When teaching my students about volume, I gave them the formulas for a cone and cylinder.   We were reading over the formulas and I was trying to come up with ways to help my students be able to understand the formulas and why the are what they are.  So we started to discuss the formulas for cylinder and cone.  I began by questioning them on what they notice about the two formulas that are similar and different.  Students quickly noticed that they are exactly the same except for cone has 1/3 in its formula were as a cylinder does not.  Then I started to question the students, why do you think the formula for a cone has the 1/3 and a cylinder does not?  I gave them a few minutes to think about the questions and discuss with their neighbors.  Before telling them if they were right or what the correct answer was, I let them do a little hands on experience (they were given sand, a film can, and a piece of paper that was already measure out correctly to turn into a cone).  The took the cone and filled it with sand.  They poured the sand into a film can until it was full.  The students quickly found out that it would take 3 cones to fill the cylinder which is why the formula for a cone has the 1/3 and the formula for a cylinder does not.

If it would have not been for my Kenan Fellowship Experience, I would have just given the formulas to the students and told them to remember them.  My fellowship taught me that I needed to explain why to students and give them a visual to help them understand.  Having the students figure the problem out on their own also gives them a sense of ownswership which will help them remember the formula much longer than just memorizing it.