Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 66125
Rectangular Prism Slices
Students are asked to sketch and describe two-dimensional figures that result from slicing a rectangular prism.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rectangular prism, slice, two-dimensional, three-dimensional, cross section, plane figure, parallel,
perpendicular, diagonal, dimensions
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RectangularPrismSlices_Worksheet.docx
MFAS_RectangularPrismSlices_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 problems on the Rectangular Prism Slices worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand that two-dimensional figures can result from slicing three-dimensional figures.
Examples of Student Work at this Level
The student does not describe the two-dimensional cross section of the prism, but instead:
Draws a three-dimensional piece that results from slicing the prism.
page 1 of 4 Draws the net of the three-dimensional shape resulting from the slice.
Draws a two- or three-dimensional view of one face, showing where the slice will be made.
Draws the results of a slice other than the one given (e.g., draws a triangle for the diagonal slice).
The student may also confuse some or all of the terms: horizontal, vertical, parallel, perpendicular, and diagonal.
Questions Eliciting Thinking
What is the difference between a two-dimensional figure and a three-dimensional figure? Can you give me an example of each?
Do you know what cross section means? Can you imagine the cross section of the prism that is revealed by the slicing? How would this cross section be different than a
net?
Which way is horizontal (vertical)? What does parallel (perpendicular) mean?
Where is the described diagonal? Are there other diagonals?
Instructional Implications
Review the difference between two-dimensional and three-dimensional figures. Provide the student with examples of figures to be classified as either two-dimensional or
three­dimensional. Ask the student to classify the figures and identify the dimensions of each. Clarify the difference between a “net” and a “slice” of the figure, explaining
that a section of a net represents a face of the three-dimensional figure. Therefore, a net is always congruent to the corresponding faces; however a slice may or may not
be congruent to a face.
Consider implementing the CPALMS Lesson Plan Can You Cut It? Slicing Three-Dimensional Figures (ID 47309). This lesson guides the student to sketch and describe a twodimensional figure resulting from the horizontal or vertical slicing of a three-dimensional figure. Be sure the student understands the difference between horizontal and
vertical, parallel and perpendicular. Model horizontal and vertical slices. Define parallel and perpendicular, and then model parallel and perpendicular slices in relation to the
base. Show the student that the dimensions of the slices can be described in terms of the dimensions of the original prism. If needed, provide additional experience with
identifying and drawing two-dimensional slices of three-dimensional figures and describing their dimensions. Consider implementing this task again to assess if the student can
sketch and describe the two-dimensional cross section resulting from each slice.
Making Progress
Misconception/Error
The student does not adequately describe the dimensions of the cross section in terms of the dimensions of the original figure.
page 2 of 4 Examples of Student Work at this Level
The student can identify and draw the shapes of the plane sections, but:
Does not describe the dimensions at all.
Describes the dimensions in terms of L, W, and H but does not specify what these variables represent.
Is not specific in describing the dimensions of the cross sections and only indicates that they “did not change.”
Incorrectly describes the third cross-section.
Questions Eliciting Thinking
You drew a rectangle for each answer. Would each rectangle have the same dimensions?
What do you mean by L, H, and W? Where are these lengths on the original figure?
What are the dimensions of each rectangle compared to the original length, width, and height of the prism?
When you make the diagonal cut, will the length of the cross section be the same as or different from the length of the prism? How will it compare?
Instructional Implications
Guide the student to relate the dimensions of the two-dimensional cross sections to the dimensions of the original three-dimensional figure. Model a concise comparison
(e.g., the height of the rectangular cross section is equal to the width of the prism and its length is equal to the length of the prism). Explain why
the length of the rectangular prism. Show the student that the length of
must be longer than
can be described as AH and model using this notation to refer to the length of the cross
section in the third problem. Provide additional opportunities for the student to precisely describe cross sections of three-dimensional figures.
Consider implementing the MFAS tasks Cylinder Slices, Cone Slices, and Square Pyramid Slices (7.G.1.3) for additional practice.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
page 3 of 4 Examples of Student Work at this Level
The student correctly identifies and draws the plane figures resulting from each slice, and describes each using specific dimensions. For example, the student says:
1. The cross section is a rectangle with a length equal to the length of the prism and a width equal to the width of the prism (or the same size as side AEHD).
2. The cross section is a rectangle with a length equal to the width (or length) of the prism and a width equal to the height of the prism, depending on the direction of the
slice (or the same size as side ABCD or CDHG).
3. The cross section is a rectangle with a length equal to AH and a width equal to the height of the prism (or forming rectangle AHGB).
Note: The student may label the dimensions of the prism and use the associated dimension labels on the two-dimensional shapes, rather than use a word description of the
resulting dimensions.
Questions Eliciting Thinking
Does the slice have to be in the middle (halfway) in order to be horizontal (vertical)? Can the horizontal slice be close to the bottom (or top) base of the prism?
What happens to the dimensions if the diagonal slice is parallel to diagonal
rather than through the diagonal
?
Instructional Implications
Challenge the student to:
Find as many different two-dimensional shapes as possible while describing the slice needed to make each one, including slices that are neither parallel nor perpendicular to
the base.
Describe slices from more complex figures such as a double cone or a pentagonal prism.
Consider implementing the MFAS tasks Cylinder Slices, Cone Slices, and Square Pyramid Slices (7.G.1.3) for additional practice.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Rectangular Prism Slices worksheet
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.7.G.1.3:
Description
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids.
page 4 of 4