The purpose of this activity is for students to combine rectangular prisms to make a new figure and understand that the volume of the new figure is the sum of the volumes of the two rectangular prisms. This will be true no matter how they put the two rectangular prisms together.

If students count the individual cubes, ask them to build the figure with cubes and consider asking,

• “Can you describe this figure?”
• “Can you explain how this figure is made of rectangular prisms?”

• Ask previously identified students to share the individual prisms they built and how they put them together.
• “What was the volume of the shape you made when you put your prisms together? How do you know?” (22 cubic units because I used 12 cubes and my partner used 10 cubes, so that’s 22 cubes altogether.)
• Highlight that the different figures students made all have a volume of 22 cubic units.
• Display the figure that Diego and Jada made.
• “What is the volume of the figure Diego and Jada made? How do you know?” (30 cubic units. I broke it into two prisms, found their volumes, and added them.)

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 Activity 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 a rectangular prism, 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).

• 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 in a different way?”
• “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.)