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 problems.
Ah, nets. We can use them to catch fish or play sports. In the 90s, some of us actually used our dial-up modems to surf the net until Sandra Bullock scared us out of it. Thanks a bunch, Sandy.
But the nets we're talking about won't help your students catch trout or play badminton. They will, however, help them create 3D solids and calculate surface areas.
We want students to develop that special, spatial, spidey-sense that allows them to break apart a 3D solid into its net. But don't forget that the reverse skill—taking a net and folding it up into a 3D solid—is also something that needs to be honed. Unlike your fishing skills, which are top-notch.
An example never hurts, right? In the figure below, rectangle IJKL is the base of the prism. The four rectangles touching rectangle IJKL fold up at a 90° angle and become the lateral faces of the prism. Finally, rectangle MNUV becomes the top of the prism. This is just one of many ways the net could be folded up to become the rectangular prism.
Other than just looking really cool, nets give students a more concrete way to see the surface area of the solid. They can find the area of each of these surfaces and add them up to find the total surface area. (And hey! They can use what they learned in 6.G.1 to get the job done.)
Keep in mind, though, that students only need to understand the nets of solids whose faces are rectangles and triangles. This means only rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids. Anything crazier than that, and your students might give you a stink-eye that stinks worse than pickled herring.