Sophie was working through some number theory and probability problems from "The Art of Problem Solving" today, things way beyond her working math level, and doing pretty well at exploring them creatively and coming up with some valid approaches and correct answers. She really enjoyed the challenge. So this afternoon after she finished some algebra work, we headed off into the probability section of her current textbook to see what we could find.
In there was some basic work and a few dice problems. She had fun with that, but as usual we pushed beyond the learning there, recalling the probability dots on the "Settlers of Catan" board game we have. We decided to mathematically work out the probabilities of different rolls from two six-sided dice and then compare to the actual frequency. Once we started rolling dice Fiona got involved too and for a while I had two girls fanatically rolling dice and calling out their sums while I marked them down.
It was the sort of thing that would have flopped with the kids if I'd told them I had a lesson plan. But because it grew out of Sophie's own tangent of interest there was lots of enthusiasm. We rolled the dice over 500 times.
The graph shows our tallies over time. The lowest line is the plot of our snapshot above. Each successive line was taken from a subsequent snapshot. Eventually our tally did approximate the nicely triangular predicted pattern, but there was a mysterious lack of 9's and a surfeit of 7's. I suspect that either our dice are a bit loaded, or Fiona occasionally mis-called her sums, opting for speed over accuracy. I guess you'd call those experimental variables.
Supper was a little late as a result of all our crap-shooting.
On another tack, today represents Noah's first day back on the math horse. We had one amazing spurt of math progress, he and I, a couple of years ago, when he completed four grade levels of Singapore Math in about 6 months. But since finishing Singapore Primary Math we have found it tough to hit our stride again. We've tried a couple of different programs with middling success. When we'd hit a little bump my tendency was to give it a few days and try again. But that didn't work well. He would dread the trying again, and I would dread his disinterest and anxiety, and we'd put it off, and it would be harder than ever to find a groove when we tried again.
We now think that the real ticket to math success with this boy is the same as it is with viola -- do a fair bit of it every day so that it gets easy, because when it's easy, it's fun. Noah easily gets discouraged and panicky if stuff feels at all unfamiliar, and that makes it hard, and then the fun is gone. So we're on a quest for math momentum now, trying to prime the pump that results in self-reinforcing success and enjoyment. Today went well. All review, but with a fresh outlook and some interesting brain teasers and some solid independent self-checking work that left him feeling confident and independent. Onwards!