Transcript: Grade Eight Math Designated ELD

Grade Eight Math Designated English Language Development: Math Problem Explanation

Introductory Slides (00:00–03:10)

Narrator: Welcome to the California Department of Education Integrated and Designated English Language Development Transitional Kindergarten through Grade Twelve Video Series.

Narrator: Designated English Language Development: Building Into and From Mathematics in Grade Eight. In this lesson, the students review how they solved a word problem using a system of equations, and practice speaking and writing skills to exchange information and ideas that build the language resources necessary to write a mathematical explanation.

Narrator: The Focal California English Language Development Standards Driving This Lesson. The English Language Development Standards at the Bridging Level are: Grade 8, Part 1, Standard 2: Interacting via Written English, where students engage in extended written exchanges with peers and collaborate on complex written texts on a variety of topics, using technology when appropriate; Grade 8, Part 1, Standard 10b: Writing, where students write clear and coherent summaries of texts and experiences using complete and concise sentences and key words; and Grade 8, Part 2, Standard 2b: Understanding Cohesion, where students apply increasing understanding of how ideas, events, or reasons are linked throughout a text using an increasing variety of academic connecting and transitional words or phrases to comprehending and writing texts with increasing cohesion.

Narrator: Watch how students move from early levels of proficiency toward the Bridging levels of these English Language Development Standards throughout the lesson.

Narrator: The Supporting California Common Core State Standards for Mathematics Used in Tandem with the Focal English Language Development Standards. The mathematics standard is Grade 8, Expressions and Equations, Standard 8c: Analyze and solve pairs of simultaneous linear equations. Students who demonstrate understanding 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: Watch how the teacher leads the students to jointly construct a cohesive written explanation for solving a mathematical problem. The students first engage in oral practice with a partner to explain how they solve the problem. Then the teacher supports the students to collaboratively write a mathematical explanation by eliciting and highlighting the language features of the genre and by facilitating ongoing discussion in which the students negotiate which language features and mathematical vocabulary to include in the text.

Teacher Introduces the Lesson (03:11–03:55)

Teacher: So, we came up with these equations and then we solved. So, we’ve done the math part of this and what we have to learn now is to explain ourselves. And it's a lot easier to explain ourselves verbally sometimes than it is in writing. And we have to get to that point where we can write down how we explain. It's not a long process but it's something that can get a little tricky. So, we're gonna practice verbally and then we're gonna practice in writing. Okay? So, I want you to look at the math part. I'm gonna give, you guys get some like, individual processing time and look at just the math that we did on Friday. And we're gonna try to verbally share with each other how we solve that before we get into the writing part.

Students Discuss in a Small Group (03:56–04:33)

Student 1: No, the problem was about families.

Student 2: A picnic.

Student 3: Twenty-three people were going to a picnic for lunch.

Teacher: Okay. Let me start over. What are we going to write down?

Student 2: Where are you going to start it, you have to add like what we’re going to talk about, not…

Student 1: Let’ use our sentence right here. That would be easier.

Student 2: That’s what I was thinking.

Teacher: So, you don’t have to like go like, this problem will help us explain, da ta da ta da. We can be very precise because we are mathematicians. So, you can be precise. What was it asking you to solve?

Teacher Introduces Writing an Explanation (04:34–04:57)

Teacher: So, we verbally went through this together. Now we're gonna try to write one together. Because we're gonna have to be able to explain ourselves in writing, as well as verbally. Some people think writing is harder. Some people think writing is easier. But remember, you're writing not like to your friend. You're writing an explanation. Like a mathematical explanation. Okay? So, I want you guys to have another partner conversation. I want you to think of just about any classes where they said you're gonna write an explanation. What did they tell you to include?

Students Discuss in Pairs (04:58–05:16)

Student 1: I think the problem, and how you solve from step to step, and how you got the answer.

Student 4: Oh, and the information.

Student 1: Yeah. From here.

Student 4: Yeah.

Looking Deeply at Classroom Instruction (05:17–05:44)

Narrator: Through extended discussions about mathematical concepts, raising students' awareness of how English works in math, and jointly constructing a mathematical explanation, the teacher moves the students along the academic language continuum from using informal language about math to writing more precise, genre-appropriate text.

Whole Group Debrief (05:45–07:22)

Teacher: So, what do you guys think should be included in an explanation? So just think of all your classes that you've learned to write. We've even done some writing in here. What should we include in an explanation?

Student 1: The steps we do.

Teacher: Okay.

Student 1: With the answer.

Teacher: All right.

Student 5: Um, the evidence.

Teacher: So, steps. And what did you say, Sara?

Student 5: The evidence.

Teacher: So, what would be evidence in a math problem?

Student 3: And the, the problem, the, yeah.

Teacher: The what?

Student 3: The problem it's giving you.

Student 2: The steps.

Teacher: The steps we did.

Teacher and Student 2: The work we did.

Teacher: Okay. What do you guys want to add to this?

Student 5: Uh, key words.

Teacher: Like what? What do you mean?

Student 5: Like total calls or, um, how many. So that's telling you like to divide or add.

Teacher: Okay. So key words. So, I'm gonna ask you guys some questions and you tell me what you think. What kind of, um, vocabulary should you use when you're writing? What do you guys think? What kind of vocabulary do you think you should use?

Student 3: The mathematic.

Student 1: Mathematic.

Teacher: Mathematical vocabulary.

Student 1: Yeah.

Teacher: So, give me an example. What would be a better word to say instead of “times”?

Multiple students: Multiplication.

Teacher: Good. What if, what would be another word instead of “plus”?

Multiple Students: Add.

Teacher: Addition. [laughter]

Teacher: Okay. So, you want to make sure that you use the mathematical vocabulary. Like even this, there's this word. What would be better than saying “I plugged that in”?

Student 4: I added.

Student 1: No. I, you, you um...

Teacher: Like I plugged it in.

Student 1: [inaudible]

Student 5: Substitution.

Student 3: Substi... yeah, substitution.

Student 1: Substitution, yeah.

Students Jointly Construct a Mathematical Explanation (07:23–12:26)

Teacher: Yeah, so we want to make sure we're using the vocabulary that we use to solve verbally and in writing. Okay? So, I actually wanted to see what you guys can come up with, and then I have your guide to help you write. So, this is your guide to help you write of what should be included in a math explanation. And we're gonna try to write one together. So how should we start?

Student 3: We solved the problem by…

Teacher: Do we, well how did, what's our answer?

Student 3: The an... wait, the answer or the problem?

Teacher: The answer first because we solved the problem. What was the problem?

Student 3: The answer for...

Teacher: Okay, I'm gonna go with it. The answer... If you don't like it you better speak up.

Student 3: Speak up. Speak up.

[Laughter]

Student 6: That's, No, why you gonna start with the answer?

Student 3: Be, so we could like, show how we got the answer.

Student 1: I think what the word problem's about.

Teacher: Okay. So, start talking and I'll start writing.

Student 3: The problem was about. No, the problem was about.

Teacher: The problem...

Student 3: Wait, can we say like the...

Teacher: You guys tell me to erase or keep going.

Student 4: No, the problem was about hamburgers.

Student 3: No, the problem was about, um, families, or I don't know.

Student 1: Twenty-three more coming.

Student 6: Picnic!

Student 1: Twenty-three, twenty-three, twenty-three people are going to a picnic.

Student 3: Yeah.

Student 1: And for lunch.

Student 6: Wait, what?

[Laughter]

Teacher: Okay. Let me start over. What are we gonna write down?

Student 6: We're going to talk about how many people ate hamburgers and how many people ate veggies lunches.

Teacher: Okay. So, we needed to find, how many, how many what? People, fish, what are we talking about?

Multiple Students: People.

[Laughter]

Teacher: Okay.

Student 6: Ate hamburger lunches.

Teacher: Ate hamburger. Okay.

Student 6: And then.

Student 4: And veggie lunches.

Teacher: And veggie...

Student 1: Burgers.

Teacher: Lunches.

Student 4: Lunches.

Teacher: All right, so have we stated what the problem, like a clear, like, idea? This is what we were trying to find and we stated our solution. Okay. So so far it sounds, we needed to find how many people ate hamburger and veggie lunches. H represented hamburgers which equaled 20, and V represented veggie which equaled 3. Now what?

Student 4: Explain how we started off.

Teacher: Okay. So how would you do that?

Student 4: First...

Student 3: The first step...

Teacher: First.

Student 3: Yeah, first.

Teacher: What kind of word is that, according to our little sheet?

Student 6: It's a language...

Teacher: It's a language feature.

Student 3: Yeah.

Teacher: Which, and what kind, of language feature is that?

Student 3: A seque...

Teacher: Yeah these are the transition words is what you guys are most used to hearing. Sequential connectives, this just means it's a sequence.

Student 3: Transitions.

Teacher: Yeah, transitions.

Student 1: To begin with we...

Teacher: Okay. Now what? I got “first.”

[Laughter]

Student 1:  First, first...

Student 3: “First.” I think we're supposed to give the problem.

Teacher: I think we already did, right?

Student 4: “First, we wrote it as an equation.”

Student 3: Yeah, yeah.

Teacher: Okay so “first...“

Student 1: We were trying to find the equation.

Teacher: You guys notice the types of words you're using?

Student 6: Yeah.

Teacher: “Wrote. Needed.” What kind of tense is that?

Student 1: Isn't it past tense?

Teacher:  Right, because we already solved this problem, right? So, make sure you stay in the past because it's already been in the past. So first we wrote, we didn't say “we write; we wrote…” …what?

Student 4: The equation.

Teacher: Okay “the equation.” What did we do next?

Student 3: We tr... sub...no, we substituted the...

Student 1: Secondly, we, or, no...

Student 3: Second...

Teacher: Do you guys like that word, “secondly”?

Student 1: No. Like I don't think it makes sense.

Teacher: No?

Students: No.

Teacher: Okay.

Student 3: Second... no.

Student 6: Next.

Multiple Students: Next.

Teacher: Okay. You guys all kind of said that at the same time. “Next.” What’d we do?

Student 3: Guys, come on.

[Laughter]

Student 6: Next…

Teacher: I told you writing's harder.

Student 6: Okay so we, we already wrote the equations down, so now we gotta put...

Student 4: We solved.

Student 3: Next we get the number that, we get the number that is...

Teacher: I think you were the one that had said this Jorge, why don't you say what we should do next? So, look at the paper right here. So, we have our equations, what did we do next?

Student 2: I forgot what I said earlier.

Student 1: We solved the equations. Before you multiply negative 6 times...

Student 2: Oh yeah.

Student 1: Times the variable.

Student 2: Multiply the negative six with the variables and the twenty-three.

Teacher: Why did we multiply the negative 6? What were we trying to make?

Student 4: Inverse.

Teacher: So, you always want to include that to make inverses. And then you would keep going.

Beyond the Lesson (12:27–11:55)

Narrator: Beyond the Designated English Language Development Lesson: Building Into and From Content Instruction. By engaging in designated English language development lessons such as this one, the students are better prepared to engage with math content materials and are more confident to explain their growing math content knowledge through collaborative speaking and reading activities in small groups and individually with increasing independence.

Students Discuss in Pairs During Math (Integrated ELD) (12:56–13:33)

Student 6: If the cost is just like, it's unknown, how are you gonna do this? Like, p + r, or are we just gonna leave it without the total?

Student 7: But the two variables were here, they already give you the price. So, you just gotta figure it out. By adding them.

Student 1: That's right, that's what I'm trying to say. Like if we—oh my bad—if we don't know the cost, we need to try to look for it and add them to these, so we could put the total of “p + r equals…” You get me?

Student 7: You could also, you could just put c for the variable, for the price. Because the cost is unknown. But you're writing two equations too. So, one with the variables and one with the numbers.

Closing Slides (13:34–14:56)

Narrator: Reflection and Discussion. Reflect on the following questions. First, how did you observe the following focal English language development standards and supporting content standards being implemented in this grade eighth designated English language development lesson? English Language Development Part 1, Standard 2: Interacting via Written English; Part 1, Standard 10b: Writing; Part 2, Standard 2b: Understanding Cohesion; and Expressions and Equations: Standard 8c.

Narrator: Second, what features of designated English language development did you observe in the lesson? Now pause the video and engage in a discussion with colleagues.

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.