I came up with a few ideas for many students to play with to get them started playing with sequences. A little tactile learning if you will... They even went a bit into the idea of series with out them really knowing (or caring).
I had them try to make a stack of ping pong balls 4 layers high with the least number of ping pong balls. (I was very careful in the write up to always say "ping pong balls" not just "balls." Just a bit of classroom management.) This of course led them all to the same solution of creating a triangular pyramid. They looked at the number of ping pong balls in each layer and how the number in each layer increased. I really like the idea of setting a challenge that would lead them to a solution, sure wish I could have figured out more of those!
|Stacked ping-pong balls|
|Poker Chips in rings|
With the foam squares they could get a little more analytical, as the patterns followed function forms they were familiar with (linear, quadratic and exponential). They made tables of numbers, graphed the results and final were able to create equations to describe the patterns.
Reflection on the process: A few students really enjoyed the change to a bit of tactile learning, something I really need to remember. The process of making connections from squares to table to graph to equation (i.e. from concrete to abstract) was, I think, highly valuable. That process is at least closer to "real math" or "real science." It also served to slow down some of the folk who like to jump straight to the equation, thinking equations are what math is all about.
The handout I gave the students is a google doc.