I've been thinking more possible uses of origami in my math classroom. I did a bit of research to see what is already out there on the internet for idea and came up with these.
1. A lit origami cube - I love the idea of making these lanterns out of different sized squares of paper to see how volume increases relate to the mathematical change in the cube measurements. If we had them make the fully lit cube that might make it more fun and the students could see the reality.
I often see questions in the math textbook that state something like "If you double the measurements of the sides of a cube, what happens to the over all volume?". This type of fun activity would give it a hands on experience so they can see what is happening.
2. Light up origami flowers - Imagine having students create these and then discuss finding the surface area of such a creation. I know that many of the problems for finding surface area in the book are straight forward problems. This would be a much more challenging application.
3. Flat paper circuits - The Exploratorium has a great little pamphlet on paper circuits. In it is a pop-up with a lit bridge. Think about the fun they might have creating the picture and then calculating the formula for the parabolic part of the bridge supports? This could be extended to creating a pumpkin that is launched and its flight path is shown with lights. They can then figure out the height and time ahead of time and set the path up with the correct points.
4. Maker Education has a wonderful information page filled with links on basics. It even includes links to create pop-ups.
I always love looking for ideas and let my mind fly free to imagine uses.