Unit 1, Lesson 4
Use Layers to Determine Volume
Grade 5
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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.
Estimate the number of cubes used to build this prism.
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
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To Gather
Connecting cubes
In the previous lesson, students reasoned abstractly about the volume of a rectangular prism when they considered the volume in terms of layers or equal groups of unit cubes. This activity continues to develop the idea of decomposing rectangular prisms into layers. Students explicitly multiply the number of cubes in a base layer by the number of layers. Students can use any layer in the prism as the base layer as long as the height is the number of those base layers.
Complete the table.
| prism | number of cubes in one layer | number of layers | volume |
|---|---|---|---|
| A | |||
| B | |||
| C | |||
| D |
Find the volume of each prism. Explain or show your reasoning.
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To Gather
Connecting cubes
In the previous activity, students saw that a rectangular prism is composed of layers and there are different ways to decompose a prism into layers, depending on how it is viewed. Students recognize that the volume remains the same, regardless of the orientation of the prism. The goal of this activity is for students to identify how different expressions represent the volume of the same prism and correspond to the organization of the layers. Students have worked with parentheses in previous grades, so the Lesson Synthesis provides an opportunity for students to revisit expressions with parentheses. Students will have more experience with evaluating expressions with grouping symbols in future lessons. Students go back and forth between numerical expressions and a geometric object, the volume of which is represented by the expression (MP2).
How does the expression
How does the expression
Find a different way to calculate the volume of this rectangular prism. Write an expression to represent the way that you calculated the volume. Explain or show your reasoning.
We learned the amount of space an object takes up is volume.
This prism has a volume of 120 unit cubes.
We learned to calculate the volume of any prism by finding the number of cubes in one layer and multiplying that number by the number of layers. We can describe this rectangular prism as having 6 layers of 20 cubes, 4 layers of 30 cubes, or 5 layers of 24 cubes. All of these expressions represent the volume of the prism:
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