This is going to be a super short blogpost. But I’m excited about a visualization I came up with today — as I was working on a lesson — for showing why Pascal’s Triangle works the way it does with binomial expansions.
I’m sure that someone has come up with this visualization before. It feels so obvious to me now. That that didn’t make me any less excited about coming up with it! I immediately showed it to two other teachers because I was so enthralled by it. #GEEKOUT
I am thinking how powerful a gif this would be. Start out with 1. Have two arrows emanate from that 1 (one arrow saying times x and one arrow saying times y) and then it generates the next row: 1x 1y. And again, two arrows emanate out of both 1x and the 1y (arrows saying times x and times y). And generating 1x^2 1xy 1xy 1y^2. Then then a “bloop” noise as the like terms combine so we see 1x^2 2xy 1y^2.
And this continues for 5 or so rows, as this sinks in.
Then at the very end, some light wind chime twinkling music comes up and all the variables disappear (while the coefficients stay the same).
Of course good color choices have to be made.
Who’s up for the challenge?
Okay, I’m guessing something similar to this already exists. So feel free to just pass that along to me. Now feel free to go back to your regularly scheduled program.