Transcript: Grade 9 and 10 Math Designated ELD

Grade Nine and Ten Math Designated English Language Development: Math Problem Explanation

Introductory Slides (00:00–03:33)

Narrator: Welcome to the California Department of Education Integrated and Designated English Language Development Transitional Kindergarten Through Grade Twelve Video Series. Designated English Language Development Building Into and From Mathematics in Grades Nine and Ten. In this lesson, the students are reviewing and practicing listening, speaking, reading, and writing skills to exchange information and ideas that build the language resources necessary to write a paragraph explaining how they solved a mathematical problem. The students will use these language resources to accurately demonstrate their understanding of mathematics content and speaking and writing now and in their mathematics class.

Narrator: The Focal California English Language Development Standards Driving this Lesson the English Language Development Standards at the Bridging Level are: Grades 9 and 10, Part 1, Standard 1, Exchanging Information and Ideas, where students contribute to class group and partner discussions sustaining conversations on a variety of age and grade-appropriate academic topics by following turn-taking rules, and asking and answering relevant, on-topic questions, affirming others, and providing coherent and well-articulated comments and additional information; Grades 9 and 10, Part 1, Standard 10b, Writing, where students write clear and coherent summaries of texts and experiences by using complete and concise sentences and key words; and Grades 9 and 10, Part 2, Standard 2b., Understanding Cohesion, where students apply knowledge of familiar language resources for linking ideas, events, or reasons throughout a text to comprehending grade-level texts and writing cohesive text for specific purposes and audiences. 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 Grades 9 and 10, Higher Mathematics Standards, Functions: Interpreting functions, Standard 8a: Analyze functions using different representations. Students who demonstrate understanding write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Students use the process of factoring and completing the square in a quadratic function to show the zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Watch for how this California standard is addressed throughout the lesson.

Narrator: Watch how the teacher leads the students in activities that move them to create cohesive explanations of the processes used in solving a mathematical problem. The students engage in mathematical discourse using newly learned language structures first through listening, then with oral practice, reading, and finally through collaborative and independent writing.

Teacher Introduces the Lesson (03:34–04:27)

Teacher: So today we're going to record experiences from a group activity by doing two things. We're gonna describe the sequence of our procedures and the reasons for different steps in a group paragraph. Everyone, what are we going to write today?

Students: A group paragraph.

Teacher: A group paragraph. So that comes after we have this experience. And we're also in our paragraph we're going to use appropriate signal phrases to indicate the sequence, process, and reasons. So, I'd like you to think for a moment right now. What are some signal phrases that you know that we've been practicing? So, phrases to indicate the sequence, the process, and the reasons. So, think for a minute right now so you can share out your tables. Please share some signal phrases that you know. Ready? Go.

Small Group Discussion (04:28–05:08)

Student 1: Umm signal, signal phrases, umm...

Student 2: I have “next” and “after.”

Student 1: Huh?

Student 2: I have “next” and “after.”

Student 1: So, “next, after.”

Student 3: “We started.”

Student 1: Yeah, “we started.”

Student 2: “By.”

Student 4: “We planted, after, in order to. We started by. In…”

Student 5: “In order to determine.”

Student 4: “To determine.”

Student 5: “To represent.”

Whole Class Debrief (05:09–06:14)

Teacher: What are some of the signal phrases that you discussed?

Student: “To determine.”

Teacher: “To determine,” right. Cuz we're trying to complete a goal, right. “To determine.” Thank you. Daniella, what's another, what's the signal phrase or vocabulary word?

Student 6: (05:24) “To represent.”

Teacher: “Represent.” Thank you. What are some words that we know to indicate the sequence? You can shout it out. What are some sequence words we know?

Several Students Responding: “To begin.”

Teacher: “To begin.”

Several Students Responding: “First.”

Teacher: “First.”

Several Students Responding: “Then.”

Teacher: “Then.”

Several Students Responding: “After.”

Teacher: Mm-hmm. Right. So, we're gonna use all of those together to describe our experiences and write a group paragraph. Take a moment to review. What does the rope represent and what does the graph paper represent? And you can tell your partners. Try to use this word “represent.” So, what does the rope represent? What does the graph paper represent?

[pause and teacher writes “represent” on the board]

Teacher: And you can tell your partners. Try to use this word represent. So, what does the rope represent? What does the graph paper represent? You can tell your partners when you're ready.

Small Group Discussion (06:15–06:32)

Student 7: The graph paper represents the size of the plot of land.

Student 8: The rope represents 100 meters. And then the graph is representing um the area that they are going to look for.

Whole Class Debrief (06:33–08:10)

Teacher: Haniel, what does the rope represent?

Student 9: 100 meters.

Teacher: Thank you. Can you use the word “represent” in a sentence?

Student: The rope represents 100 meters.

Teacher: Thank you. And let's see. Dylan, what does the graph paper represent?

Student 10: The graph paper represents the area.

Teacher: Mm-hmm. The area of?

Student 10: Of the land.

Teacher: Mm-hmm, where they're gonna dig up the gold right?

Student 10: Yes.

Teacher: Hopefully, they'll find gold.

Student 10: Uh-huh.

Teacher: Thank you. Okay, so at your tables your job is to answer those questions. And you have some space here where you took notes yesterday. So, in a minute I'll give you a chance to describe your ideas from yesterday so that you can prepare for the writing activity that comes next. So, we need to answer the question but you probably have different things that you need to do in a sequence. So, take a moment to look at your notes from yesterday. Look at your notes from yesterday. I have these notes from yesterday. You should have more than this. And if you don't, then you'll work with your team to determine the sequence as well as the answer to the questions.

[pause]

Teacher: Okay, I'm going to ask you to share at your table the notes and ideas that you have so far. And then you can work for a few minutes with each other just to try and work out those answers. Okay. Let's begin.

Small Group Discussion (08:11–10:37)

Student 11: The largest one is be a square so I put 25 and 25 on each sides.

Student 8: Yeah.

Student 11: So, I got… What's this?

Student 8: Perimeter.

Student 11: Yeah, perimeter. I got 100 and then I wrote I got 625.

Student 8: Okay. So, for my, my, umm, plot of land I got perimeter, umm, 98 and then the area I got 544. So, we just graphed, umm, the land that we were gonna draw.

Student 11: But in 625 is bigger. She said the largest one is more big one. So, 625 is bigger.

Student 8: Yeah and I put 544.

Student 11: So yeah you need to change it I think.

Student 8: Um-hmm.

Student 11: It says at first umm we…

Student 8: Measured.

Student 11: Graph 100 acres. So, we need to cut in half. Like 50 and 50. So we guess like which number plus which number equals 50.

Student 8: Yeah, so we just first measure the, the graph we measure.

Student 11: Yeah.

Student 8: So …

Student 11: So, first…

Student 8: First we got the materials.

Student 11: First... We got the materials.

[students writing]

Student 11: How do you spell...?

Student 8: Materials.

[other students in background talking]

Student 8: Then the second step was to measure the rope and measure the rope.

Student 11: Use this to measure, so largest one.

Student 8: Yeah, so we just measured. Measured the rope and...

[students writing]

Student 11: When you were second.

Teacher: Show me thumbs up if you think you are ready to start writing.

[students shake head no]

Teacher: Not yet. Ok.

Whole Class Debrief (10:38–12:26)

Teacher: So, you had a nice discussion about the procedures. And you were also taking notes. That's good. I also...

[pauses]

Teacher: Thank you. I also gave you some reminders for how to use some of the vocabulary that we've been practicing like “determine, represent.”

[Teacher points to a chart on the board]

Teacher: Different verb forms. So, look at “used” and then “using.” So here this was an action. This is describing the reason or the purpose. So different forms of the verb. So, your job now is to write your paragraph as best you can. Everyone should be writing. I want to see different kinds of handwriting and I want to show you some reminders as well of what you can be doing. So, since you're only writing one paragraph, maybe you think, well I can't write all the time. That's okay. You can also be giving suggestions. Maybe you want to read aloud of what's been written so far. Maybe you want to check the paragraph requirements from your checklist [teacher holds up a checklist] and make sure that you're doing all of these things here in the dots. Okay, so everyone should be participating and adding to the paragraph even if you're not all, you're not all writing at the same time. You can certainly take turns writing. Okay, how are we feeling so far? Good?

Students: Good.

Teacher: Good. Feeling good. Okay, so let's... let's see the magic. Let's see it happen. If you need help, raise your hand. You have partners, too.

Students Work on Group Paragraph (12:27–16:48)

Student 1: What procedures did you use? First, we measured the perimeters. Put that down.

Student 2: Oh, we need an introduction.

Student 1: Umm, to start with. To start with we first...

Student 2: [writing] To start…

Student 1: To start with we measured the perimeter. We measured the perimeter. And put a period.

Student 2: Uh-hmm.

Student 1: Period. Second, we, we counted the area of the perimeter.

Student 2: [writing] Counted, okay. Second.

Student 3: Or we added.

Student 8: To represent the plot of land we used, umm, we used addition and multiplying to, umm, to find out the area and perimeter.

Student 9: Yeah.

Student 8: Okay, so... [student writing] to represent. To represent the land, we used... we used addition and multiplying.

Student 9: Multiplying.

Student 8: [student writing] Multiplying to, to represent the area and perimeter.

Student 9: Um-hmm.

[student writing]

Teacher: Haniel, did you... have you explained what the different objects represent? Yes, that's what you are doing now. So, while she's writing that you can think about how to describe this and this [teacher points to rope and the paper].

Student 8: Oh.

Student 9: So, yeah.

Student 11: Could we write down there?

Student 8: So... the second step was that we measured the rope and decided where the land was going to be and what it was representing. So...

Student 9: The rope, umm, means 100 meters.

Student 8: Uh-hmm.

Student 9: And the land represents the area of ...

Student 8: Land. Of the land.

Student 9: Represents the land.

Student 8: So... So, you can write it now. Just write it.

Student 9: Ohh. [rereading the sentence in a quiet voice

[camera shows student writing]

Student 4: First, we analyzed the information.

Student 12: And.

Student 4: To know.

Student 12: In order to ...

Um-hmm.

[student writing]

Student 4: In order to find out the largest, no.

Student 12: In order to solve the problem.

Student 4: In order to... [student writing]

Student 12: Solve the problem. The situation.

Student 4: But what's the situation?

Student 5: Umm, the...

Student4:  In order to solve...

Student 12: The situation because you already say, said.

Student 4: The term.

Student 12: To solve the situation.

Student 4: Information in order to solve the situation. To find the largest...

Student 12: Possible.

[student writing]

[other students in background talking]

Student 4: The most gold. Possible. To find the most gold possible.

Student 12: Um-hmm.

Student 4: [rereading the sentence in a quiet voice] Information in order to solve the situation. Of finding…

Student Share Out Their Group Paragraph (16:49–17:25)

Teacher: Umm, I'd like you to read aloud what you have so far. Ok, even if it's just one sentence, I want you to read it aloud. Begin.

Student 1: Our goal was to determine what was the largest possible area. To start with we measured the perimeter. Certain. Second, we counted the area of the perimeter.

Student 13: Umm, our goal was to determine the largest area with the rope of 100 meters. And to represent the perimeter we used the rope, which is 100 meters.

Beyond the Lesson (17:26–17:56)

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 writing activities in small groups, as a whole class and individually with increasing independence.

Students Discuss in Pairs During Math (Integrated ELD) (17:57–18:20)

Student 14: Divide... we... we divide. Uh-hmm. By 2. [student writing on their paper]

Student 10: [in Spanish] ¿Qué se va hacer aquí? (What are we going to do here?)

Closing Slides (18:21–19:42)

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 nine and ten designated English language development lesson? English Language Development: Part 1, Standard 1, Exchanging Information and Ideas; Part 1, Standard 10b, Writing; Part 2, Standard 2b, Understanding Cohesion; and Interpreting Functions: Standard 8a.

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.

[pause]

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.