Exploring Surface Area and Volume of Rectangular Prisms

Terri Breyfogle, Kris Peterson, Luther Berkeland, Dave Kohutko, Jen Clementson, based on an original activity from the CMP2 book Filling and Wrapping, Investigation 2.1.
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In this lesson, students are given cubes that measure 1 cubic inch. They are asked to find all of the unique arrangements possible to build rectangular prisms. They must record the length, width, and height as well as find the surface area and volume for each arrangement. Students will answer questions that will help them explore least surface area, most surface area, and help them develop a method for finding volume of a rectangular prism. They will then do an extension problem to test their findings.

Learning Goals

Learning goals:
1. Students will connect dimensions of a rectangular prism to its volume and surface area.
2. Students will understand that rectangular prisms may have the same volume but drastically different surface areas.
3. The students will develop a method for finding volume and surface areas of rectangular prisms that will be used in new situations.

Context for Use

This lesson was taught following the conclusion of another unit on area and perimeter. The class was a multi-ability 6th grade classroom. The lesson took one full 60 minute class period, and the follow-up activity will require at least another 15-20 minutes the following day. Students will need to have wooden or plastic cubes to build with, and dot paper would be appropriate for those who are ready to attempt to sketch their figures.

Description and Teaching Materials

Students should be provided with 24 cubic inch blocks, a lab sheet, and dot paper (optional). The teacher will introduce the activity by providing a model of a rectangular prism and asking students about the number and type of faces, what is meant by the term "surface area" and what is meant by the term "volume." The teacher will then clarify directions on the lab sheet and let students work in their small groups (3-4 students per group). The students will build all possible rectangular prisms from 24 cubes and will record their finding in the table on the labsheet. Students will further explore other possible arrangements by being given different amounts of cubes to arrange. The teacher will pull the class together after approximately 20-30 minutes of working and discuss their findings for the 24 cubes. Following that discussion, students may continue to work on other cube arrangements.

Teaching Notes and Tips

Be sure to talk about the fact that taking a prism and turning it on its side has not changed its dimensions, therefore, it is not a unique prism. Also, before the students begin to work, give them the suggestion that they should have a system to their building so that they don't miss any arrangements.


Homework will be assigned after more practice. The teacher will use informal assessment while students are building their models and recording their data.

References and Resources

Attached is the labsheet that should be given to the students along with the inch cubes and dot paper (optional).

Using Cubes to Explore Volume and Surface Area (Microsoft Word 2007 (.docx) 12kB Apr6 09)