Chess games

Fantastic Video for scientific notation and exponential growth:

https://www.youtube.com/watch?v=Km024eldY1A

23 million Dollar Books, Pricing Algorithms Compete on Amazon

Found this great story as a hook for exponential functions:

http://www.michaeleisen.org/blog/?p=358

Basically a book called "the Making of a Fly" reached over 23 million dollars in cost when the pricing algorithms for two companies continuous competed with each other. Michael Eisen caught some of the prices over a few days and figured out the ratio between them:

Here is a current pricing of the book:

ZD Net also found some great screen shots to help tell the story. Its perfect for exponential growth:

Itunes Vs. Amazon, Linear versus exponential fit

great linear versus exponential fit:
https://twitter.com/mjfenton/status/460984209922732033

Pay it Forward

I am a big fan of the movie Pay it Forward. Not only is the film a tearjerker, but I think "paying it forward" could unfold into a great math lesson.

Here is how "paying it forward" works:

1. Do something nice for three people

2. Don't ask them to pay you back, ask them to pay it forward and do something nice for 3 other people.

Trevor explaining Pay it Forward to his class

I am thinking of questions like "how long would this take to effect everyone on Earth?" Students can interpret the word "long" to represent both iteration and time. 

I think its surprising that it would only take 21 iterations to reach the current population. Its also interesting to discuss how 3^20 is not nearly enough, but 3^21 is way more than enough to reach everyone everywhere. 

We could go pretty far with our modeling around this problem, but I would my students take the lead. They need to ask questions like:

-can everyone pay it forward? (think babies, deaths, etc)

-not everyone would pay it forward, so how do we deal with that in our model?

-why doesn't paying it forward seem to work in the real world?

I am thinking of starting by showing the trailer:

And at some point I want to show a visual of 3^x. I would use Desmos or Geogebra for the function, but I really want to find other ways to show the idea of exponential growth. This tree has up to 3^5 (or you can view it below).

Students can always read the original story.