Lesson 1

What Is Volume?

Warm-up: Which One Doesn’t Belong: Objects Made of Cubes (10 minutes)

Narrative

The purpose of this warm-up is for students to compare four objects made of cubes and reason about their configuration. Responses related to the orientation of the object and the number of cubes in each will be applicable to the upcoming activities.

For all warm-up routines, consider establishing a small, discreet hand signal that students can display to indicate they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or a different subtle signal. This is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

Math Community

• After the warm-up, ask students to reflect on both individual and group actions while considering the question “What does it look and sound like to do math together as a mathematical community? What am I doing? What are you doing?”
• Record and display their responses under the “Doing Math” header. Students might mention things such as: we talked to each other and to the teacher; we had quiet time to think; we shared our ideas; we thought about the math ideas and words we knew; you were writing down our answers; you were waiting until we gave the answers.

Launch

• Groups of  2
• Display image
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

Activity

• 2-3 minutes: partner discussion
• Share and record responses.

Student Facing

Which one doesn’t belong?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• “What do objects A, C, and D have in common?” (Each side or face of the shapes is a rectangle. They are all made from cubes of the same size.)

Activity 1: Build Objects with Cubes (15 minutes)

Narrative

The purpose of this activity is for students to recognize that objects with the same volume take up the same amount of space. The word bigger is intentionally vague to elicit ideas about length, width, and height and encourage students to reason about the number of cubes.

Monitor for the language students use to explain their choices such as longer, wider, taller or reference to the number of cubes. Students may choose to use connecting cubes to build the objects to compare and clarify their arguments (MP5). As students discuss and justify their decisions, they have opportunities to create viable arguments and critique one another's reasoning (MP3). The discussion and comparison of students' arguments helps illustrate the need for precise mathematical vocabulary and prepares students to learn the meaning of volume (MP6).

MLR2 Collect and Display. Collect and record the language students use to compare objects. Display words and phrases such as: “bigger,” “longer,” “wider,” “taller,” “shorter,” “how many,” “more than,” “less than.” During the synthesis, invite students to suggest ways to update the display.

Launch

• Groups of  2
• “Now you will compare objects to determine which is bigger, including some from the warm-up.”

Activity

• 5 minutes: individual work time
• 5 minutes: partner work time
• As students work, monitor for students who discuss ‘bigger’ in terms of the number of cubes.

Student Facing

1. Which is bigger? Explain or show your reasoning.
2. Which is bigger? Explain or show your reasoning.
3. What does it mean for an object to be “bigger”?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• Share responses for both problems. Encourage students who make different choices to explain their reasoning.
• Display the first pair of objects.
• “How would you describe the amount of space each object takes up?” (It’s the same for both shapes. They are made from 8 individual cubes.)
• “We call the amount of space an object takes up its volume.”
• Display the second pair of objects.
• “Which object has greater volume?” (They are the same. They are both made from 8 cubes.)
• “What is different about the two objects?” (One is a cube and the other is not. One is taller than the other.)

Activity 2: Build and Order (20 minutes)

Narrative

The purpose of this activity is for students to build solid objects and compare them by their volume. Students count the number of cubes in each object and may recognize that the shape and orientation of the object doesn’t matter when comparing volumes. Encourage students to build any object in which the cubes connect, not just rectangular prisms.

If there is extra time, students could try drawing their objects on dot paper (blackline master). It is not an expectation that students use the dot paper, but some students may like to try representing their objects with it.

Representation: Access for Perception. Read directions aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language, Attention

Required Materials

Materials to Gather

Materials to Copy

• Isometric Dot Paper Standard

Required Preparation

• Each group of 2 needs 24 connecting cubes.
• Have copies of centimeter dot paper available for students who would like to try drawing their objects.

Launch

• Groups of 4
• Give each group a pile of connecting cubes.

Activity

• 10 minutes: group work time
• As students work, collect a group’s objects that all have a volume of 9 units but have different arrangements.

Student Facing

1. Each group member:
1. Take a handful of connecting cubes.
2. Build an object.
2. Order the objects by volume.
3. Repeat.
4. Each group member:
1. Take 9 connecting cubes.
2. Build an object.
5. Order the objects by volume

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• Display 3 or 4 objects all built using 9 cubes.
• “What is the same? What is different?” (Some of the objects are taller, some are shorter. Some of the objects are wider. They are all made with 9 cubes.)
• “How do the volumes of these objects compare? How do you know?” (They are all the same because each object takes up the same amount of space or has the same number of cubes.)
• “How much space does each object take up?” (9 cubes)

Lesson Synthesis

Lesson Synthesis

“Today, we built objects out of cubes and compared them by the amount of space they take up. We call this an object’s volume.”

Display the images from the activity or the objects made from cubes.

“How are the two objects the same?” (They are both made from 8 cubes. There are four cubes next to one another on the bottom layer.)

“How are the two objects different?” (One of them is a cube and the other looks like a tower. One of them is taller than the other.)

“These two objects look different, but take up the same amount of space, that is they have the same volume.”

Math Community

After the Cool-down, revisit the “Doing Math” list of actions. Ask students to discuss with a partner where they saw evidence of the actions during the rest of the day’s lesson. As a whole group, add any missing actions and revise earlier ideas.

Cool-down: Which Has More Volume? (5 minutes)

Cool-Down

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