A propos of nothing the other day, Tabitha asked a strange question.
Tabitha (six years old): Why are zero and half the same?
Me: They aren’t.
T: Like seven is one more than six, but zero and half are the same. They’re both nothing.
Me: One half? if you have half of something, that’s more than nothing.
T: But half, the number, that’s the same as the number zero.
Recall that last fall, she was not convinced that one-half was a number at all.
She now accepts that one-half is a number. But she hasn’t really dealt with the idea that there are numbers between other numbers. She is doing a bit of beautiful kindergarten logic here. Her premise is that there is only one number less than 1, namely 0. She has also accepted that one-half is a number less than 1. Therefore, one-half and zero are the same.
And—rightly—she is suspicious of this conclusion. The logic is sound, but it doesn’t make sense.
I go to work on that first premise.
Me: Oh. I see. Well, one-half—the number—is between zero and one.
I draw this picture, which I feel is certain to be totally unconvincing.
I was writing upside down. Forgive the crummy 2′s. Note the complex fraction. Take that, Common Core!
But then again, we hadn’t talked about one-half being a number since October. That last conversation seems to have been fermenting all this time, so maybe this one will do the same.
To be continued, I am sure.