A plane cuts a right square pyramid perpendicular to its base. What could be the shape of the cross section that is formed
Answers
Draws the net of the three-dimensional shape resulting from the slice.
Draws a two-dimensional view showing the face and where the slice will be made.
Draws the results of a slice other than the one given.
The student may also confuse some or all of the terms: horizontal, vertical, parallel, perpendicular, vertex, and base.Questions Eliciting ThinkingWhat 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 pyramid 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 should the slice go that is perpendicular to the base but not through the vertex?Instructional ImplicationsReview the difference between two-dimensional and three-dimensional figures. Provide the student with examples of figures to be classified as either two-dimensional or three-dimensional. 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 two-dimensional 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. If needed, review the dimensions of a pyramid (e.g., the length and width of the base, height, lateral edge, and slant height). Show the student that the dimensions of the slices can be described in terms of the dimensions of the original pyramid. 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 ProgressMisconception/ErrorThe student does not adequately describe the dimensions of the cross section in terms of the dimensions of the original figure.Examples of Student Work at this LevelThe student can draw the shape of the correct two-dimensional cross section resulting from each slice, but:Does not clearly describe how the dimensions compare to the original figure.
Describes the dimensions in terms of W, B, and/or 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 “are not the same.”
Questions Eliciting ThinkingWhat do you mean by B (or W) and H? Where are these lengths on the original figure?To what part of the pyramid can you compare the square? How does the size of the slice compare to the size of the base of the pyramid?What are the two dimensions of the triangle resulting from the slice? To what part of the pyramid can you compare the base and height of the triangle?What type of quadrilateral resulted from the horizontal (or vertical, non-vertex) slice? How can you describe the lengths of the sides?Instructional ImplicationsGuide the student to relate the dimensions of the two-dimensional figure to the dimensions of the original three-dimensional figure. Model a concise comparison (e.g., the height of the triangle is equal to the height of the pyramid and the base of the triangle is equal to the length of the base edge of the pyramid). Provide additional opportunities to precisely describe cross sections of three-dimensional figures.Consider implementing the MFAS tasks Cylinder Slices, Cone Slices, and Rectangular Prism Slices(7.G.1.3) for additional practice.
Answer:
TASK RUBRICGetting StartedMisconception/ErrorThe student does not understand that two-dimensional figures can result from slicing three-dimensional figures.Examples of Student Work at this LevelThe student does not describe the two-dimensional cross section of the pyramid, but instead:Draws the three-dimensional pieces that result from slicing the pyramid.
Draws the net of the three-dimensional shape resulting from the slice.
Draws a two-dimensional view showing the face and where the slice will be made.
Draws the results of a slice other than the one given.
The student may also confuse some or all of the terms: horizontal, vertical, parallel, perpendicular, vertex, and base.Questions Eliciting ThinkingWhat 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 pyramid 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 should the slice go that is perpendicular to the base but not through the vertex?Instructional ImplicationsReview the difference between two-dimensional and three-dimensional figures. Provide the student with examples of figures to be classified as either two-dimensional or three-dimensional. 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 two-dimensional 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. If needed, review the dimensions of a pyramid (e.g., the length and width of the base, height, lateral edge, and slant height). Show the student that the dimensions of the slices can be described in terms of the dimensions of the original pyramid. 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 ProgressMisconception/ErrorThe student does not adequately describe the dimensions of the cross section in terms of the dimensions of the original figure.Examples of Student Work at this LevelThe student can draw the shape of the correct two-dimensional cross section resulting from each slice, but:Does not clearly describe how the dimensions compare to the original figure.
Describes the dimensions in terms of W, B, and/or 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 “are not the same.”
Questions Eliciting ThinkingWhat do you mean by B (or W) and H? Where are these lengths on the original figure?To what part of the pyramid can you compare the square? How does the size of the slice compare to the size of the base of the pyramid?What are the two dimensions of the triangle resulting from the slice? To what part of the pyramid can you compare the base and height of the triangle?What type of quadrilateral resulted from the horizontal (or vertical, non-vertex) slice? How can you describe the lengths of the sides?Instructional ImplicationsGuide the student to relate the dimensions of the two-dimensional figure to the dimensions of the original three-dimensional figure. Model a concise comparison (e.g., the height of the triangle is equal to the height of the pyramid and the base of the triangle is equal to the length of the base edge of the pyramid). Provide additional opportunities to precisely describe cross sections of three-dimensional figures.Consider implementing the MFAS tasks Cylinder Slices, Cone Slices, and Rectangular Prism Slices(7.G.1.3) for additional practice.
Step-by-step explanation: