In this number talk, Mia Buljan engages her third grade learners with a one-digit by two-digit multiplication problem, 5x14. She comments that her students have shown that while some numbers are easier for them to decompose (for example, tens and fives), with other numbers it is more difficult for students to mentally identify “friendly” numbers to use to help solve the problem. She invites students to share the different solutions they found, and then defend their thinking.
In a debrief with coach and colleague Erika Isomura, Buljan notes that ambiguity of language can make this kind of mental math particularly challenging for learners: do they really understand the difference between three groups OF 36 and 36 composed of three groups?
3rd Grade Math: One-Digit by Two-Digit Multiplication
Mia Buljan, Glassbrook Elementary School, Hayward Unified School District, Hayward, California
MIA BULJAN: So I'm Mia, Mia Buljan and I teach 3rd grade at Glassbrook elementary which is in South Hayward, and this is my third year at this school and in this grade level.
ERIKA ISOMURA: And my name is Erika Isomura. I teach 5th grade at the same school and I think I've been here fourteen years. This is the only school that I've taught at.
MIA BULJAN: When I've been doing number talks, multiplication number talks with my kids and, um, so we did today, we did five times fourteen. And, um, it, they really do see that you can break, you can do five, you know, ten, five 10's and five 4's. Like that's very clear to them. Like, the other ones we've done are, like, four times twelve, and, like, five times thirteen, like, I've always done, like in the teens...times some of the number. And, um, they very clearly see that you can separate it by tens and ones and do that separately. And then I did, after I did four times twelve, I did four times eight, and there was a lot of, like double, doubles, and there was a lot of, like, counting by eight, you know, counting repeat in position, but nobody thought to do, like, four times four and four times four, or two times eight and two times eight, or whatever that would have been. Um, so it is interesting, they don't necessarily see those little pieces where there are ten and the ones even, even when they first meet it. That's where...and in fact, I use that to introduce the, to sort of push on them about the idea of, like, what if there was no ten, like, what else is friendly? And they're like, well, 2's and 5's and so if you have all these eights lined up here, like, is there, and there's no friendly ten, like, what else would be friendlier? Well, I could do five, well, what would that look like?
ERIKA ISOMURA: Mm-hmm.
MIA BULJAN: And they do it. So, um, so, uh, super interesting that bigger numbers can be a helpful way of, like, naturally decomposing and maybe apply that to smaller numbers.
ERIKA ISOMURA: Yeah. I just, it just never dawned on me to even try smaller numbers. You know, it's fifth grade so we started in the teens and work it up.
MIA BULJAN: And they memorized seven times eight, right. ERIKA ISOMURA: So, why bother going to the one digits? Then it was like, oh interesting. MIA BULJAN: Good information. ERIKA ISOMURA: They were just completely floored by one digit numbers. MIA BULJAN: So, do I, okay, so I only use seven of them, I didn't use all of the division ones. The division
ones that are more problematic for me were like the, um, you planted thirty-six plants in three rows. ERIKA ISOMURA: Oh yeah. Smarty. MIA BULJAN: Uh, like, to me, the language was pretty ambiguous, like, I, like I couldn't think of how,
um, like you have to bring a lot of understanding of, sort of equal groups to that, and my kids aren't
there yet. And so I sort of pulled those out because I didn't want to, like befuddle them on purpose, like ahead of time. So, so, like, to me there was no, like, clear argument that you could make looking at it, that they weren't saying three groups of thirty-six versus thirty-six in three different groups.
ERIKA ISOMURA: Mm-hmm.
MIA BULJAN: You know what I mean? Like there's nothing about the language that really indicated it, and so, um, so, like, I, I, I wasn't entirely sure that they were going to bring everything they needed to understand that. So I did pull those out, but I love the other division problems. And I had everybody do their own.