Use Layers to Determine Volume
10 min
Narrative
The purpose of this Estimation Exploration is for students to consider the information they need to find the volume of a rectangular prism and use the structure of a rectangular prism to think about a reasonable estimate. Students can see the 9 cubes on the front layer, but it is difficult to see how many layers there are.
This is the first time students experience the Estimation Exploration routine in grade 5. Students are familiar with this routine from a previous grade, however, they may benefit from a brief review of the steps involved.
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
Teacher Instructions
- 1 minute: quiet think time
- 1 minute: partner discussion
- Share and record responses
Student Task
Estimate the number of cubes used to build this prism.
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample responses:
- Too low: 30 or fewer
- About right: 60–100
- Too high: 200–300
Activity Synthesis (Teacher Notes)
- “Why are multiples of 9 good estimates?” (We can see the layer of 9 cubes.)
- “What information would help you to find the exact number of cubes in the prism?” (The number of layers of 9 cubes. How deep the prism goes.)
- “Based on this discussion does anyone want to revise their estimate?”
- Optional: Reveal a picture that shows the number of layers, 10.
Standards
- 5.MD.5.a·Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
- 5.MD.C.5.a·Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
20 min
15 min
Knowledge Components
All skills for this lesson
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Use Layers to Determine Volume
10 min
Narrative
The purpose of this Estimation Exploration is for students to consider the information they need to find the volume of a rectangular prism and use the structure of a rectangular prism to think about a reasonable estimate. Students can see the 9 cubes on the front layer, but it is difficult to see how many layers there are.
This is the first time students experience the Estimation Exploration routine in grade 5. Students are familiar with this routine from a previous grade, however, they may benefit from a brief review of the steps involved.
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
Teacher Instructions
- 1 minute: quiet think time
- 1 minute: partner discussion
- Share and record responses
Student Task
Estimate the number of cubes used to build this prism.
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Sample Response
Sample responses:
- Too low: 30 or fewer
- About right: 60–100
- Too high: 200–300
Activity Synthesis (Teacher Notes)
- “Why are multiples of 9 good estimates?” (We can see the layer of 9 cubes.)
- “What information would help you to find the exact number of cubes in the prism?” (The number of layers of 9 cubes. How deep the prism goes.)
- “Based on this discussion does anyone want to revise their estimate?”
- Optional: Reveal a picture that shows the number of layers, 10.
Standards
- 5.MD.5.a·Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
- 5.MD.C.5.a·Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.