I’m wondering what mathematical experiences would help make this more intuitive. Playing around with a hexagonal pattern block for a couple of minutes helped me get a feel for it. Does this show the need for concrete as well as virtual materials – even at higher grades?
@James… I don’t think it is a joke, but I was perplexed a bit as to why the arrow didn’t do what I had originally predicted. I had missed that in the way that the octagon was spun at the beginning, it didn’t keep the arrow on the my left side when the back of the octagon.
So, when I saw that the answer was different than I had predicted, it took me a second to catch up. That’s what I was referring to.
@Andrew – so most people don’t predict correctly? I guess I can see that. I guess most people would expect the arrow on the back to rotate the “same direction” (clockwise) as the arrow on the front, and don’t see what the reflection is going to do?
I read the comments first so I knew what was going to happen and I still couldn’t wrap my head around it when I watched it. I’m curious now about the differences in the thinking between the handful of folks who knew what would happen and the majority of us who predicted wrong. Any thoughts on the reasons?
I like this, it is pretty simple, the trick to see past it is to understand that that when side A is at noon, side B without flipping it, is at 3 o’clock, when flipped, it is at the shown 9 o’clock. So when side A is at 2 o’clock, through the paper side B is at 5 o’clock, however when flipped it is at 7 o’clock(how it is shown, due to it being flipped), not the expected 11 o’clock. Side A isn’t flipped, side B is flipped(when shown), so both go in opposite directions.
These are the kinds of things that I love. When you can get inside their mind, turn it around, and then let the students explore why it works, those lightbulb moments are brilliant. I’m just trying to think if I could use it in a lesson plan early in the year in a 3rd grade class? Possibly what it would tie into/connections to be made?