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6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problem.
“Students in Grade 6 [….] find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine.”
7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
It seems surface area of pyramids is covered in 6th. Is it addressed again in 7th?
If 7.G.6 is read more narrowly, it sounds like:
7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two-dimensional objects composed of triangles, quadrilaterals, and polygons and three dimensional-objects composed of cubes, and right prisms.
which excludes pyramids. If it is read more broadly it sounds like:
7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- dimensional objects composed of triangles, quadrilaterals, and polygons and three dimensional-objects composed of triangles, quadrilaterals, and polygons, cubes, and right prisms.
The broad reading allows for pyramids, but if it is correct, it makes me wonder why cubes and right prisms appear in the standard, since if the standard is suggesting composing new three-dimensional shapes from two-dimensional ones this could be done for cubes and prisms also (and for dodecahedera, etc.). I guess it seems a bit strange that
Whichever reading you take, surface area of pyramids is fair game in Grade 7 since it was introduced in Grade 6. I see your point that it falls through the cracks of this particular standard if you take the first reading. With the second reading there is still some reason to keep cubes and right prisms in the wording, however, in that it indicates what sorts of volume problems are appropriate. In Grade 7 students might be computing surface areas of pyramids, but they are not yet computing the volumes of pyramids as a matter of course.
CCSS.Math.Content.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Why wouldn’t this include the volume of a pyramid as it is a 3-D shape composed of a polygon as the base and triangles as the laterral faces?
I notice volume of cones are in 8th, but for some reason volume of pyramids does not seem to be specifically mentioned in 7th or 8th.
Well, you can form the surface of the pyramid this way, but I wasn’t thinking of that as a 3-D object. The solid pyramid cannot be formed by cubes and right prisms. That’s why I thought surface area of a pyramid was fair game, but not volume. On the other hand, I think cones include pyramids in Grade 8 (a pyramid is a cone on a polygonal base).
Your response makes sense, but we don’t find a standard for surface area in 8th grade. In fact, we don’t see surface area of cones and spheres anywhere throughout middle and high school. Are we interpreting correctly?
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