Surface Area of a Cylinder

[jisimons]

Good afternoon,
We are debating at what grade does surface area of a cylinder first appear. Can you please clarify for us? We see in 7th grade that 7.G.4 introduces the students to the relationship between radius and diameter which allows students to develop formulas for circumference and area. In 7.G.6, students solve problems for surface area of 2-d and 3-d objects composed of triangles, quads, polygons, cubes and right prisms. We are debating between the fact that these 2 standards combined give access to the cylinder or that cylinders are excluded because they are not polygons. Can you please assist us with this?

[Bill McCallum]

Your interpretation is plausible in the following sense. First, you can think of a cylinder as composed of a quadrilateral in the sense that you can make a cylinder by forming a rectangle into a tube. Second, given the radius of a cylinder you can use the formula for the circumference to find the side length of the rectangle that made the cylinder (the other side being the height of the cylinder). That said, I’m not sure it is exactly what we had in mind with these two standards. My instinct is to see where this reasoning naturally arises in a fully developed curriculum based on the standards. That might well be in Grade 7 as you suggest, but it might be later. The main point I think is not to try to find a catalog of every formula for volume and surface area, but rather to take opportunities to calculate these things as they arise naturally, using geometric reasoning, as in the idea above of unfolding the cylinder into a rectangle. In the end, it’s the ability to think this way that will stand students in good stead, rather than “knowing the formula.”

[bumblebee]

Where, in your opinion, would it be fair to assess being able to find the surface area of a cylinder?

[Anonymous]

To me it seems like anytime after students have a good grasp of surface area, and also a firm grip on area of a circle. So that might put it in 7th grade or maybe 8th grade (or maybe not at all…is that ok?). As Bill mentioned earlier in the discussion, it depends on how the curriculum is designed. I really like the idea of surface area of a cylinder as a study of nets and 3D figures – digger deeper into the concept of surface area. I guess it also matters how you would assess it. How would you assess it?

[Bill McCallum]

I agree with abieniek’s ideas for where you might teach this. I would add that you don’t have to assess everything you teach, and since this is not explicitly in the standards it is not required that it be assessed.

[Author]

Posts