Slowing down at the end of a long, active spring day. Stormy clouds are rolling in. Tabitha and I watch them together for a couple of minutes from the west-facing window at the top of our stairs.
I ask Tabitha if I can ask her a quick math question.
She consents.
Me: How many tens are in 32?
Tabitha (7 years old): Three.
Me: So quick! How do you know that?
T: 10, 20, 30. Easy.
A silent moment elapses.
T: And there’s 10 tens in a hundred.
Me: Yes. Lovely. So true.
How many tens are in 200, though?
T: Twenty.
Me: Whoa!
T: Yeah.
Another silent moment elapses.
T: Asking “How many tens are in 30?” is like asking “How many ones are in 2?”
Me: Wow. I had never thought of it like that. And is it also like asking “How many hundreds in 300?”
T: Except I don’t know that one.
Me: You don’t know how many hundreds are in 300?
T: No.
Me: Three.
T: Oh. I thought it was tens in 300.
So what do we learn?
The power of silence and of conversations in quiet moments. Both times a silent moment elapsed in this conversation, Tabitha continued with an idea of her own. And both are gems.
And there’s 10 tens in a hundred. Many grade school worksheets have attested that there are 0 tens in 100, when what they really mean is that there is a 0 in the tens place in 100. We can do a lot more mathematics with the ten tens in 100 conception than we can with the 0 tens in 100 one.
Asking “How many tens are in 30?” is like asking “How many ones are in 2?” This right here is powerful stuff. For Tabitha, ten is such an important part of the structure of numbers that it behaves like one. Ten, for Tabitha, is a unit—a thing that you count.
If you are new to this blog (and many of you are—Welcome!), you may not have spent four minutes with video. Do so now, please. Consider it your Talking Math with Your Kids homework. It’ll be fun. Promise.
Starting the conversation
Wait for a quiet moment. Ask for consent. Ask How many tens are in 32? Listen, follow up and allow a few moments of silence.