Filling Cylinders

Today our class explored finding volume of a cone.  To do this I first showed them a cone and a cylinder (of same radius and height) and just had them list similarities and differences.  The things they came up with were awesome: the cone and cylinder are both circular, they have the same size circle for a base, they are the same height, the cone tapers off to a point, etc.  The next question I asked is “Which one has more volume?”.  When some students responded that they have the same volume because the radius and height is the same for both I tried to remedy this by placing the cone inside of the cylinder so they could see it doesn’t fill up the same amount of space….still weren’t seeing it. (any ideas why? Because I thought for sure that would prove to them the cone has less volume).  Anyway, I let them stick with their original conjectures about the volume of a cone as compared to a cylinder.  I used rice and I filled up the cone to the top and I poured it into the cylinder and just asked the students if that filled the cylinder.  I FINALLY got them to see that clearly the cone and cylinder are not same volumes.  Then asked them to make a guess at how many scoops of rice from the cone it will take to fill the cylinder.  Most students chose 2 because they picture the cone in the cylinder and thought with the left over space they could make one more cone.  I’m thinking this is because they’re viewing it from a 2-D angle and not from a 3-D perspective.  The students really gave some awesome responses. I continued this process and allowed students to change their estimates (which they call estimation180) until the students realized that it would take 3 scoops of the cone to fill the cylinder! The students were blown away that the extra space actually creates two more cones, not just 1 more.  It was a really cool activity that allowed students to visually construct the formula for volume of a cone.  Sorry no pictures (i’m terrible at remembering to do that).  If you’re interested in the activity sheet I used, let me know and I’ll drop box it.