The first is a tri-tetraflexagon. I'd recommend printing out the template below, cutting out (b) and writing the numbers shown on (a) on the back. Then fold as shown in (c) and tape as shown in (d). When you flip is over, you should see all ones on the back. Where is the third side?
The second is the surprisingly not redundantly named tetra-tetraflexagon. As before, cut out (b) and then cut along the dotted lines. Next, write the numbers on the back as shown in (a). Fold as shown in (c) and tape as shown in (d). When you flip it over the back should be all twos. Maybe you can find the third side, but can you find the fourth side?
Finally, the challenge we have been working towards. Folding this properly, though challenging, is not the challenge. For this hexa-tetraflexagon you will first cut out the shape in (b). Then write the letters as shown in (a). I'd highly recommend pre-creasing each square before starting to make the folds labeled with arrows in (a). Then fold again as shown in (c), and finally put it all together as shown in (d). The flap that has a 3 and 1 on it reverse from the tape shown in (d) should show a 1 so that the reverse of the 2 side is the 1 side. Hopefully at this point, with some tinkering you can find the third and fourth sides. At last you are ready for the real challenge, can you manipulate it to find the fifth and sixth sides without ripping it? How many times did you rage quit and have to make a new one?
You're welcome for making your brain smarter. PDF of the pictures can be found here.
By: Jim Town - Mathematics Specialist at ACOE Core Learning
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