Exponential Water Tank

Apparently some guy once said, "The greatest shortcoming of the human race is our inability to understand the exponential function." I'm pretty sure I'm not on board with that statement, but I do agree that exponentials are very challenging to make sense of. Linear growth is intuitive; exponential growth is not. 


This video shows a tank of water filling up at an exponential rate. I think it would be interesting to have kids watch to really think about how fast its growing, and talk about what it means for something to grow at the same rate, or a constant rate. I wish there was a side-by-side video or another version showing linear (or quadratic) growth. 

http://bl.ocks.org/hanbzu/9787042

Another thought with this video: use it in the introduction to exponentials and have kids make some predictions, do some graphing, etc. The clock in the corner is handy. Less handy is the fact that there's no marked height anywhere. If you projected onto a whiteboard could you mark height? 

Mario's a Baller

http://www.supercompressor.com/tech/13-things-you-probably-didn-t-know-about-nintendo

See fact #9: Mario has a 27’ vertical leap.

This seems like a fun addition to "How High Can Your Teacher Jump?" or any kind of proportional reasoning kind of thing.

What would we look like if we measured human heights in pixels? What would that mean for how tall Mario is compared to a human? How much bigger is Big Mario vs. Little (pre-mushroom) Mario? How big would YOU be if you ate a mushroom (or alternatively, if you're full size now, how tall would you be after running into a goomba)?

Do kids even recognize pixelated Mario anymore these days?