John has always shown an aptitude for math, beyond what the standardized tests capture and the perfect grades on worksheets that come home. While in kindergarten, his teacher had him help teach the other kids during individual work time because he didn't just get the right answers, he understood the mathematical concepts behind the answers, and could translate them for his fellow five year olds.
We make a math problem out of every possible opportunity. In fact at dinner the other night, when Caroline asked if we would ever install solar panels on our house, I got to give my first lesson in return on investment. John grasped it right away, and understood that we wouldn't live here long enough for it to make sense.
So when he asked me one night to explain division I figured, why not? He told me the problem he'd been trying to figure out: 47 ➗ 7 = ?? He understands multiplication, and had figured out its relationship to division, but was stumped with this one. So we drew circles, I explained remainders (I figured we'd wait for decimals for another day), and it was ON.
It didn't take long for him to tire of "the easy ones" so we tried some long division. No problem. So we kept going. One problem after another, adding double digit multiplication to the mix. Carrying digits, figuring remainders, counting multiples.