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I use wrapping paper. I have them bring boxes in (all shapes and sizes) and then tell them that they must write and solve an equation for exactly how much wrapping paper to use. When they have an answer, I give them a glue stick, scissors, and the exact amount of wrapping paper that they asked for. Then they must "check their work". If they get it correct, then they should have enough wrapping paper to cover their box, with no extra. If they have too much or too little, then they need to refigure and adjust their equations. At the end of the lesson, we simplify our equations, and 99% of the we end up with the correct equations for solving surface area. Those that do not have the correct equation have normally made simple errors and we discuss those.
This works even better if you use the type that has a grid on the back. I have them put this on the outside and actually count the number of squares first. Then I have them figure out "shortcuts" (the formula)
Commenting to follow. I have problems with this every year as well. Hoping to get some better ideas.
There are free 3-D nets online that I’ve printed for my students to cut out, fold, and assemble so they can understand nets of solids. These would probably help with surface area too, since students would be able to see the individual shapes involved and understand what area formulas are needed for each solid.
This!
There are also a few interactive websites for nets. Check out GeoGebra, learner.org, etc. Just search online for interactive nets of solids.
I echo all the comments on netting. Seeing the shape as parts with areas and then putting it together can be really helpful.
I’ve also gone backward on netting. For example, I’ll have a big cylinder and wrap a rectangle around the lateral and cut out two circles for the bases. Then I unwrap it or have a student unwrap it so they can see the lateral area is just a big rectangle. Then they put it back on to see what on the cylinder will make base and height for the lateral rectangle.
Additional real world examples like printing and packaging costs can also help, especially if they have to decorate a lateral area with limited supplies.
I used to have students do a project where they had to repackage a product so the surface area was smaller but the volume stayed the same or increased. They all had fun with it and learned a lot at the same time