What Have We Learned This Year?

As I complete weekly reports throughout the year, I ocassionally purposely slip in a little math, just for the record.  But really, this year, I had been feeling that we hadn't done a ton of math.  SpiderGirl never mastered the multiplication tables, worked much with area and volume, or advanced in fractions, all things that had been on her learning plan.  BatBoy has been exploring many mathematical concepts, but still, not much to go into a report.  So I thought.  When I began working on their final reports for our Distributed Learning school, I realized just how much they have learned this year.

Isn't That Odd?

BatBoy has been exploring odd and even numbers for awhile, just categorizing them in his head and finding patterns.  He came to a conclusion a month or two ago that odd numbers had 'middles' and even numbers didn't.  I've tossed in the idea lately that the pieces of even numbers can be paired off; in essence, they are divisible by two.  But, that didn't (yet) disagree with the 'middles' theory and BatBoy seemed to disregard it.  In the past week, however, BatBoy has encountered two troubling numbers:  zero and one.