Surface Area

I thought I would try a "hands-on" approach to teaching the surface area of cylinders today. So, last night, I go to to store and buy all things that are packaged in cylinders (Pringles, Slim Jims, Raisins, Fried Onions, packets of Crystal Light, etc.). During my geometry classes, I had the students come up and grab a cylinder and ask them to find the surface area of the cylinder using any of the provided tools (scissors, string, scotch tape, string, and a tape measure). Some of the tools I put out just for fun to see what the kids would do with them. I discussed with the students that surface area is the area of the surfaces of the figure. I then asked them, using their cylinders, what figures we would need to take the areas of to find the surface area of the cylinder. I also told them that the cylinders they were using were not "precious memories" to me and that if I didn't get them back in the exact shape I gave them out, it would be okay. I hoped that with this statement, the students might get the idea to cut the cylinder to separate the "middle part" (as they were calling it) from the two circles. I thought they might see this early on, but no. Some of the kids were wrapping the tape measure around and around and around the cylinder to find the surface area. Others were taking actual measurements. These kids were at least trying out their idea! Finally, one student decides to cut the rectangle from the two circles. When the other students saw this, they started cutting their cylinder the same way. After a few minutes, I hang the parts of the cylinder (in this case it was a Pringles can) using magnets so that the students can see the three distinct parts to the cylinder. First, I ask, "What figures do you see?" Students: "2 circles and a rectangle." Great! So, we have to find the area of these three figures. How do you find the area of a circle? Students: Pi times the radius squared. Excellent! How do you find the area of the 2nd circle? One student even replied, "The same way, so 2 pi radius squared." What a reply! Then the tough part: the area of the rectangle. I asked the students, "How do you find the area of a rectangle?" Students: Base times height. At this point, I thought we were on a roll. Now, the big question, "What is the base?" Students: The base of the rectangle. It's what we multiply by the height." Finally, a girl in the back says, "It's the circumference of the circle." YES!!!! After all of this, we were able to get the formula for surface area of a cylinder!

Was it great? Maybe. A lot of kids enjoyed trying to find the surface area of the cylinders I had brought to class. Some of them just like cutting them up. Next time, I want to have cylinders for every student. Guess I better start eating Pringles now.

For surface area of a sphere, I did this activity. I think the students enjoyed this activity more than the previous cylinder one. It was very interesting and I recommend trying it in your classroom!