Things I am excited about:
* Teaching kids about variables in the 7th grade! My kids are doing a couple of days of looking for Mystery Numbers given things like "You take a mystery number, add 5 to it, then divide by 8, then square what you have, and the final result is 100. What was the mystery number?" and either working backwards or drawing arrow flow diagrams in order to reason backwards in their heads. It has been crazy cool, because they are then able to take an equation written with "??" as the mystery number, and then use the same backwards logic to solve it WITHOUT ANY ROTE TEACHING!!
And all of this, they did without having been introduced to the notion of x!! (The equations transition to using smiley faces. I don't get why we keep asking all kids to use the terrifying "x" upon introduction to variables. Isn't a smiley face much less intimidating?)
Then, the plan is that I'll model some function machine type of predictable behavior until they get sick of me and they can tell me what I should return if they give me a number called "BLAH". Then they do the same exercise in writing until they get really good/comfortable at representing generalizations using simple algebraic symbols. Then we do some cooler visual patterns.
* My realization: Asking kids to make equations from tables is MUCH LESS COOL than giving them an evolving picture and asking them to find an equation that predicts the picture at any stage N in the future. I'm doing this across all grades and the kids can't seem to get enough of it.
* Another (far more experienced) teacher and I are planning for our classes to do Dan Meyer's cup-stacking activity together. I'm really excited, because 1. I've never run an activity before with two classes of kids, half of whom I don't know. 2. I know this activity has worked superbly for me in the past, and it's a perfect opportunity for me to get feedback from another super experienced colleague on how to fine-tune my delivery and questioning and scaffolding.
I'm nervous, but I think it has potential to be glorious!!
Addendum 31/8/11: Here are some links... Mystery Numbers, What are variables, and Visual patterns to algebra.