I will display an image of a circle with a radius of 3 units on the SmartBoard. I’ll ask students to think how we could determine the number of unit cubes that could fit on the circle. This is to remind students that we know how to find the area of a circle. Next I will show a cylinder whose base has a radius of 3 units. Then, I'll ask how many layers of unit cubes can fit. This is a short recap of the work we have already done with prisms.
I made sure to include cylinders with radii given and diameters given so that students have a chance to use the wrong value. When they do make this mistake, I will tell them: “It’s okay. I put that problem there on purpose to trip you up!”. On GP5 I purposely ask students not to calculate the volumes to compare the cylinder to the cube. I want them to have to explain using reasoning only. (MP3).
The first 4 problems mirror the guided practice. Problem number 5 requires a bit of proportional reasoning. I will have students work independently for at least the first few minutes; at least for problems 1-4. I can use this as another check for understanding. The extension problems provide more opportunities to enhance a student's problem solving abilities (MP1). Problem 7 is not too difficult but problem 8 can be quite tricky. Here, I think the easiest solution is to use the surface area formula as a model to help find the height of the cylinder so that the volume can be calculated. (MP4).
There are 4 problems on the exit ticket. The first problems asks students to explain how to find the volume of a cylinder in two steps. The second and third problems simplify ask students to find the volume of the given cylinders with a radius and then a diameter given respectively. The last question requires that students find the height of the cylinder given its volume and diameter.