Bean counting, fraction war, and other new tricks for an old dog

I enjoyed all three activities in class this week--I would use fraction war, in particular, as an activity for near the end of the period, when it's time to experiment with the lesson. If I had fun, then I would imagine kids might like it, too. I had done a (simpler) version of the manipulatives activity in my Math for Elementary Education class last year; for that, I had to buy my own little manipulatives kit, and I'm glad I did: Now my 7-year-old asks to play with it, and we've "played" by grouping unit blocks and longs (tens). See below:

But the integer activity was an eye-opener for me--and it took me a while to get there. As I say with so many math lessons we've encountered this fall, I don't remember learning this way when I was in school. I've never had a problem with integer rules--I'm obedient math student through and through--but I hadn't seen (or certainly don't recall) a demonstration of operations of positive and negative numbers. I still have to think deliberately about why, when subtracting a larger negative number, we would pair positive and negative numbers to create zero, but I do grasp it.

We have a few classes to go, and I look forward to more activities that test my rote knowledge. Looking at the intermediate and middle school standards, I would love to see more on statistics--we haven't done probability yet, have we? And slope--which we addressed a little bit in this last class--and, dare I say it, geometry. The Pythagorean Theorem, area formulas and angle measurements are, naturally, the only thing I liked about geometry--because they involve plugging in numbers. Don't ask me why anything works the way it does.