standard_description: 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.
problem_activity: Narrative
The purpose of this activity is for students to find the volume of a figure composed of two rectangular prisms and recognize that volume is additive. In the previous activity, students physically put two rectangular prisms together and then decomposed a figure into two rectangular prisms. In this activity, they are given an image of a figure composed of two rectangular prisms and asked to find the volume. They can do this in many ways. During the synthesis, connect the different strategies students used to the decomposition of the figure into two rectangular prisms.
As students experiment with different ways to group the cubes to efficiently count them, applying what they already know about the volume of rectangular prisms, they are looking for and making use of the structure of geometric objects (MP7). As students begin to generalize the idea that volume is additive, they are looking for and expressing regularity in repeated reasoning (MP8).
MLR7 Compare and Connect.
Synthesis: Invite students to prepare a visual display that shows the strategy they used to find the volume of each figure. Encourage students to include details that will help others interpret their thinking; for example, using specific language, or using different colors, shading, or arrows. Give students time to investigate each other’s work.
Advances: Representing
Launch
Groups of 2
Activity
5 minutes: individual work time
5 minutes: partner discussion
As students work, monitor for students who:
find two (or more) rectangular prisms that can be put together to make the figure and adding their volumes.
find the number of cubes in a base layer and multiplying by the number of layers, even though the base layer is not a rectangle (figure d).
Student Facing
Find the volume of each figure. Explain or show your reasoning.
a.
[IMG]
b.
[IMG]
c.
[IMG]
d.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students did not decompose the figures into rectangular prisms, encourage them to build the figures with connecting cubes and ask, “how can you decompose the figure into two rectangular prisms?”
Activity Synthesis
Display Figures c and d.
Ask selected students to share their way of splitting each figure.
“Who broke the figure up the same way? Who broke it up differently?”
“Can you think of other ways you could break up these figures?“ (I can cut them into several layers—3 horizontal layers for c, and 5 vertical layers for d. Each layer is a rectangular prism.)


aligns: no