Students must learn about attributes of 3-dimensional shapes and develop meaning for the volume formulas.
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See the standards throughout the grades: http://www.corestandards.org/Math/Content/MD/
G2.b. List specific characteristics of prisms, pyramids, cylinders, cones, spheres by using appropriate language including perpendicular and parallel, height, slant height, base(s), apex.
M3.e. Determine surface area of polyhedra and cylinders by decomposing them into nets.
M3.f. Derive the formulas for the volume of prisms, cylinders, cones and pyramids.
M3.b. Determine area and volume of composite shapes by decomposing them into familiar shapes.
M3.d. ... Part 2--Similarly explore the distinction and relationship between surface area and volume of a rectangular prism.
When students derive the formulas, they are much more likely to remember them and apply them correctly.
Provide opportunities for students to note the characteristics of prisms, pyramids, cylinders, cones, and spheres using vocabulary they have developed. Always have students describe, then name, to help them associate the characteristics of the shape to the shape name.
Slides for Chapter 13 in Mathematics for Elementary Teachers with Activities, 5th edition by Sybilla Beckmann.
G2.b Online activity to explore cross sections of different geometric solids: cone, double cone, cylinder, pyramid, and prism. Manipulate the cross section with slider bars, and see how the graphical representation changes. Cross Section Flyer by Shodor
G2.b Online exploration of Platonic solids by Wolfram Alpha
M3.e Manipulative to create nets for 3D shapes Magformers
M3.e Online game on identifying nets for a cube. Cube Nets by NCTM Illuminations
M3.f Videos to derive volume formulas for pyramids, cones, and spheres 3-Act Math on Volume
M3.d Online activity on volume of cylinders Popcorn Picker by Dan Meyer’s 3 Act Math
M3.d Problems to maximize volume given constraints on dimensions Open Middle Problems