3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Who doesn't love taking things apart to see how they work? Dissecting a frog might not be your students' favorite school project (unless they're big fans of formaldehyde stench), but they'd probably all agree that it's pretty fascinating, if not a teensy bit gruesome.
Three-dimensional solids are the same way. We're used to seeing a cube as a cube, but all kinds of interesting things happen when we start cutting it up to look at its insides. And thankfully, geometry smells a lot nicer than the biology lab.
Students should know that slicing and dicing a 3D solid will give us a 2D cross section, like a slice of bread or a chopped-up carrot. Really emphasize the fact that the same 3D shape can have a bunch of different 2D cross sections, depending on how we slice it. Cutting off the corner of a rectangular prism will give us a triangle, but cutting it parallel to one of its faces gives us a rectangle. We can even come up with all kinds of unexpected polygons if we slice the thing at odd angles.
It can be tricky for students to visualize some of the weirder cross-sections, so include as many visual aids as you can. (Here's a good one on the cross-sections of a square pyramid, and here's an interactive activity where students can "cut" a cube into different pieces.)
It's worth noting that students only need to identify and describe the shapes of various cross-sections for this standard—they don't need to calculate anything just yet. This one's ripe for hands-on activities, too; you can bring in different clay shapes or food products and slice 'em up for your class, using different angles to show the different planes that you can get from a single solid.
The cross section of a frog is a lot more messy and complicated, so we'll leave that to the professionals.
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