The second post I had the pleasure of reading, or rather seeing, was about a "magical" octagon. The octagon was shown on one side an arrow pointing straight up, so at noon like on a clock, then the octagon was flipped on its x axis(or horizontally) to show an arrow pointing at 9 o'clock. The "magic" happens when he flips the octagon back over to the 12 o'clock facing arrow and turns it to about 2 o'clock and asks about the other side, where would the arrow be pointing? The assumed expected answer is if you go clockwise from 12 o'clock to 2 o'clock, the other side would go from 9 o'clock to 11 o'clock, however the time on the other side was at 7 o'clock, then again he turned the 2 o'clock to 3 o'clock and the other side instead of going forward in time, went backward in time to 6 o'clock. My comment was about how neat the show was, but also that it was simple to see as long as you understand the trick. The trick to understanding why is that imagine when it is on side A(the 12 o'clock side), that you can see through the shape to see that the arrow on side B is pointing at 3 o'clock, so we know the arrow is 3 hours ahead of side A, now when the octagon is flipped on its x axis, the image you see flips from 3 o'clock to 9 o'clock. When the octagon on side A is turned to have the arrow pointing at 2 o'clock, 3 hours ahead is 5 o'clock, then flipped, 7 o'clock, which is what it shows in the video link. Pretty neat, but easy to see if you understand image flipping.
Saturday, September 14, 2013
For the teacher I had the pleasure of reading their blog and commenting on is Mr. Dan Meyer, a clever teacher who loves math and visual queues. In the first post it was trying to visualize how many pennies can be fit in a circle and of that data, make a quadratic function. The interactivity and visual queues are the key that make this project great. Students don't know why quadratic functions are important, and this project of pennies in a circle help give students the means to an end on what you can find out from quadratic functions. My comment was simple, it was talking about the love I have for math and how much I appreciate new ideas for visual queues, which I find important in teaching.