Discovery: Surface Area

To make your lesson on surface area fun AND help students really understand the concept, try adding a special "dissection lab" day into your middle school geometry unit.

Students really need to get hands-on with nets of 3d figures in order to understand the concepts behind the formulas for surface area.

I think it is a huge mistake to just present students with the formulas and teach them how to plug in.  Obviously, the formulas can be useful, but if students develop the formulas themselves, they can then reproduce them at any time without memorizing.  They also actually understand the process and why it works.

Print nets on colored paper and tape them together ahead of time.  When you start class, set up like a science lab and tell students that their job is to "dissect" the specimen in front of them and then find the total area of all of the "skin." 

Students will need a ruler and scissors.

Here are some additional items you can put out to make it a little more fun (optional):
- foam trays
- tweezers
- small scissors
- push pins

Start by laying out the assembled 3d shapes on trays.  Lay out the dissection tools, and instruction & recording sheets (see link below).  Students start by taking measurements before they are allowed to cut.

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Try a simple polyhedron first (a cube or rectangular prism).  Once students take measurements, have them record the types of faces and how many there are of each.  Allow them to find the total surface area on their particular figure, then develop a formula for the surface area of ANY rectangular prism/cube.

When you introduce the cylinder, give the same prompt and structure, but try to avoid giving hints.  Once students "unroll" the cylinder and lay it flat, allow them to figure out that the length of the rectangle is equal to the circumference of the circle.  This hands-on exploration will activate their brains and help them make the connections!

After opening up the "specimen," students take detailed measurements of all the faces in the net.  They calculate the surface area, then develop a formula.

Here is the net I use - Download Net (free)

You can also buy worksheets to guide your students through the cylinder dissection activity.  Click the image below for more information.

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