by Dave Youngs.
Baffling Bands introduces two puzzling paper structures that, at first glance seem impossible to make. Both structures are related to the paper figure called the hypercard pictured below. Constructing these bands will exercise both spatial visualization abilities and problem-solving abilities.
The HyperCard is made by cutting and folding a single piece of paper. No glue or tape is used. If your students have not made a HyperCard before, they should make one before trying to do Baffling Bands.
The challenges in this Puzzle Corner are twofold. First, try to make the two structures pictured by cutting and folding strips of paper, and then taping them to form bands. The second challenge is much tougher-- begin with bands (strips of paper taped into loops) and then cut and fold them into the two shapes pictured. This is possible, even though it may not seem so.
Students may go through quite a bit of paper while working on this problem. While lengths of cash register tape are ideal for this activity, strips cut from the long dimension of 8.5" X 11" scratch paper will also work. Either way students should be encouraged to recycle their scraps.
Spatial visualization problems like Baffling Bands are often very frustrating for adults and students alike. You need to think about how your students handle frustration and let this guide you as you plan a way to use this problem in you classroom. When I used Puzzle Corner activities, I tended to introduce the more difficult problems, like this one, only after students had successfully completed several easier problems. I also tried to minimize the pressure on students by explaining that many of them might find these problems difficult, and that they shouldn't worry if they did not solve the problems. All I asked for was an honest attempt.
I hope your students find this problem challenging but not too frustrating.