Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

Students explore the volume of a box based on the amount of unit cubes that can fit inside of it in this student interactive, from Illuminations. They are prompted to come up with a rule for determining the volume of a box when its width, depth, and height are known.

This task is from Tools 4 NC Teachers. Students build and explore volume as they build boxes and rectangular prisms.

This resource is from Tools4NCTeachers.In this lesson, students are given boxes to cut apart.  As they decompose the boxes, students notice the 2-dimensional shapes used to construct their 3-dimensional boxes.  A printable student recording sheet is provided within this lesson.Remix to include pictures of student work samples.