Not long after I witnessed a Kindergarten conversation about why there are so many 1s in the teen numbers, I visited the same classroom. This time, it was Nicole who asked a question that knocked my socks off. “I wonder if 100 is a teen number?” When I asked why she thought it might be she said, “Because it starts with a 1.” Her partner nodded, nudged her to take her turn, and they returned to their game. Several days later, I returned, for their end-of-unit discussion about the teen numbers. What follows is a lightly edited version of the first part of their conversation.
We’ve been talking a lot about teen numbers. The other day we talked a little about something someone said that I’ve been thinking a lot about. They said, “What is it with all of the ones in teen numbers?” That was their question. They weren’t sure why teen numbers all seem to have 1s in them. I was wondering if anyone had any ideas about that. [Long wait time.] Any ideas about that?
Isaiah: Um we could um like, this is actually a question but is um you know how 100 starts with a 1? Are the 100s like technically a teen?
Nicole: That’s what I asked!
That’s really funny because you know what? That’s also something I’ve been wondering. Do you have any ideas about that? I know you asked me that question, but what do you think? Do you think that those numbers, because they have a 1 in them, are teen numbers?
Nicole: I think 100 is a teen number because all of the teen numbers start with a 1 and 100 starts with a 1.
Isaiah: I don’t think so, because they’re too high of a number.
Alexa: And they’re not in the teens.
What do you mean they’re not in the teens?
Alexa [goes up to the class numberline, posted at the bottom of the board]: They’re not like with the other teen numbers and our number line says only these are the teens.
She points to labelling on the class numberline, added during a previous discussion, that calls out the teen numbers.
Then she walks over to 100, showing how far away 100 is from those teen numbers.
Isaiah: There can’t be two places that have the same thing. Like it can’t be like teen numbers, then 20s, 30s, 40s…90s, teens.
What do you think Conor?
Conor: Um my sister and brother said that 10 and 11 and 12 are not teen numbers because they don’t have the teen at the end.
That’s something we’ve talked about before too.
Conor [goes to the number line and points to 1]: This starts with a 1 so why isn’t this a teen number too?
Oscar: We don’t know if 100 is a teen number, you could look it up on a computer or something, but since it isn’t with the group it still could be a teen number.
Pablo: 100 is like 10 except is has an extra zero.
Isaiah: So technically it is maybe?
Why? What did Pablo say about 100 that reminds us of a teen number?
Isaiah: Two things that remind me – the one in front and after the 1 there’s a zero. …Also, 10+0 equals a teen number, 10.
The discussion continued, but became repetitive, with students sharing the same ideas that had already been shared...
The rest of this discussion will be described in my next blog (see Part 2), but for now I’d like to pause and reflect on what we’ve heard so far. There was so much that was remarkable to me.
These students are interested in and excited about mathematical ideas. They are curious. They pose questions, articulate their own thinking, and listen to others’ ideas. They make mathematical arguments (e.g. 100 isn’t with the group; you wouldn’t have teens, 20s, 30s…90s, and then teens again; 1 starts with 1, is it a teen number?). It seems clear that they think of themselves as mathematicians (identity) and are active participants in using mathematics as a tool (agency).
These kindergarteners have noticed something important about the teen numbers—they all start with 1. That leads them to wonder about another number that starts with 1, 100. This is a powerful mathematical observation, one they will begin to make sense of in grades 1 and 2 as they come to understand that, in our base-10 number system, the quantity represented by digits in a numeral depend on their place (e.g. that the 1 in 14 represents a ten, and the 1 in 100 represents a hundred).
Which brings me to the teacher’s role. We don’t actually hear much from the teacher in part 1 of this discussion, but she’s doing so much teaching. She takes up the students’ question. She encourages them to discuss and make mathematical arguments about it. She elicits a range of ideas, hearing from six different children in a short span. To me, she’s teaching her students what it means to do mathematics.
And yet, as ideas start to repeat, she has a decision to make. Knowing the difficulty of the ideas at play, she has to be thinking about how to connect students’ excitement and curiosity about this question to the related idea that is the goal for the end of Kindergarten—that the teen numbers are composed of 10 ones and some number of ones. She’s likely also thinking about the related grade 1 idea, that the teens are composed of one ten and some number of ones, and that the 1 in the teen numerals stands for those 10 ones (or 1 ten)—a “stretch” for most 5- and 6-year-olds, but an idea these students have been circling around…
Where would you go next in this discussion? Do you want to know what the teacher did? See Part 2.