Suzanne McSpadden interviews several students after the lesson.

7th Grade Math - Area and Perimeter*Antoinette Villarin, Fernando Rivera Middle School, Jefferson Elementary School District, Daly City, California*

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- Clip Transcript PDF
- Student Work Samples Set 1
- Student Work Samples Set 2
- Student Think Sheets Set 1
- Student Think Sheets Set 2
- Pizza Crusts MARS Task & Student Work PDF

SUZANNE MCSPADDEN: I'm Mrs. McSpadden, math coach, and I had the pleasure of observing the lesson. So we've invited the four of you as students who participated in the lesson to just share some thoughts that you had. So was there anything, maybe you just want to talk first about how you felt about the lesson. Anything you learned, anything that surprised you about your own learning, just your general feelings. Then I'll ask you some more specific questions.

STUDENT 1: Everything made more sense because then -- being in area and perimeter that there is multiplying and in perimeter you just add the length and width, but then in area you multiply them. So, it made more sense to me.

STUDENT 2: For me it was basically review. I felt that Mrs. - I felt they did really good and I didn't really learn anything new, but I did gain some self-confidence on the subject. Something I was kind of fuzzy on from having to find the perimeter for the sides when you just have the area, I kind of got a little clearer on that.

SUZANNE MCSPADDEN: Cassie, you said for you it was kind of a review. Was there a point at which that little bit of self-confidence that you gained, can you think of a point in the lesson where that happened for you?

STUDENT 2: Basically it was starting from the beginning to the end of the lesson. So mainly I was, mainly I was like pretty well briefed in that, but mainly, as I said it was mainly finding the perimeter with the area and having the shape. Like if you had 36 and it was really skinny, I would probably think it was either 2 and 19 or 1 and 36. Or if it was the square it would be 6 by 6 and maybe I just got that little bit of confidence in the subject, just kind of boosted a little up. (fade out) Basically I was already very prepared when I took the first one, but if I was to take another, I think I would be more prepared because I brushed up on it. Like maybe areas were a little faded, they were brushed cleaner. Like the really cloudy one that I didn't really touch up too much on in sixth grade, with finding the perimeter based on the area, that one was really cleaned up and sparkling now. So I'd probably bring that, might do a little better on it. That little boost.

SUZANNE MCSPADDEN: And for my last question, I'd just like to get your thoughts on working with a partner, how that helped you, or how that helped your partner. Do you want to talk about just working, talking to somebody, how that felt for you in your going through the task? Alex, let's start with you.

STUDENT 3: I would tell her the way I did it, and then I would ask her how she did it, then sometimes it would be different. So I would learn her way too, and she would learn my way. So we would both have a different strategy to do it again.

SUZANNE MCSPADDEN: Shyra? That's a little bit like what you were talking about earlier. Do you want to add anything to that?

STUDENT 1: Having a partner to me is easier because if you don't get something, at least your partner knows something about it. And it's easier for you to understand with your peers telling you what you need help on, instead of a teacher just telling you what to do because sometimes you might get confused on what the teacher is saying. (fade out) I was thinking that of two numbers that would equal 36, and tried to draw it out. And when I started to do it, I was thinking of more possibilities, but then as soon as I tried to stop thinking of more possibilities, all of a sudden more started popping up in my head.

SUZANNE MCSPADDEN: And at what point did you stop and think, "Well, maybe do they have different perimeters?" Did that question come into your mind?

STUDENT 2: Yeah, 'cause then it said it needed more crust. So I was thinking, "How can I make a perimeter that doesn't have a lower crust and have more?"

SUZANNE MCSPADDEN: Alex, how about you? What was going on, how were you thinking about the problem?

STUDENT 3: Since 6 times 6 is 36, I just tried multiplying other numbers higher than 6, and whatever those two numbers were I wrote them down. But then there's nothing that you can do that 7 times something would equal 36, and 8 times something would equal 36. Then 9 times 4 equals 36, so I just kept going like that.

SUZANNE MCSPADDEN: And because the pizzas had to have a different crust, did you stop and think about the different amount of crust around the edges? Did you stop and think about that while you were working, the possibilities?

STUDENT 3: Yeah, like if anything was lower than 6, or if both numbers were lower than six, then the crust would be lower. Then if both numbers were higher, I just kept them because (inaudible) both numbers couldn't be that higher.

SUZANNE MCSPADDEN: And I see that you drew rectangles. How did that help you?

STUDENT 3: Because it could help me figure out how much to add and how many long it is. Yeah.

SUZANNE MCSPADDEN: So you used labeling to help you figure out perimeter, for example?

STUDENT 3: Yeah.

SUZANNE MCSPADDEN: Right. Cassie.

STUDENT 1: Something that I was doing, we were given tiles. I started with a simple one that I already knew equaled 36. So I took 4 times 9, and then I grabbed 36 tiles and I had them in colored rows so that I could see that they were all different. They were all in separate rows and so once I had them, I figured out that the perimeter was bigger. Then something you can do once you have that is, this sometimes works but not always, you can decrease one and increase the other. That wasn't really working because 3 times 10 is... no. And so I started thinking, and I thought well what is, what is 36 divided by 2, and I had 18. And I would have probably made this bigger 18 inch length thing if the desk was long enough, so I had to move the end down below. I drew it onto my paper, the area was 36, and so what I did on both of them, I showed how I put the perimeter. So I had in parentheses the length times the width. Then in one case it was 4 plus 9 and the other 2 plus 18. In the first one 13 times 2 is 26, which is a little more than 24. The other one I got 21 and multiplying that by 2 is 42 and showed, so that is obviously a lot bigger than 4. So if I would have had enough time I probably would have done all four options because the other one is, I see what Alex had is 3 times 12 and 1 by 36. If I had enough time I would have added those. (fade out) Nothing more than what I already said.

SUZANNE MCSPADDEN: Thank you so much for your honest responses and your really great participation in the lesson. Thanks. You all made it special. Thank you.

STUDENTS: You're welcome.

In this clip, four students are interviewed following the lesson. It's always interesting to hear what students have to say about a lesson. Suzanne McSpadden, our math coach, engaged them in reflecting on their own learning.

Abilities varied among these students, and the surprising similarity among almost all of them was their renewed sense of confidence after this re-engagement lesson. In this discussion, each student described some sense of understanding the material better. One student explains how the difference between area and perimeter "made more sense" and another student describes that "though it was review" for her, the lesson helped make "things more clear." There was a sense of doing better on the task this second time around because there was a new way to look at the problem - whether through partner work or using manipulatives. I found this student debrief very valuable to watch because it allowed Patty and me to further understand student thinking beyond the student discussions we had in class and the think sheets that were submitted at the end of the lesson. It's always helpful to hear more about a lesson from the student perspective.