**2013**

7/3/13 – Transitioning to CCSS

7/10/13 – Geometric Constructions

7/17/13 – Curriculum Discussion

7/24/13 – Class Syllabus & Explaining CCSS to Parents/Students

7/31/13 – Starting the Year off Right

8/7/13 – GeoGebra with @jensilvermath

8/14/13 – Integrating Algebra and Geometry

8/21/13 – Interactive Notebooks

8/28/13 – Proofs

9/4/13 – Transformations

9/11/13 – Standards Based Grading

9/18/13 –

Surface Area of a Cylinder where art thou?

Surface Area of a Cylinder is not found in the CCSS curriculum, so the question was posed to Bill McCallum where it should fit…this was the question and his response.

Original Question:

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?

His response:

“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.”” – 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.”” – Bill McCallum

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