I've been teaching the topic of NETS for a long time and find that students enjoy seeing how 3-dimensional figures are made out of their 2-dimensional flat form, which we call its "net". Still, I'm looking for a new way to end the unit with some kind of very challenging bonus question that's nearly impossible for anyone to figure out completely in one period, or which could even provide enough of a challenge to warrant having separate groups of students perform their investigations for an entire period of fifty minutes and still be intrigued, if not perplexed. Any ideas?
Caught Up In Nets
YES, a few years ago I came up with something that I think is just the thing you're looking for, with all the aspects of problem-solving people need to develop when they're analyzing things in the real world. It's this: At the end of the unit, after everyone's mastered the basic well-known nets, like the pyramid, the cylinder, and the cuboid, put a paper bag up on the table in the front and pull out a Chinese take-out carton, specifically one that has the famous and traditional Chinese take-out carton shape.
It must be closed, and the only rule is that the students cannot open it. (It's best to have a few of the smaller sized ones, so you can hand one to each group of students to examine as they work together.)
Now, you can have either have empty ones taped closed or ones filled with a treat, such as fried rice, which gives the opportunity to have the class share the reward at the end of a solid work period.
It's important to have one unused one (or at least one that's been cleaned to open and disassemble for the class at the end, and I recommend you avoid greasy dishes, as it will make the final examination messier than it needs to be (white rice or empty is fine and most Chinese restaurants are happy to provide a few free of charge if you explain what you're planning to do with them. (But place an order anyway!)
By the way, you should try to do this exercise yourself at home first, as it's harder to get right than you might think, but it really is engaging!
Then have each group cut out their best attempt and assemble it, using tape instead of the wire that real ones have, and they'll see if it would hold food well, or if food would run out the sides or leak from corners...
Then, of course, allow the students to open a real one containing food and enjoy!
Students really seem to sink their teeth into this one!