We had a great 10 or 15 minutes of class today just trying to practice visualizing volume. This is the first time I have taught this to a non AP class, so I didn't wanted to assume anything by skipping to the calculation part. I brought in 5 or 6 objects that are solids of revolution (like a vase, bowl, glass etc) and had my students try to make them in front of the class with the iPad app 123d Make. Basically, you draw a shape like this:
And it rotates it around the axis on the right to make a solid like this:
This was really, really fun and it was so cool to have immediate feedback for their ideas. The idea of the calculation was still a bit tricky from here, but at least they had no problem with the visualizing part.
The other cool part about the program is that it makes patterns you can use with real cardboard to make the objects that you see.