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# What is Volume?

In this lesson, students will recognize volume as an attribute of solid figures and learn to calculate volume by counting cubes. This is a great introduction to the formula V = L x W x H.

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Students will recognize volume as an attribute of solid figures and calculate the volume of simple rectangular prisms by counting cubic units.

(10 minutes)
• Show students the two containers, one filled partly with water.
• Ask your class how much water they think is in the filled container. Students will likely guess using cups as a unit. Record and praise their guesses, acknowledging the units they are using.
• Wonder aloud how you might measure how much “space” is inside the containers. Let them struggle with this idea as they consider using different strategies. You don’t need to solve this right now, just get them wondering and strategizing.
• Now show them a rectangular prism and ask if it would be easier to measure the space in this container or the glass, again, just getting them thinking.
• Come back to the idea of units. Ask them to work in groups to think of a unit that could measure space inside of objects. Give students 2 minutes to discuss this in groups.
(5 minutes)
• Have each group share out their thinking. Discuss the different units they propose. It’s okay if groups struggle and don’t have an idea.
• Propose using marbles or circles to measure the space. Ask how many marbles (or other size cylinders) might fit inside the objects you have.
• If no student has raised this concern, ask students if the cylinders account for all of the space in the figure. Students should note that since they don’t fit exactly together, there will be space not measured in between them.
• Ask students what shape might work better—ones that fit flush without extra space in between.
• If they don’t think of it, suggest cubes. Discuss this suggestion.
(10 minutes)
• Explain that, because the cubes fit together perfectly we use cubic units to measure the space inside an object, called volume. Because cubes have three dimensions (length, width and height), we write it as units³.
• Distribute a paper cup of small cubes and a few sticky notes to each student or pair.
• Instruct students to make a shape with the cubes. Have them write the volume of their shape on the sticky note (i.e. 10 units³). The shape can be irregular.
• Have students circulate the room and observe others’ shapes and volume.
• Now have students create another shape with their cubes and write the dimensions of their shape and the volume on a new sticky note (i.e. 3 x 2 x 2; 12 units³). They may notice the formula shortcut, but it’s okay if they don’t see it yet. Share in small groups.
(15 minutes)
• Pass out grid paper or blank paper and have students go through that same process three more times, each time doing their best to draw the shape and record the dimensions on the diagram along with the volume.

Support

Enrichment

• Challenge students to find the formula (or shortcut) to calculating volume. Have students find the volume of shapes where only the dimensions are provided, or shapes where they need to measure the dimensions themselves.
(5 minutes)
• Draw a simple rectangular prism on the board (with individual cubes visible) and ask students to calculate the volume.
(10 minutes)
• Discuss the following question as a class: How does what I measure influence how we measure?

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