Patty Ferrant describes the role of homework in her classroom community to deepen understanding, to connect to high school expectations, and to jumpstart classroom conversations. Her students share their homework, clarify each other’s thinking, and extend each other’s understanding. Students ask questions, listen attentively, and model academic language.

8th grade math - Pythagorean Theorem*Patricia Ferrant, Thomas R. Pollicita Middle School, Jefferson Elementary School District, Daly City, California*

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PATTY FERRANT: Because even like the whole homework thing, it's like, I'm never going to go over that homework with them. That's them. That's if they care about it, which they do because as I'm running around giving them that credit that they attempted it, they're all having these good conversations, um, to help deepen their understanding. You just need to try the homework. They really focus on homework and in high school, they still do. That's...I don't know, that's their philosophy or whatever, and they grade it and it counts a lot. And for me, it's like thirty percent of your grade and it's completion, it's effort. Your job right now is to talk to your partner about your homework while I'm taking attendance. Let's go!

STUDENT: And I think...and then for milk chocolate, it's divided by two. You got that?

STUDENT: Do the [inaudible] change.

STUDENT: The equation I got was 5p + 8o = 354 and geometry teacher had said [inaudible], so pentagons plus...p + o = 60. Now I must [inaudible] this equation by five and I get 5 pentagons plus 8 octagons equals 354. And now I subtract it by 5 pentagons plus 5 octagons equals 300 and I got 54, and divided by negative 3.

STUDENT: It's still, I don't know. Because the pentagon has...there you go.

STUDENT: Same thing.

STUDENT: Can I see your equation again? It'll be...

STUDENT: It's wrong.

STUDENT: Yeah, there you go. And there's eighteen octagons, right?

STUDENT: Like, for that one yesterday, it got me confused.

STUDENT: Okay, um...

STUDENT: So my first equation was p + o = 60 and then for my other one, I got...the other equation was 5p + 8o = 354.

STUDENT: And we had to do elimination because...what type of equations are these both?

STUDENT: Isn't it, um, part-part-total? Yeah, part-part-total.

STUDENT: Yeah.

STUDENT: Yeah. And then after I got 5p + 8o = 354 and then you're supposed to subtract... You're supposed to subtract, I don't know why I put add. And then equals three hundred, and then I got 3o and...yeah, 3o and then 54, and you're supposed to divide it by three and o = 18.

STUDENT: Okay, good. STUDENT: And then for this one I substituted eighteen instead of...what is it? Eighteen? Yeah, eighteen. And then I got 5p + 144 = 354. And then you're supposed to subtract it because it's a positive, and then you're supposed to divide it by 5, and p = 42. Then I did again — p + o = 16 and then I did...

STUDENT: You substituted?

STUDENT: Yeah, I substituted and 42 + 18 = 60.

STUDENT: I did the same thing but I also did the times...I multiplied 8 with the equation x + y = 60 and then I did elimination.

STUDENT: On this part right here?

STUDENT: Yeah and I got x is 42.

STUDENT: x is 42?

STUDENT: Mm-hm. And of course we still have to do elimination because either way it's a part, and plus part equals whole. And if you have a part plus part equals whole, you have to do elimination.

STUDENT: So...

STUDENT: So we have 42 pentagons and 18 octagons.

STUDENT: Oh, yeah.

PATTY FERRANT: Even if they don't get it and then they have that partner, they do rely on each other. Like, they're realizing that working together helps them a lot.

I try to give homework the emphasis it needs, in terms of students being organized and prepared, but also recognize that our major work in the classroom is in engagement with each other around mathematical ideas and discourse.