Today’s classroom goal was to build connections between the volume of a cylinder and its matching cone (same radius and same height) and the analogous prism/pyramid pair.

There is a classic demonstration filling a cylinder/cone pair with water or sand. It takes three cones to fill the cylinder. An extensive youtube search shows only two videos of this demonstration: one that is terrible and one that is horrendous. My co-teacher and I filmed our version yesterday, and it is a challenging video. The geometric figures are transparent and do not show up well on video. Using plain water added to the trouble. We could have colored the water or used colored sand.

Our film begins with a pyramid and a prism in a tight shot. Hands move the objects to demonstrate that that have matching bases and heights. Then a screen asks the viewer to guess how their volumes will compare. The pyramid is filled with water and poured into the prism three times. A screen of text tells the viewer than a prism has three times the volume of a pyramid with the same Base and height. We then see a cone and cylinder. We go through the same process, except this time the cylinder is filled and poured into the cone three times. The final screen reads, “A cone has one-third the volume of a cylinder with the same height and Base.”

After watching the two-minute video, students were asked to write in their own words the volume relationships they observed. Then they were reminded that the volume of a prism can be calculated with the formula V=Bh and they were asked to modify that formula to represent the volume of a pyramid.

Students in general did very well with these requests. Most students were able to describe the relationship between the objects’ volumes. (Poor examples said, “the prism is bigger than the pyramid,” or “they have the same height and base.”) A high percentage of students wrote a formula for the volume of a pyramid that read V = Bh ÷ 3.

The worksheet proceeded by asking students to calculate the volume of a cylinder and then the volume of its matching cone. This allowed students to transfer the theoretical knowledge that “a cone is one-third the volume of a matching cylinder” to the practical knowledge that they could divide the cylinder’s volume by three to calculate the volume of its matching cone.

The questions were laid out in a sequence that really helped most students develop the concepts we wanted. There were plenty of expressions of understanding during the day.

In other logistics, the video had no dialogue or instruction, just a music track. This made headphones unnecessary and made the iPods much easier to work with.