PATTY FERRANT: My name is Patricia Ferrant. I teach at Pollicita Middle School in Daly City, California.

Video Transcript from Lesson Part 1 http://www.insidemathematics.org//classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem PATTY FERRANT: My name is Patricia Ferrant. I teach at Pollicita Middle School in Daly City, California. PATTY FERRANT: Remember you took your quiz, your assessment the other day and it was called right triangles, and there are some things we need to address. When you see a right triangle, what do you think of? In your head. And I want you to think of big ideas. What's the big idea? So tell your partner. STUDENT: Pythagorean. STUDENT: Pythagorean. Yeah. PATTY FERRANT: I see people looking around the room still. That's awesome! Anchor posters. Aaliyah is eyeing somebody. Not sure why. So what is that big idea? Because obviously we're still reviewing, getting ready for our assessment. Go ahead, [inaudible]. Start us off. STUDENT: A squared plus B squared equals C squared. PATTY FERRANT: So that's something that you've now, I think, kind of memorized. I want to know what that means. Talk to your partner. STUDENT: So A squared plus B squared equals two pieces of the area of Damian's land equals to the area of Nickolas s land, which is C squared. STUDENT: A squared plus B squared equals C squared because you need to find the area of the hypotenuse. STUDENT: I thought she was going to say be more precise, so I was going to say the two areas of Damian's land would equal the area of my land. PATTY FERRANT: All right, go ahead, Fernando, start us off. STUDENT: A squared is one of the legs, is like...is like that. And then B squared is the other leg. When you add them together it equals the hypotenuse squared. PATTY FERRANT: So you need to add on, rephrase, restate, clarify. Go for it. STUDENT: If you add the lengths of A squared and B squared and find the square root, that's what the hypotenuse is. PATTY FERRANT: Okay, can someone clarify that? Just trying to make sense of it. So she's saying something about finding the hypotenuse. I'm still not a hundred percent sure, convinced. Go ahead, Aliyah. STUDENT: You find the hypotenuse by finding the square root of C squared. Inside Mathematics Page 1 of 5 www.insidemathematics.org

Video Transcript from Lesson Part 1 http://www.insidemathematics.org//classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem PATTY FERRANT: I'm convinced that a lot of you really do understand how to find the length of the hypotenuse, but what if I'm finding the length of one of the legs? If I want to find the length of a leg and I know the areas. So I know Nickolas s area of his land. I know all the areas. How do I find the length of the leg? Talk to your partner. What would you have to do? STUDENT: So how you find one of the legs is if you have one of the areas of the legs, you have to square root it and see if it matches up. STUDENT: You would square the hypotenuse and use the other leg and then subtract it, and find the square root. STUDENT: You have to find the square root of the area of both legs to get the lengths. PATTY FERRANT: I just want to know how do I find the length of a leg. STUDENT: Well, you just square root the area and then, um, that one leg and the other leg, the square root of those...i mean, the areas will equal to the hypotenuse. PATTY FERRANT: What were you asked to do on the assessment? STUDENTS: Find the leg. PATTY FERRANT: Find the what of the leg? The area of the leg? STUDENTS: Length. PATTY FERRANT: The length of the leg. You were trying to find the length of the leg. Okay, so this is what we have. Here is Student 1, here's Student 2. I want you to look at their work, try to make sense of it and decide who do you agree with and why. Or who do you disagree with and what advice would you give them, because this is real work. This happened. This is our class. So people are still confused, which is fine, but how can we support them? So think by yourself first. If you agree with Student 1, can you either restate something she said? Can you explain some more? Can you clarify? STUDENT: So you know that A squared plus B squared equals C squared. You know C squared equals twenty-six squared, and then A squared is ten squared. So all you have to do is subtract twenty-six squared minus ten squared, and get the area of B squared. And you find the square root of the B squared, which will be the length of the leg. PATTY FERRANT: Then what's up with Student 2 and 3? No one agrees with them? Or does someone agree with Student 2 or 3? STUDENT: So what I'd advise them to do is square root the area of that one length and you'd find the length of the leg. PATTY FERRANT: Great! Restate what he just said to your partner about Student 2's work. Inside Mathematics Page 2 of 5 www.insidemathematics.org

Video Transcript from Lesson Part 1 http://www.insidemathematics.org//classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem STUDENT: Do you know? STUDENT: Because Student 2 only found the area of the leg. He didn't find the square root. That's how you find the length of the leg. He just found the area of that one there. STUDENT: All right. PATTY FERRANT: Do you agree with what Jacob said or disagree about Student 2? STUDENT: I agree with Jacob about, um, Student 2, that they only stopped at finding the area and they also need to square root it to find the length. PATTY FERRANT: Because they're trying to find what? STUDENT: [Inaudible] of the B...they're trying to find the length of B squared. PATTY FERRANT: The length of B squared, which is the what of the triangle? STUDENT: The leg. PATTY FERRANT: The leg. All right. Are you convinced? Because that's what you're trying to think about. Are you convinced? STUDENT: A squared is the ten squared and twenty-six squared is C squared, not B squared. PATTY FERRANT: Think about what she just said. Look at your diagram and then look at Student 3's work. I mean, do you guys agree with what Raeann is saying? STUDENTS: Yes. PATTY FERRANT: Okay and this happened. Just being honest, this happens throughout all my classes. This was a common misconception common error. So then, I want to know advice. What are we going to say to the students to make sure this does not happen again? So start us off. So Romin, go ahead. What advice would you give? STUDENT: Try to look more at the triangle and not at the numbers. PATTY FERRANT: Romin is saying, like, look back at that diagram, not just looking at numbers. So then, what questions could the person maybe ask themselves to make sure that they are substituting in the right place? What do you think, Chloe? STUDENT: Do you know what the hypotenuse is? PATTY FERRANT: Is that a good question? Do you guys already know what the hypotenuse is? STUDENTS: Yes. Inside Mathematics Page 3 of 5 www.insidemathematics.org

Video Transcript from Lesson Part 1 http://www.insidemathematics.org//classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem PATTY FERRANT: So then, maybe that goes back to what Romin said. He's like, "Okay, so make that connection. The hypotenuse has to do with which land?" And it's which land in the relationship? STUDENTS: C squared. PATTY FERRANT: C squared. Look at what they said C equals. C is about what? STUDENT: Twenty-eight. PATTY FERRANT: Twenty-eight, okay. So let's do what Romin said. Let's go back to the diagram. Something should pop in your head right away. Like something right away. There's a red flag. Right away you should be like, "What?" How long is this length? STUDENTS: Ten. PATTY FERRANT: How long is this length? STUDENTS: Twenty-six. PATTY FERRANT: And now I'm looking at the diagram. That's what Romin said to do. And how long is this length according to this person? STUDENTS: Twenty-eight. STUDENT: It can't be longer than... PATTY FERRANT: Wait, so what's the issue? It can't be longer than what? STUDENTS: Longer than the hypotenuse. PATTY FERRANT: So that's making sense of your answer, not just finding an answer but making sense of it, and seeing if it matches up back to that diagram. So here's Student 4 and here's Student 5. What advice are you going to give that person that was confused? STUDENT: The Student 4, he...so since they already give you one of the lengths of legs and they give you the length of the hypotenuse, so he, like... Well, what I did when we took the test was I just guess and check. Like, I started from, like, twelve and then worked my way up to twenty-four. PATTY FERRANT: What's the concern here: Student 4, Student 5? Who's struggling? What's the concern? How are we going to help them out? And I would love to hear from somebody who hasn't talked yet today, because if you're talking, you are helping yourself make sense of it. You're also helping others. So if you haven't spoken today, who do you agree with and why? Or who do you disagree with and what advice do you have? Inside Mathematics Page 4 of 5 www.insidemathematics.org

Video Transcript from Lesson Part 1 http://www.insidemathematics.org//classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem STUDENT: I disagree with Student 5 because they did what Student 3 did confused the hypotenuse as being a leg, and then they tried to find length by using what you do to find the hypotenuse. PATTY FERRANT: Do you agree or disagree with what Damian said? STUDENT: I agree with Damian because they are like doing the same thing to find...they're doing the same rule to find the hypotenuse, but instead they're trying to find the leg. PATTY FERRANT: So what advice do we say to Student 5? STUDENT: Do not confuse the hypotenuse as one of the legs. PATTY FERRANT: Does that make sense? STUDENTS: Yeah. PATTY FERRANT: Yeah, don't confuse that. And that goes back to what Romin said before. You need to make sense of that diagram. You need to make sense of that diagram. Great! Anybody has a last word? Inside Mathematics Page 5 of 5 www.insidemathematics.org

Video Transcript from Lesson Part 2 http://www.insidemathematics.org/classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem/lesson-part-2 PATTY FERRANT: I want you to give advice to your peers that's your friends in this classroom to help them be successful on the MARS test next week. What do you do when you're stuck? What strategy should they try? I want you to find someone new right now and go give them advice. So one person in the group leaves. Go fast, go! We only have, like, three minutes. STUDENT: Uh, when you're done with the problem, keep checking, check it two times, and check the anchor poster if it makes sense. STUDENT: When you're stuck take a deep breath and calm yourself and don't get [inaudible]. STUDENT: Double check your answers. Make sure each aspect of your problem is correct because if not, the outcome will be wrong. Do a three-read for at least every problem, check your answers, and be sure, um, you're neat so you won't get lost in your work. STUDENT: And you go with your gut. Yeah. PATTY FERRANT: Did your partner give you advice on a good strategy or did you give your partner a good advice on a strategy? What's a strategy? Anyone. A strategy you can use. Aaliyah? STUDENT: Do a three-read. PATTY FERRANT: A three-read. That is definitely, I think, number one. What do you do when you're stuck, Jazzlyn? STUDENT: Use the anchor posters. PATTY FERRANT: Oh my gosh, use the anchor posters! Absolutely! What else? STUDENT: Draw pictures. PATTY FERRANT: Draw pictures! Draw pictures! Absolutely draw pictures! What other strategies? Yeah? STUDENT: [Inaudible] PATTY FERRANT: Say again. STUDENT: Equations. PATTY FERRANT: Make some equations. Perhaps there's going to be a situation that if you make an equation it's going to make sense. So making equations, drawing pictures. Yeah? STUDENT: Make a table. PATTY FERRANT: Making systematic. Inside Mathematics Page 1 of 2 www.insidemathematics.org

Video Transcript from Lesson Part 2 http://www.insidemathematics.org/classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem/lesson-part-2 STUDENT: Labeling. PATTY FERRANT: Oh, thank gosh you said that! Labeling anything you know. Ashley? STUDENT: Don't rush. PATTY FERRANT: Don't rush. Yeah. Don't rush. You have as much time as you need. Double check your work. So especially if you're done early, double check that work. STUDENT: Underlining important things. PATTY FERRANT: Underlining, highlighting important information. Absolutely. Be organized, be systematic so you're not getting lost in the work and it's making no sense. I think it goes back to making sure you label things, underline things. Um, are you allowed to use calculators? STUDENT: Yes. PATTY FERRANT: Yeah, use them, but don't just one time. Double check what you put in a calculator because sometimes we put things in a calculator that doesn't even make sense to us. Um...oh wait, and make sense. What should you always try to make sense of? STUDENT: Everything. PATTY FERRANT: Everything but...okay, you got an answer: five. What should you do? Make sense of it. What does five mean? Inside Mathematics Page 2 of 2 www.insidemathematics.org

Video Transcript from Students Discuss Homework http://www.insidemathematics.org/classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem/students-discuss-homework 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. Inside Mathematics Page 1 of 2 www.insidemathematics.org

Video Transcript from Students Discuss Homework http://www.insidemathematics.org/classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem/students-discuss-homework 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. Inside Mathematics Page 2 of 2 www.insidemathematics.org

Video Transcript from Reflection on Peer Advice http://www.insidemathematics.org/classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem/reflection-on-peer-advice PATTY FERRANT: And I am sure something in the beginning of the year in my, like, in the culture stuff in the way beginning I mean it goes on we came up with strategies of what do you do when you're stuck. So I know there's some anchor poster floating around about just what strategies. What can you do? Um, and then if I'm seeing it, I'm asking them, "So what can you do?" And, um, I mean, the majority of them are going to say, like, "I can look at my notes. I can look at the anchor posters. I can connect to something I've learned before. Um, I can ask my partner." It's like...and they actually always know they can ask a partner. Like, that's just a given. Um, but I think the one thing that, especially in the beginning of the year and towards the middle, and I try not to do as much at the second half of the year is my questioning. Like, kind of letting them figure out how to get unstuck by themselves. So I know in the beginning, like, yeah, I'm going to ask them lots and lots of questions to...to, um, to help deepen their understanding, or help them make some connection, or where could you look kind of deal. But as they're maturing, I'm trying to get them to figure it out on their own. I want you to give advice to your peers that's your friends in this classroom to help them be successful on the MARS test. And the idea of valuing each other and working together that's what's expected of them. Um, and they know that I value it, and I think they finally realize, like, they value it too. That's the one thing that in the culture of the classroom, they realize, like, they're learning from each other, putting all those resources together and internalizing it and using it on their own. The content will come. Are you trying? Are you persevering? Are you not giving up? I mean, they all have, I think, a confidence they never had before. They'll say what they think and they'll have opinions, and I had to work really hard all year on saying, "Think. Have an opinion." Like, whether if it's right or wrong. Like, to really be thinking deeply about what we're doing that, I think for all of them took a long time: to have a comment or a response that wasn't something easy they could talk about. They've realized they've gotten smarter and a lot of it is from that pushing in the beginning of the year, that you will get smarter in here. Inside Mathematics Page 1 of 1 www.insidemathematics.org

Video Transcript from Reflection on Lesson http://www.insidemathematics.org/classroom-videos/public-lessons/8th-grade-math-pythagorean-theorem/reflection-on-lesson PATTY FERRANT: They had an assessment last week and I've done a few but on...like, we'll say the Pythagorean Theorem, but I don't care if they don't even know the name of that, um, but the whole relationship if you see right triangles, so that relationship of "a squared + b squared = c squared. They had a quiz, or a, you know, a little assessment and some of them did very well, and some of them are still struggling. So I'm going to, um, just show some student work and have a discussion about that. The assessment I gave was the right triangles and students had a story that had to do with areas of land, and we used students' names, um, in our classroom and we discovered that the areas of Damian's land was equal to the area of Nickolas's land. When I looked at the students' work we found that when the two legs...the length of the legs were given, students could use the Pythagorean Theorem, but when a hypotenuse and a leg was given there was some difficulty, um, finding out the length of the other leg. That's my formative assessment and it's guiding me on what I'm going to ask next, or what type of problem I want to propose next. Knowing what they know and don't know just makes every decision for me, so I did a re-engagement lesson. They couldn't just say...like, I would always say, "What relationship? Like, what relationship do you know?" And they can't just say, "a squared + b squared = c squared." I'm like, No. But what is that relationship? So then that's when they would say, " Nickolas's and Damian's land," or whatever class it was from and then they'd have to...they would connect it to the picture. So it's, like, what's interesting is on the MARS assessment that was just given, that screen ratio, um, and even the irrational irrational numbers has Pythagorean Theorem and I know when I saw some of my students' work, they're drawing those areas in. And so, to me, like, the kid who's drawing that area in is proving to me they understand that relationship of what "a squared + b squared = c squared means. They realize what supports are around them and it's not just the teacher but it's the other students, and that talking to them, "This is building on this and this person," and then the restating, and then the adding-on, and those strategies they're getting that that's making it make sense for them. I'm really trying to build, like, everybody else holding each other accountable the culture where it's like, I can't expect that my partner is going to be sharing this with me, and what am I going to do if they're not. I'm going to call them out. To really be thinking deeply about what we're doing, that, I think, for all of them took a long time. It's just being asked over and over and over to think and to try and have access to something, and to know it matters what they think, and it's okay if it's wrong. I remember, like, us having conversation about, like, "So what does it mean when I'm asking you to think in your head? Red flag should be going off in your head. Like, what does this remind me of? Or when did I see this last?" And it's like all these questions. Inside Mathematics Page 1 of 1 www.insidemathematics.org