Powers of 2 and Paper Folding

I love this site: http://www.freemars.org/jeff/2exp100/powers.htm

Fraction Exponents

Use the digits 0 - 9, without repeats, to fill in the boxes below:

One possible answer:

Law of Exponents Problem

Use the digits, 0 -20, without repeats, to fill in the blanks below:

Spoiler, possible answer below:

Adding Context to Scientific Notation

The world of the small is a great place to introduce scientific notation. This FEI gallery is fantastic and often includes the measurements in the photos: http://flic.kr/ps/DDQp3  I am going to use a bunch of these in my lessons. We could do a daily activity, asking "how many meters is that?"

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.