Decomposing Bases for Area
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to recognize prisms and their bases. This concept reinforces what was discussed in the previous lesson where students found the volume of different prisms and non-prisms. Students first determine whether or not a given figure is a prism and then shade and describe the base of the prism. As students work on the task, monitor for students who are using precise language to describe the reason that a figure is a prism.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time, followed by time to discuss their answers with a partner. Follow this with a whole-class discussion.
Student Task
-
Which of these solids are prisms? Explain how you know.
A B C D E F -
For each of the prisms, what does the base look like?
-
Shade one base in the picture.
-
Draw a cross-section of the prism parallel to the base.
-
Sample Response
- A, B, C, and E are prisms since there is a base shape that is the same on each end with vertices connected by line segments.
- The base for A is a square (any of the faces). The base for B is a pentagon (in the front or back). The base for C is a triangle (on the top or bottom). The base for E is a quadrilateral (on the top or bottom).
- Answers vary.
- Students' drawings should be the same shape as the base of each prism: A: square, B: pentagon, C: triangle, E: quadrilateral
Activity Synthesis (Teacher Notes)
The goal of this activity is to remind students that a figure is a prism if the cross-section, when cut parallel to the base, has the same size and shape as the base of the figure. Select previously identified students to share their reasoning. Invite students to share the bases that they shaded and their drawings of the cross-sections.
Anticipated Misconceptions
If students struggle to see why figure B is a prism, consider asking:
- “How do you know if a solid is a prism?”
- “Is the base of a prism always the bottom?”
Standards
- 7.G.3·Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
- 7.G.A.3·Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
15 min
10 min
Knowledge Components
All skills for this lesson
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Decomposing Bases for Area
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to recognize prisms and their bases. This concept reinforces what was discussed in the previous lesson where students found the volume of different prisms and non-prisms. Students first determine whether or not a given figure is a prism and then shade and describe the base of the prism. As students work on the task, monitor for students who are using precise language to describe the reason that a figure is a prism.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time, followed by time to discuss their answers with a partner. Follow this with a whole-class discussion.
Student Task
-
Which of these solids are prisms? Explain how you know.
A B C D E F -
For each of the prisms, what does the base look like?
-
Shade one base in the picture.
-
Draw a cross-section of the prism parallel to the base.
-
Sample Response
- A, B, C, and E are prisms since there is a base shape that is the same on each end with vertices connected by line segments.
- The base for A is a square (any of the faces). The base for B is a pentagon (in the front or back). The base for C is a triangle (on the top or bottom). The base for E is a quadrilateral (on the top or bottom).
- Answers vary.
- Students' drawings should be the same shape as the base of each prism: A: square, B: pentagon, C: triangle, E: quadrilateral
Activity Synthesis (Teacher Notes)
The goal of this activity is to remind students that a figure is a prism if the cross-section, when cut parallel to the base, has the same size and shape as the base of the figure. Select previously identified students to share their reasoning. Invite students to share the bases that they shaded and their drawings of the cross-sections.
Anticipated Misconceptions
If students struggle to see why figure B is a prism, consider asking:
- “How do you know if a solid is a prism?”
- “Is the base of a prism always the bottom?”
Standards
- 7.G.3·Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
- 7.G.A.3·Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.