HexBox and PentaBox Projects

Both of these projects are simple, and provide students with useful models of prisms, one with hexagonal bases and the other with pentagonal bases. When studying volume and surface area, it is very helpful for students to have their own model. If they have created the model themselves, it has greater value to them.

The first project is called the "HexBox", short for Hexagonal Box. The pattern is shown below. If students have access to Geometer's Sketchpad, it would be best if they constructed their own pattern. They would first construct a square, then add the "tabs" by constructing parallel lines, and angled lines. They would then rotate the first square 60 degrees about a corner, and repeat this process. This project can also be constructed using compass and straightedge; however it is a tedious construction when they have to do it 6 times; it might be best to ask them to construct the first two squares (with "flaps") and then let them trace them to complete the pattern. The bottom of the box is, of course, hexagon. They would then need to construct an additional hexagon to form the top of the box (attached, as shown below).

PentaBox: This is a box with a pentagon for the top and bottom, much like the Hexbox above. Constructing a pentagon with Sketchpad is easy to do, but the compass construction of a pentagon is a challenging construction.

Another option is to ask the students to write the steps of the construction, which will provide them valuable review of these constructions, whether with Sketchpad or using compass and straightedge. Writing the steps in the constructions gives student valuable experience in writing mathematics, and helps reinforce the steps in the student's memory.

A very good use of the HexBox and PentaBox projects is to ask the students to write the volume and surface area formulas directly on the box, on the faces and/or bases. Of course, this is best done before the pattern is folded. Writing the formulas reinforces them in the students' minds, and helps them to remember the formulas, as well as the meaning of volume and surface area. It might be helpful for the teacher to point out that the pattern before it is folded represents what we call surface area. Students can be asked to imagine the completed box filled with water; the volume of the box is the amount of water it would take to fill the box.