Lesson 11

This warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.  During the synthesis, ask students to explain the meaning of any terminology they use such as volume, base, height, length, and width.

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”

• 1 minute: quiet think time
• 2–3 minutes: partner discussion
• Share and record responses.

• “What do Figures A, C, and D have in common?” (They all show individual cubes. They all have 5 as one of their side lengths.)

The purpose of this activity is for students to practice finding the volume of rectangular prisms given a real-world context. The first problem provides a diagram like students have seen in earlier lessons to illustrate the context. The other problems do not provide a picture so students will need to visualize or draw a sketch of the situation. Going from the words of the problem to a mental image to a solution strategy are all important aspects of making sense of and solving a problem (MP1).
Because these are real-world problems, each rectangular prism sits on a natural base. Monitor for students who use this structure and use the formula connecting volume to the area of the base and the height relative to that base.

• Groups of 2

• 8 minutes: individual work time
• 2 minutes: partner discussion
• Monitor for students who find the volume in different ways, either using different bases or using 3 measurements for the length, width, and height.

• Ask selected students to share their solutions for the second problem.
• “How are the strategies the same? How are they different?” (They both got the same solution, but one person multiplied \(4\times9\) to get the area of the base and then multiplied the result by 5, but the other person chose to multiply \(4\times5\) first.)
• “How is the third problem different from the first two?” (It does not give us the length and width of the closet. It just gives the area of the floor.)

The purpose of this activity is for students to solve a real-world problem that involves finding the volume of a figure composed of two right rectangular prisms. Unlike many other figures students have seen, this one can be decomposed into two rectangular prisms in only one way. Students may rearrange the two prisms to make a single, long rectangular prism.

• Display the picture of the garden from the student workbook:

  

  

• “This type of garden is called a raised bed garden because the plants are not in the ground.”
• “If we planted a garden at our school, what vegetables would you want to grow?”

• 5 minutes: individual work time
• 5 minutes: partner discussion
• Monitor for students who break the garden into two rectangular prisms, finding the volume of each, and for students who put them together to form a single rectangular prism.

• Display the diagram of the garden from the task.
• Invite students to share how they found its volume.
• “What do the two parts of the garden have in common?” (They are both 4 feet tall and 3 feet wide.)
• “What is different about the two parts of the garden?” (The length. One piece is 10 feet long and the other piece is 8 feet long.)
• “How could you put the pieces together to make a single rectangular prism?” (The sides that are 3 feet by 4 feet fit together and the length would be 18 feet.)