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In this section, we close out the lesson and invite students to reflect on their learning.


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

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ANTOINETTE VILLARIN: This is when I would tell my class that I wish we had math all day long! Okay? But Ms. Ferrant, I talked to her, and you’re gonna continue this lesson tomorrow. ‘Cause there’s another part to it, or, Monday! Yeah. I thought it... Monday. So you’re gonna continue the lesson, so in the last 2 or 3 minutes, we want you to do some reflection about what you did. Okay? So finish up your last idea, and then up here on the board, I have a question that says, “Reflection”. I’d like you, privately by yourself, to tell us, If you were given the Pizza Crust problem again, do you think you would be successful at it? And why. So if she gave you the Pizza Crust problem a week from now, how would you do? Do you think you’d be successful? and why. Okay? Please answer that question and then we’ll come around and collect your papers, So you want to make sure your name’s on your paper. So make sure you answer the reflection question before you leave, ‘cause we want to know what your thinking is.

ANTOINETTE VILLARIN: Can you tell me, here, you built it on the side? So that we know, just say “I built it with my tiles.”

ANTOINETTE VILLARIN: Can you see the question? Okay.

ANTOINETTE VILLARIN: Should we just tell them to leave everything on their desks?




PATTY FERRANT: Keep writing!

ANTOINETTE VILLARIN: Okay, tell me what you understand, okay? When you say, “I completely understand it” Tell me what “it” is. Huh? Okay, what does that mean, how to solve it? What does that mean?

ANTOINETTE VILLARIN: How to draw it out? Okay. So you can tell me.. draw what out? When you say “draw it out,” what does “it” mean?



ANTOINETTE VILLARIN: Okay, now hold on to it.

ANTOINETTE VILLARIN: Are you giving them their treats now?


ANTOINETTE VILLARIN: I’ll just tell them on their way out.

ANTOINETTE VILLARIN: All right, um, go ahead and wrap up your reflection, yes, Alex? Yeah, just keep it on your desk, we’ll come by and clean up for you, and pick up your papers. Make sure your name is written on your paper, and I just wanted to say thank you for coming in and letting me teach a lesson, you guys are an awesome class.

In this part, we wanted students to reflect on whether the re-engagement lesson helped them in correcting any mistakes they had made on their first attempt at Pizza Crusts. Since our goal was to address these misconceptions, we wanted to know if students felt that they could be more successful a second time around.

In looking through the student think sheets (scans of which can be accessed below), I notice that students are now able to describe area as the number of square units inside the shape. I see this, as students are actually drawing it and creating visual models on their papers. Previous to this re-engagement, it was rare that students had done this. Here, they are now able to focus on 36 squares, creating different rectangles with varied perimeters and the same area. They are now explaining their thinking more, justifying the reasoning behind their math. They finish the lesson with a stronger ability for proving their thinking.