Transcript: Grade Eight Math Integrated ELD

Grade Eight Math Integrated English Language Development: Solving Word Problems

Introductory Slides (0:00–2:55)

Narrator: Welcome to the California Department of Education Integrated and Designated English Language Development Transitional Kindergarten Through Grade Twelve Video Series. Narrator: Mathematics with Integrated English Language Development in Grade Eight. The students have been engaging in tasks where they solve real-world application problems using systems of equations as part of a unit on linear equations. In this lesson, the students work collaboratively to unpack and solve a word problem using a system of equations and key information from the text. At the end of the lesson, the students engage in a class discussion, explaining how they unpack the problem and solve the equation.

Narrator: The California Common Core State Standards for Mathematics Driving the Lesson: The Mathematic Standard is Grade 8, Expressions and Equations, Standard 8c: Analyze and solve pairs of simultaneous linear equations, where students solve real-world and mathematical problems leading to two linear equations in two variables. Watch for how this California standard is addressed throughout the lesson.

Narrator: The supporting California English Language Development Standards used in tandem with the Mathematic Standards. The English Language Development Standards at the Bridging Level are: Grade 8, Part 1, Standard 1: Exchanging Information and Ideas, where students contribute to class, group, and partner discussions by following turn-taking rules, asking relevant questions, affirming others, adding relevant information in evidence, paraphrasing key ideas, building on responses, and providing useful feedback. And Grade 8, Part 1, Standard 12a: Selecting Language Resources where students use an expanded set of general academic words, domain-specific words, synonyms antonyms, and figurative language to create precision and shades of meaning while speaking and writing. Watch how students move from early levels of proficiency toward the Bridging levels of these English language development standards throughout the lesson.

Narrator: Watch how the teacher leads the students toward accurate expression of their math content knowledge by providing opportunities for them to collaboratively read and analyze academic texts with a partner, unpack and discuss the meaning of the mathematical concepts within the problem, write a linear equation, and then explain how they solve the problem using domain-specific vocabulary.

Teacher Introduces the Lesson (2:55–3:54)

Teacher: So, there are three key features that we are gonna try to do today. One, we are gonna solve a system of equations problem which we've been doing for a really long time. Two, we are gonna communicate with others how you solved it. So, we were really gonna practice verbally explaining to each other how you solve the problem. You always—I always ask you guys “why, why, why,” so you are used to that explaining part, but now you're gonna try to explain it from start to finish. And then if we have time we're gonna begin our explanation, the writing part of it. Okay, so we are gonna start off with a new problem. So, I'm gonna pass this out to you guys and the first thing I want you to do is read it quietly to yourself. We are gonna look at this chunk by chunk by chunk, so I broke it up into little pieces. So, you and your partner, you guys are gonna have an extended conversation now. And I want you guys to look at each piece of this text, and I want you to write what is it talking about. What information is it giving us?

Students Discuss in Pairs (3:55–5:03)

Student 1: And it costs six dollars and eighty cents, plus 90 cents for each topping.

Student 1: So, that's the cost of each topping.

Student 1: The cost for... for the cheese pizza and the topping.

Student 2:  It's like the cost of the pizza and the toppings.

Student 3: So, it's talking about how many of the toppings you have to put on both of the pizzas...

Student 4: Okay but, I don't get it because it's saying "How many toppings need to be added to a large cheese pizza from Pizza Hut and Round Table.”  Like, what is it basically trying to say?

Student 3: It's like, basically saying that you're, you're just putting like, toppings on both of the pizzas. So, you're adding toppings to it.

Student 4: But, like, you know, OK. But how about if you want a pizza without toppings?  Is it still going to cost the same thing?

Student 3: Did you read the question? In order for the pizza to cost the same... so it's saying that how many of the toppings you had to put on both pizzas for them to equal the same?

Student 4: Ok. Now I get it.

Looking Deeply at Classroom Instruction (5:04–8:44)

Teacher: Okay, so how, so, what are we trying to find? Yet?

Student 5: How to make the large cheese pizza from Pizza Hut... I mean not, not Pizza Hut—yeah, Pizza Hut—cost the same amount as the one from Round Table.

Teacher: Okay.

Student 6: How many toppings do we need to add to be equal?

Teacher: Okay. So, you guys are all saying exactly what we want to hear. So, we're looking for toppings, we're looking for equal cost, all of that. So, now I'm gonna challenge you. I want to see if you guys can write equations, because how many unknowns are we talking about here? Like, how many pizza companies are we working with?

Students: Two.

Teacher: So, we're comparing two things, so how many equations do you guys think we should write?

Students: Two.

Teacher: Okay, that's your challenge. See if you can write the two equations.

Student 4: I don't get it because, if the cost is, just like, unknown. How are we going do this? Like b plus r... or we just gonna leave it without the total?

Student 3: But the two variables are here; they already give you the price.  So, you just gotta figure it out.

Student 4: That's what I'm trying to say, like if we—oh, my bad. If we don't know the cost we will try to look for it and add 2b so we could put the total of b plus r equals… You get me?

Student 3: You could just put c for the variable, for the price because the cost is unknown. But you're writing two equations, too. One with the variable and one with numbers.

Teacher: So, what was your guys' thoughts in writing?

Student 3: Since this one is already like, that's the—I think you call it “initial cost” or “price”? And then the 90 cents is the one that is constantly moving.

Teacher: And how do you know the 90 cents was the one that was constantly moving?

Student 3: Because it's saying that your...

Teacher: What in the text tells you?

Student 3:  It says “plus the 90 cents for each topping,” so it says “each,” that means that you could keep adding it.

Teacher: Okay. And then how did you know that this would be “initial” like you had said.

Student 3: Because it's saying that the pizza in general is just six dollars and eighty cents.

Teacher:  Okay. So, Janessa what did she just tell you?

Student 4: She said that, okay, this was “initial” because... wait, that's right?

Teacher: You can do the second one if you want, based on what she just said, so…

Student 4: So, this one was “initial” because, like she say, that it's seven dollars and thirty cents plus. And then we, we were talking about... and then, this one was the... What was this one called again? Not “the initial...” what was that word called?

Student 3: It's constantly moving?

Student 4: Yeah! That's, that, because if it's constantly moving, is it behind for each topping?

Teacher: Okay, so do you guys know— you're saying, “constantly moving,” and you said from the text you found that it said “for each,” right? So, instead of “constantly moving” what term would you say? Because “constantly moving,” that's not really like a mathematical term, so what term would represent something that is constantly moving? I want to see if you guys can figure that part out. It's like... It's like right there, right? So, you guys have—your explanation is great, but we want to see if we can pull out that vocabulary. So, what does it mean when something is constantly moving? What would be the vocabulary we used in the past? Or “constantly changing” because you don't know it, right? So, I want you to think about it, if you can figure it out, because I think it's right there.

Teacher: So, I heard some great conversations. You guys were even using the text to help you try to answer the questions and why you put things the way you did. I do have one group that I'd like for them to share, and then if anyone wants to add in that'd be even better. So, I'm gonna pick on Maijur and Janessa. I want you guys to give us the first equation for Pizza Hut. What from the text told you to use that?  And then we are going to talk about it.

Student 3: So, the equation for a Pizza Hut is “six point eighty plus point ninety x equals to c.”

Teacher: And can you define your variables for all of us please?

Student 3: p plus r equals c.

Teacher: What did you, what does x stand for? That's what I meant.

Student 3: Oh, like what it means?

Teacher: Yeah!

Student 3: So, it's basically saying that that's the additional cost, so you're adding that to the the initial cost of, which is six point nine—eighty.

Teacher: Okay, let's help Maijur. She has a great equation, but what does her x mean? Like, it's just a letter variable right now. Like, what does that mean—what does it stand for?

Student 7: For each topping.

Teacher: Okay, so each topping. Okay, and then c would stand for what?

Students: The cost.

Teacher: Okay, now, using the text, why did she put the “six eighty” here and the “ninety cents” there, and I want you to pull it from the text. What vocabulary in the text told you that is what it should look like? Do you guys want to share?

Student 8: Okay. Sure. You go first.

Student 9: No, you go.

Student 8: Okay, so the six dollars and eighty cents is the cost of a large pizza at Pizza Hut and then the “ninety cents” or the “point ninety” is the cost for each topping. That's why she put x right by it because we don't know how many toppings are needed, and that's why the cost is unknown.

Teacher: Okay, I want to keep going with that. So, mathematically what word are we trying to say, but we're just it's not there yet?

Students: The sum? No. It’s called the… So, for each, we talked about, she said like for every…

Teacher: What are some other words that all mean what you guys are saying right now? Okay, let's have a partner conversation. Think about that. If we don't get to the writing part it's okay.

Student 4: I don’t know what it is. Did you use the word yesterday?

Teacher: We did not use this when we were writing yesterday. But we've used it before when we did the bowling problem.

Student 3: I remember I wrote it down.

Student 4: Then look at the paper of the bowling.

Teacher: And we did it for another problem. I think for the baseball caps, maybe. We've used that vocabulary before.

Whole Class Debrief (11:55–14:16)

Teacher: So, what is that? Say it louder.

Student 9: The rate of change.

Teacher: The rate of change. So, Elijah started off with slope and Ernesto heard us say that and he's like, "Wait a second, it's rate of change." So, what is the rate for Pizza Hut?

Teacher: Ninety cents for each topping. Remember those vocabulary words, “for each.” So, what would Round Tables rates be? And what from the text tells you that? The “for each” right here. Okay, so we spent a long time talking about this text, but now you guys have a very, very thorough understanding of the text. The equations, what they mean, why we use what we used, the rate—we pulled out all of these vocabulary words. “Rate” was not in that text. “Initial value” is not in that text. “Variable” was not in that text. But yet, you guys were able to pull that out based on the conversations you guys we're having with each other. So, we're gonna do one more thing. We're gonna set it up, and then we'll pick this up where we left off, because we’ve got to get to the rest of our objective. We need to start solving it. So, we deconstruct it and do all that stuff. I want you guys to at least set up the first part. Okay? So, talk to your partner and see if you guys can set up how would you figure out this problem.

Student 3: You could do a ratio, so you could put “six dollars and 80 cents.” And then under that you put... You could just add that to the 90 cents.

Teacher: So, what did she do?

Student 10: She inputted y for y.

Teacher: So, y for y. What method is she using? So, do you guys remember what it's called? Say it louder and proud, because you were right.

Students: Substitution.

Teacher: Substitution. So, tomorrow we'll get into the writing part of this and really figuring out how do we explain this to partners how we solved, how can we write this in our own words.

Reflection and Closure (14:17–15:13)

Narrator: Reflection and Discussion. Reflect on the following questions: First, how did you observe the following focal content standards and supporting English language development standards in implemented in this grade eight integrated English language development lesson? Expressions and Equations, Standard 8c. English language development, Part 1, Standard 1: Exchanging Information and Ideas. And Part 1, Standard 12a: Selecting Language Resources. Second, what features of integrated English language development did you observe in the lesson? Now pause the video and engage in a discussion with colleagues.

Closing Slides (15:14–15:33)

Narrator: The California Department of Education would like to thank the administrators, teachers, and students who participated in the making of this video. This video was made possible by the California Department of Education in collaboration with WestEd and Timbre Films.