Volume of Prisms
5 min
Teacher Prep
Setup
Narrative
This Warm-up reinforces the idea of using unit cubes and fractional-unit cubes as a way to measure the volume of a rectangular prism. The reasoning here prepares students to solve problems involving volumes of prisms later in the lesson.
Launch
Give students 2–3 minutes of quiet work time. Follow with a class discussion.
Student Task
-
How many cubes with an edge length of 1 inch fill this box?
- If the cubes had an edge length of 2 inches, would you need more or fewer cubes to fill the box? Explain your reasoning.
- If the cubes had an edge length of 21 inch, would you need more or fewer cubes to fill the box? Explain your reasoning.
Sample Response
- 120 cubes. Sample reasoning: 10⋅3⋅4=120
- Fewer. Sample reasoning: 8 cubes with edge lengths of 1 inch fit into a cube with edge lengths of 2 inches, so there will be fewer cubes.
- More. Sample reasoning: Each cube with edge lengths of 1 inch can be packed with 8 cubes with edge lengths of 21 inch, so there will be more cubes.
Activity Synthesis (Teacher Notes)
Select several students to share their responses and reasoning. After each person explains, ask students to indicate whether they agree. To involve more students in the discussion, consider asking:
- “Who can restate ’s reasoning in a different way?”
- “Does anyone want to add on to ’s reasoning?”
- “Do you agree or disagree with the reasoning? Why?”
Tell students that they will use their understanding of the volume of rectangular prisms to solve other geometric problems.
Standards
- 6.G.2·Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
- 6.G.A.2·Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas <span class="math">\(V = l w h\)</span> and <span class="math">\(V = b h\)</span> to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Volume of Prisms
5 min
Teacher Prep
Setup
Narrative
This Warm-up reinforces the idea of using unit cubes and fractional-unit cubes as a way to measure the volume of a rectangular prism. The reasoning here prepares students to solve problems involving volumes of prisms later in the lesson.
Launch
Give students 2–3 minutes of quiet work time. Follow with a class discussion.
Student Task
-
How many cubes with an edge length of 1 inch fill this box?
- If the cubes had an edge length of 2 inches, would you need more or fewer cubes to fill the box? Explain your reasoning.
- If the cubes had an edge length of 21 inch, would you need more or fewer cubes to fill the box? Explain your reasoning.
Sample Response
- 120 cubes. Sample reasoning: 10⋅3⋅4=120
- Fewer. Sample reasoning: 8 cubes with edge lengths of 1 inch fit into a cube with edge lengths of 2 inches, so there will be fewer cubes.
- More. Sample reasoning: Each cube with edge lengths of 1 inch can be packed with 8 cubes with edge lengths of 21 inch, so there will be more cubes.
Activity Synthesis (Teacher Notes)
Select several students to share their responses and reasoning. After each person explains, ask students to indicate whether they agree. To involve more students in the discussion, consider asking:
- “Who can restate ’s reasoning in a different way?”
- “Does anyone want to add on to ’s reasoning?”
- “Do you agree or disagree with the reasoning? Why?”
Tell students that they will use their understanding of the volume of rectangular prisms to solve other geometric problems.
Standards
- 6.G.2·Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
- 6.G.A.2·Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas <span class="math">\(V = l w h\)</span> and <span class="math">\(V = b h\)</span> to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.