Using paper models of 5 proportional towers, the students collected data about the height of each tower, the surface area of the towers, and the volume of the towers.   

The students were then given a series of questions about the ratio of each of these measurements.                     

Students found that if the lengths were in a ratio of a to b, then the areas were in a ratio of a squared to b squared, and the volumes were in a ratio of a cubed to b cubed.

What was really surprising was that the height of tower 1 to tower 5 was 1 to 5, but the surface area of tower 1 to tower 5 was 1 to 25, and the volume of the tower 1 to tower 5 was 1 to 125.  That's a really big dog!!!  All of these ratios make sense when the students actually see the ratios right in front of them