Fixed Volume

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The students will understand the relationship between volume and surface area.

Big Idea

Beans, beans, the magical volume tool.


15 minutes

In this lesson students will be exploring right rectangular prisms with a fixed volume.  A background in creating right rectangular prisms will aid students in future lessons as they deepen their understanding of volume. 

To begin this lesson I start with a quick demonstration using construction paper and beans.  I take two sheets of construction paper and tape one on the edge the “hotdog” way and the other on the edge the “hamburger” way.  I ask students to write down their prediction of which container will hold more beans or if they will both hold the same. 

Once students have recorded their predictions I have them share their thinking with their groups.  After a few minutes I the attention back on me as I perform the quick experiment.  I start by filling the hotdog container by placing it standing up inside the hamburger container.  After filling the first container I lift the container and allow the beans to begin to fill the second container.  Students are amazed at what they see; about 2/3 of the students were incorrect in their prediction. 

I wrap up this quick experiment by asking students a few questions to glen meaning from the demonstration. 

What was different about the two containers?  What was similar about the two containers?  What surprised you most about the demonstration? 


30 minutes

Although the first activity focused on a fixed surface area, I will now have the students move into an activity that focuses on a fixed volume.  Students will be working with their partners to construct as many unique right rectangular prisms as they can using 64 cubes.  Before releasing them to work we review the properties of the right rectangular prism. 

For each prism that the students create I ask them to make a quick sketch on a piece of paper so that they can refer back to it as they continue creating.  Each prism must contain all 64 cubes.

This activity can also be done with a smaller number of cubes such as 24. 


15 minutes

By the end of the lesson I would like students to make a connection between fixed volume and surface area.  The opening activity showed students that a fixed surface area does not mean equal volume.  I make the connection in the second activity by asking students to think about the surface area of some of the shapes they created. 

Alright, now that you guys have created quite a few different right rectangular prisms, let’s look at the surface area of those prisms.  Take a second and look back to some of your sketches.  What were the surface areas?

I allow students some time to work with their partner to determine the surface area of the prisms.  I then bring them back to a whole group discussion as we look for some potential patterns in fixed volume and surface area. 

The students begin to quickly see that shapes with the same volume do not necessarily have the same surface area.  The goal here is for students to identify that volume does not indicate surface area and the relationship between them is similar to area and perimeter.