We don't talk about it as much as we should but one of the fundamental goals of education is cultivating alertness, producing students who notice and think about everything around them. One way of achieving this is to show kids new ways of looking at the ordinary.
There are few things more familiar and mundane than a blank sheet of paper, but from a material science standpoint, that paper has some cool properties. Paper doesn't like to stretch or compress. Normally that would make for an object that didn't like to bend. Bending usually entails stretching because the outside of a curve has more area than the inside due the thickness of the material being bent. A sheet of paper, though, is so thin that this difference is negligible. Think about a pipe; the circumference of the inside is noticeably less than that of the outside. Now think about a tube made by lining up opposite edges of a piece of paper. The circumference of the inside is less than that of the outside but the difference is very small.
This bend-but-not-stretch property means that paper can only be bent into a certain family of shapes. You can make a tube or a cone or even an extruded sine curve but you can't, for example, make a dome.
These properties of paper also make it a great medium for discussing the properties of shape. In sheet form, paper is almost synonymous with flimsy, but if you form a sheet of paper into a tube or a cone* it can support a surprising amount of weight. Sandwich the previously mentioned extruded sine curve between two other sheets and you get a very strong board relative to its weight. Add another layer with the extrusions at right angles and the performance is even more impressive.
Paper-based manipulatives and projects are a great way of teaching a number of concepts in geometry, physics and engineering. More importantly though, they make the point that the most unexceptional class of things imaginable is, in fact, pretty exceptional.
Here are some project ideas. If you like what you see check back because I'll be updating this post.
The Platform Contest
Old Time Paper Models