The purpose of this activity is for students to build and determine the volume 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.

• Display Card E.
  • “¿Cómo construyeron este prisma rectangular?” // “How did you build this rectangular prism?” (I counted 8 cubes, and then made a stack of 8 cubes.)
  • “¿Cuál es el volumen de este prisma rectangular? ¿Cómo lo saben?” // “What is the volume of this rectangular prism? How do you know?” (8 unit cubes, because I counted 8 cubes.)
• Display Card A.
  • “¿Cómo construyeron este prisma rectangular?” // “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.)
  • “¿Cuál es el volumen de este prisma rectangular? ¿Cómo lo saben?” // “What is the volume of this rectangular prism? How do you know?” (24 unit cubes, because there are 3 sets of 8 cubes and .)

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).

• Invite students to share how they found the volumes of the rectangular prisms.
• Display the image of the first prism.
• “La expresión  representa el volumen de este prisma. ¿En qué parte del prisma ven 5 grupos de 8 cubos?” // “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  .)
• “¿Qué tienen en común estos prismas rectangulares?” // “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 “¿Alguien vio las capas de otra manera?” // “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.)