but not both.
Uses the same (incorrect) formula for both surface area and volume (e.g., 8.2·4·6=196.8).
Questions Eliciting Thinking
Why did you choose those steps? What are you trying to find? Is there a formula that would help you?
Why did you find the area (or perimeter) of a face of the cube? How can that help you find the surface area (and volume)?
I see you found the surface area (or volume). What else is asked for in this problem? Do you know how to calculate that?
page 2 of 5 How are surface area and volume different? How is the edge length used to calculate each one?
Instructional Implications
Review the concept that the surface area of a composite solid can be found by decomposing the solid into familiar shapes and finding the surface area of the parts. Provide
opportunities for the student to decompose both two-dimensional and three-dimensional figures into familiar two-dimensional and three-dimensional shapes. Ask the student
to clearly identify the decomposed parts and any relevant dimensions. Include a review of 2-D nets that represent 3-D figures so the student can make the connection
between finding the sum of the areas of the individual 2-D shapes that comprise the net of the 3-D figure. Consider implementing the MFAS tasks Skateboard Ramp and
Pyramid Project (6.G.1.4) to give the student practice drawing a net from a 3-D figure and labeling its dimensions. Use solids other than cubes to begin this discussion so
students do not immediately jump to shortcuts (e.g., “multiply the area of one side by six”) that do not apply to all prisms.
Be sure the student understands the distinction between volume, area, and surface area, reviewing each concept as needed. Ensure that the student is familiar with a
variety of solids, as well as terms used to describe their parts and dimensions such as base, face, height, and edge. If necessary, review area formulas and ensure the
student understands that the surface area of a prism or pyramid can be calculated by adding the areas of its component parts. Guide the student in systematically
decomposing the solid, drawing the net, identifying relevant dimensions, and calculating areas. Consider implementing the MFAS tasks Windy Pyramid and Rust Protection
(6.G.1.4) to give the student practice finding the area of a net.
Provide manipulatives for the student to explore in order to gain hands-on experience calculating volume of rectangular prisms while discussing the meaning of various
volume formulas. Have the student explain the meaning of each part of a formula, including variables and constants.
Moving Forward
Misconception/Error
The student makes significant errors when calculating surface area or volume.
Examples of Student Work at this Level
The student:
Uses order of operations incorrectly when evaluating a formula.
Reverses the values for surface area and volume.
Finds the area of each face without finding the sum of all the faces for surface area.
Questions Eliciting Thinking
What formula are you trying to use? What order of operations is implied in this formula?
What is the difference between volume and surface area? How do you calculate each one?
Can you complete the problem by finding the total surface area?
Instructional Implications
Be sure the student understands the distinction between volume and surface area and review both concepts, as needed. Ensure that the student is familiar with
rectangular prisms in general and cubes specifically, including terms used to describe their parts and dimensions such as base, face, height, and edge. Ensure the student
understands and has an opportunity to practice finding the volume of prisms by finding the area of the base and multiplying by the height of the prism. Point out the cube
as a special case in which all dimensions are equal.
Further, review area formulas and ensure the student understands that the surface area of a solid can be calculated by adding the areas of its component parts. Then allow
the student to practice with finding the surface area of a cube to discover that a more efficient method is to find the area of one face and to multiply by six since the faces
are the same size. Provide additional opportunities for the student to find the surface area of solids and composite figures. Guide the student in systematically decomposing
the solid, drawing the net, identifying relevant dimensions, and calculating the area of each figure.
Guide the student to explain what each variable and constant in a formula represents. Reinforce this by asking the student to find, for example, the surface area of “all but
the top” of a cube, and have the student explain what changes they will need to make to the formula. Have the student explain if the formula for volume must also be
altered for this scenario. Then move into problems that include scenarios involving fraction and decimal edge lengths.
Almost There
Misconception/Error
The student makes a minor mathematical error.
Examples of Student Work at this Level
The student:
Makes a calculation error.
Rounds the answer (or an intermediate step) incorrectly (e.g., rounds 551.368 to 551.36 and rounds the intermediate step of 134.48 to 134.4).
page 3 of 5 Places the exponent belonging to the units on the number (e.g.,
cm and
cm).
Neglects to label units or labels them incorrectly.
Questions Eliciting Thinking
I think you may have made a calculation error. Can you check your work?
What rules do you remember for rounding a number? Can you revise your estimation and finish the problem?
How did you decide which units to use for each answer? What is the difference between
cm and 403.44
?
Instructional Implications
Provide specific feedback, and allow the student to revise his or her work and assign correct units.
Provide additional practice opportunities. Include shapes whose dimensions are given by rational numbers.
Provide practice problems for which the student must calculate the surface area and/or volume of a variety of solids, such as the MFAS task Prismatic Surface Area (7.G.2.6).
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 shows work and successfully calculates:
The surface area as 403.44
The volume as 551.368
(or 403 or 403.4).
(or 551, 551.4 or 551.37).
Questions Eliciting Thinking
Is there another way you could find the surface area and volume? Can you explain what each part of the formula you used means?
How would the process be different if this were a rectangular prism without all equal edge lengths?
If two of these cubes were stacked on top of each other, would the volume and surface area each be doubled? Explain.
Instructional Implications
Represent the dimensions of the figure with variables and challenge the student to write a single expression for finding the surface area and volume of the cube.
Provide practice problems involving solids with fractional edge lengths and problems in which surface area and/or volume is given but the student must identify a missing
measurement.
Provide opportunities for the student to explore how changing a dimension of a figure affects the surface area and volume.
Consider implementing other MFAS tasks such as Chilling Volumes and Composite Surface Area (7.G.2.6) in which the student must calculate the volume and surface area of
composite figures.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Cube Volume and Surface Area worksheet
Calculator
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
page 4 of 5 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
Description
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional
objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MAFS.7.G.2.6:
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
Work toward meeting this standard draws together grades 3–6 work with geometric measurement.
page 5 of 5