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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

Build Rectangular Prisms Cards

To Gather

Connecting cubes

Activity Narrative

The purpose of this activity is for students to build and determine the volumes of rectangular prisms from images. In the Activity Synthesis, students look at two related prisms to encourage them to think about 8 unit cubes as a layer.

MLR8 Discussion Supports. During small-group discussion, invite students to take turns sharing their responses. Ask students to restate what they heard, using precise mathematical language and their own words. Display the sentence frame: “I heard you say . . . .” Original speakers can agree or clarify for their partner.
Advances: Listening, Speaking

Launch

Groups of 2
Give students access to connecting cubes.
“You are going to build the rectangular prisms shown on cards. Before we look at the cards, what information in the image will help you build the prism?” (The number of unit cubes in each layer and the numbers of rows and layers.)
Share responses.
“Now you each will pick a card, build the prism, and find its volume. Explain how you found the volume to your partner, and then pick another card.”

Activity

Monitor for students who discuss:
- How many unit cubes are in each layer.
- How the unit cubes are arranged in each layer.
- How many layers are in the prism.
Mathematical Community: As students work, monitor for examples of the “Doing Math” actions.

The prisms on the cards are completely packed with unit cubes.

Pick a card.
Build the rectangular prism.
Find the volume. Explain how you found the volume to your partner.
Repeat.

4 multicolored prisms.

Student Response

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Advancing Student Thinking

If students count each individual cube to determine the volume of the prism, consider asking,

“How did you decide to find the volume?”
“How many unit cubes are in each layer? How many layers are there?”

Activity Synthesis

Display Card E.
- “How did you build this rectangular prism?” (I counted 8 cubes, and then made a stack of 8 cubes.)
- “What is the volume of this rectangular prism? How do you know?” (8 unit cubes, because I counted 8 cubes.)
Display Card A.
- “How did you build this rectangular prism?” (I saw that there are 8 unit cubes on the top layer in 2 rows of 4. Then I built it up until it was 3 units high.)
- “What is the volume of this rectangular prism? How do you know?” (24 unit cubes, because there are 3 sets of 8 unit cubes and .)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Connecting cubes

Activity Narrative

The purpose of this activity is for students to find the volume of larger rectangular prisms shown in images. In previous lessons, students built rectangular prisms out of cubes and counted the cubes to determine the volumes of the rectangular prisms. In this activity, the prisms were intentionally chosen to encourage students to use the layered structure of each prism to determine their volumes (MP7). When students connect this structure to the operation of multiplication and use expressions and equations to find the volume, they decontextualize the geometric structure to solve the problems (MP2).

Representation: Access for Perception. Invite students to identify correspondences between the visual representation and the prism made of connecting cubes. Make connections between representations visible through gestures or labeled displays.
Supports accessibility for: Visual-Spatial Processing, Conceptual Processing

Launch

Groups of 2
Display the first prism.
“How would you describe this prism?” (There are 5 layers and each layer has 8 cubes, or there are 2 layers and each layer has 20 cubes.)
Give students access to connecting cubes.

Activity

10 minutes: independent work time
2 minutes: partner discussion
Monitor for students who use the layered structure to determine the volume.

The prisms are completely packed with unit cubes. Determine the volume of each prism. Explain or show your reasoning.

Student Response

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Advancing Student Thinking

If students count individual unit cubes to find the volume of each prism, consider asking,

“How did you decide to find the volume?”
“What is the same about these prisms? What is different?”

Activity Synthesis

Invite students to share how they found the volumes of the rectangular prisms.
Display the image of the first prism.
“The expression represents the volume of the prism. Where do you see 5 groups of 8 cubes in this prism?” (The top is 2 by 4, so there are 8 cubes on the top layer. There are 5 of those layers so that is .)
“What do these rectangular prisms have in common?” (All are 5 units high. All can be broken into 5 equal layers or groups. All have a side that is 4 units long. All can be broken into layers with 20 cubes.)
If time permits, ask “Who saw the layers differently?” (For the first prism, I used the side layer of 10 cubes. I multiplied 10 cubes by 4 layers to get 40 cubes.)