Exploring Surface Area and Volume of Rectangular Prisms
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.
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
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
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)