The students in this video are developing the concept of volume as they attempt to answer the question: How many small cubes will fit into the large (yellow) cube? Five of the small cubes fit along each side of the large cube and students are provided with cubes and rods of various sizes to assist them in their investigation. This activity provides students with opportunities to consider a variety of methods of calculating volume as they listen to and assess each other’s ideas.

A couple of students are using the notion of starting with a smaller cube inside, for which they can count the number of small cubes used (64), and then figuring out the outside, but they have difficulty finding a solution. They may be having difficulty differentiating area and volume.

One student uses the notion of building up layers. This is a mathematically fruitful notion that eventually might lead to the notion of volume via integration, i.e., volume as an infinite sum of areas.