This problem from the 1988 AJHME gave my older son a little trouble today:

Problem 24 from the 1988 AJHME

We talked through it tonight and it turned out to be a really fun problem to talk through. It is surprisingly tricky to keep track of the rotations. Here are his initial thoughts about the problem, and you’ll see that he’s still having a bit of trouble with it:

Next we decided to make a hexagon and a square out of our Zometool set and actually make the rotations. That led to a fun conversation about what would happen if you rotated the square all the way around the hexagon:

Finally, I decided to try out the problem with my younger son and see if he had any different ideas. This was also an interesting conversation – especially when he wondered about what would happen if we rotated the square all the way around the hexagon:

So a fun little problem about mentally rotating a triangle around a square. Definitely a tough problem for kids to visualize, but a great problem to use to get them to talk about math.