Lesson 7

The purpose of this warm-up is for students to notice there are different sized cubic units. This will be useful as students use standard units to measure the volumes of right rectangular prisms in upcoming activities. While students may notice and wonder many things about these cubes, the characteristics of a cube and size of the cubes are the important discussion points. 

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”

• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “The little cube represents a cubic foot. The big cube represents a cubic yard. About how many of the big cubes could we fit in our classroom?” (Answers vary. If time permits, measure the lengths and widths of the classroom, round them to the nearest yard, and check the reasonableness of the estimates.)
• “We have been using cubic units to measure volume, but haven’t defined the size of the unit. The choice of the unit depends on the size of the object.”

The purpose of this activity is for students to consider how the size of an object impacts the unit we use to measure the volume of that object. Since this is the students’ first experience with these cubic units of measure, it may be helpful for them to see the actual length of a centimeter, inch and foot. Have rulers or cubes available to provide extra support to visualize the size of the cubic units of measure. Because there are no mathematically correct or incorrect answers, this activity provides a rich opportunity for students to discuss and defend different points of view (MP3).
The launch of the activity is an opportunity for students to share their experiences and ask questions about the objects to ensure each student has access to the context. If it is helpful, display images of the items for students to reference.

• Groups of 2
• Write the list of objects (moving truck, freezer, etc…) on a display for all students to see.
• “Take a minute to read this list. What do you know about these objects? What do you wonder?”
• 3 minutes: partner discussion
• Share a few responses.
• Display the image from the warm-up.
• “In this activity we are going to consider using different cubic units of measure to find the volume of different sized objects. There is no right or wrong answer in these questions, but be prepared to explain your choice.”
• Give students access to rulers and yardsticks.

• 2 minutes: independent work time
• 5 minutes: partner discussion
• As students work, monitor for students who discuss how big or small the object is when choosing the size of the unit of measure. Ask these students to share during the synthesis.
• If students finish early, ask them to find other objects they would measure the volume of using the different cubic units of measure. If the objects are in the room, they could estimate and check their estimates.

• “How did you decide which units made sense?” (I tried to pick a unit that was not much smaller or much larger than the object being measured.)
• “What if I only wrote 24 as the volume for the freezer? What questions would you have?” (I would wonder 24 what? If we don’t know the unit of measure, we don’t know how big the freezer actually is.)
• Display: 24 cubic centimeters, 24 cubic inches, 24 cubic yards
• “What is the same about these measurements?” (They are all 24 units. They are all cubic units.)
• “What is different about these measurements?” (They are different sizes. Cubic centimeters and cubic inches are a lot smaller than cubic yards.)

This Info Gap activity gives students an opportunity to determine and request information needed to measure the volume of rectangular prisms using different sized units. 
The Info Gap routine requires students to make sense of problems by determining what information is necessary and then ask for information they need to solve them. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6). Since this is students’ first experience with the Info Gap routine, the Launch provides an opportunity to rehearse the routine together.

• Groups of 2
• Display Sample Problem Card from student workbook.
• “This is a diagram of a freezer. What is the volume of the freezer?”

• Read the problem aloud.
• Listen for and clarify any questions about the context.
• “Some of the information you need to solve this problem is missing, and I have it here. With your partner, decide what information you need to solve the problem, and create a list of questions you can ask to find out.”
• 1–2 minutes: quiet think time
• 2–3 minutes: partner discussion
• Invite students to share 1 question at a time.
• Record each question on a display, and respond with, “Why do you need to know _____ [restate the information requested]?” Students should provide a justification for how they will use the information before the information is revealed. For example, if students ask: “What is the width of the freezer?”, respond with, “Why do you need to know the width of the freezer?”
• Answer questions using only information stated on the Sample Data Card below (do not reveal):
  • The width of the freezer is 2 feet.
  • The length of the freezer is 4 feet.
• Record information that is shared on the display. Give students time to decide whether they have enough information to solve the problem.
• Repeat until students decide they have enough information to solve.
• 2–4 minutes: independent work time

• In each group, distribute a problem card to one student and a data card to the other student.
• After you review their work on the first problem, give them the cards for a second problem and instruct them to switch roles.

• Share the correct answers, including the units, and ask students to discuss the process of solving the problems.
• “What questions did you ask to help you find the volume?” (What is the height of the dumpster? How much space does Jada have in her backpack?)
• “What units were used for each problem? Did those units make sense?” (Cubic feet and cubic centimeters. Yes because a dumpster is big and a juice box is relatively small.)