Volume of Right Prisms
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to encourage students to think about how the area of the base affects the volume of prisms with the same height and affects the height of prisms with the same volume. This is a review of previous work students have done with volume, in which they found the volume of a rectangular prism by multiplying the area of a base by the corresponding height of the prism. The ideas in this Warm-up are revisited later in this lesson, so it is important that students can clearly explain how they ordered their prisms based on them having the same volume and how they found the height of the prism with base C.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time followed by time to discuss their explanations with a partner. Follow with a whole-class discussion.
Student Task
Rectangles A, B, and C represent bases of three prisms.
- If each prism has the same height, which one will have the greatest volume, and which will have the least? Explain your reasoning.
- If each prism has the same volume, which one will have the tallest height, and which will have the shortest? Explain your reasoning.
Sample Response
- Prism C will have the greatest volume and prism A will have the least. Since the volume is the area of the base multiplied by the height, the base with the greatest area will have the greatest volume, even if all the heights are the same.
- Prism A will have the tallest height and prism C will have the shortest. Since the volume is the area of the base multiplied by the height, the base with the least area will have the tallest height, and the base with the greatest area will have the shortest height.
Activity Synthesis (Teacher Notes)
The purpose of this discussion is to clarify the relationship between a prism’s area, height, and volume. Select students to share which prisms they found to have the greatest and least volume and the tallest and shortest height. Record and display their responses for all to see. Ask the class if they agree or disagree. If students all agree, ask a few students to share their reasoning. If they do not agree, ask students to share their reasoning until they reach an agreement.
If there is time, display this question for all to see: “If each prism has the same volume and the prism associated with base B has a height of 6 units, what is the height of the prism associated with base C?”
Have students share the volume of the prism with base C and their reasoning. Record and display the responses for all to see.
Standards
- 7.G.6·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.
- 7.G.B.6·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.
10 min
15 min
Knowledge Components
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Volume of Right Prisms
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to encourage students to think about how the area of the base affects the volume of prisms with the same height and affects the height of prisms with the same volume. This is a review of previous work students have done with volume, in which they found the volume of a rectangular prism by multiplying the area of a base by the corresponding height of the prism. The ideas in this Warm-up are revisited later in this lesson, so it is important that students can clearly explain how they ordered their prisms based on them having the same volume and how they found the height of the prism with base C.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time followed by time to discuss their explanations with a partner. Follow with a whole-class discussion.
Student Task
Rectangles A, B, and C represent bases of three prisms.
- If each prism has the same height, which one will have the greatest volume, and which will have the least? Explain your reasoning.
- If each prism has the same volume, which one will have the tallest height, and which will have the shortest? Explain your reasoning.
Sample Response
- Prism C will have the greatest volume and prism A will have the least. Since the volume is the area of the base multiplied by the height, the base with the greatest area will have the greatest volume, even if all the heights are the same.
- Prism A will have the tallest height and prism C will have the shortest. Since the volume is the area of the base multiplied by the height, the base with the least area will have the tallest height, and the base with the greatest area will have the shortest height.
Activity Synthesis (Teacher Notes)
The purpose of this discussion is to clarify the relationship between a prism’s area, height, and volume. Select students to share which prisms they found to have the greatest and least volume and the tallest and shortest height. Record and display their responses for all to see. Ask the class if they agree or disagree. If students all agree, ask a few students to share their reasoning. If they do not agree, ask students to share their reasoning until they reach an agreement.
If there is time, display this question for all to see: “If each prism has the same volume and the prism associated with base B has a height of 6 units, what is the height of the prism associated with base C?”
Have students share the volume of the prism with base C and their reasoning. Record and display the responses for all to see.
Standards
- 7.G.6·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.
- 7.G.B.6·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.