I found a lot of apps that calculate area and volume, but none that demonstrate where the formulas come from. So that's my app idea!
To make a manageable app, I was thinking one that demonstrates finding the volume of a prism. Ideally it would allow the user to choose different base shapes, but that might be too big the first time around. So maybe just rectangular or triangular the first time around.
For example: A rectangular prism
The user would input the units (cm) and the dimensions of the base: 6 x 2, and the app would demonstrate finding the area of one "layer" to fill the prism. It would draw a layer of 12 blocks (or one rectagular layer that is 6 x 2), 1 unit high, and show that the area of the base is 12 square cm.
Then it would ask for the height of the prism: 3. It would build the prism by adding two more layers on, for a total of 3, then show that to get the volume, the area of the base is multiplied by 3 to get 36 cubic cm.
If there were time, it would be awesome to have a menu at the beginning allowing the user to choose other shapes for the base: triangle, hexagon, even circles. But each would require separate programming because each would need different input dimensions to find the area of the base (triangle needs base and height, hexagon needs side and apothem, etc).
This could really continue semester after semester, to add pyramids/cones (which is a neat visual where you show that 3 pyramids fit in a prism), and even move on to surface area.I've got another idea about showing how to find the area of a hexagon by dividing it into triangles. Could give more details if desired.