Transcript: Grade Four Math Integrated ELD

Grade Four Math Integrated English Language Development: Justifying a Mathematical Argument

Introductory Slides (00:00–02:36)

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 Four. In this lesson, the students are collaboratively solving a word problem and learning how to justify their thinking in writing. They collaboratively construct a mathematical argument and will ultimately color code the different structural components of their arguments.

Narrator: The California Common Core State Standards for Mathematics Driving the Lesson. The mathematics standard is Grade 4, Number and Operations in Base Ten, Standard 5: Use place value understanding and properties of operations to perform multi-digit arithmetic, where students multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Students illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Watch for how these California standards are addressed throughout the lesson.

Narrator: The supporting California English Language Development Standards Used in Tandem with the Mathematics Standards. The English Language Development Standards at the Bridging Level are: Grade 4, Part 1, Standard 1: Exchanging Information and Ideas, where students contribute to class, group, and partner discussions, including sustained dialogue, by following turn-taking rules, asking relevant questions, affirming others, adding relevant information, building on responses, and providing useful feedback. And Grade 4, Part 1, Standard 10a: Writing, where students write longer and more detailed literary and informational texts collaboratively and independently using appropriate text organization and growing understanding of register. 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 prepares the students to justify their mathematical thinking by providing opportunities for them to discuss the problem with their peers using learned language structures and vocabulary.

Teacher Introduces the Lesson (02:37–03:02)

Teacher: One of the things we're going to do is—before we even do the math, we're going to think about it. We're actually going to think about our thinking. Number one, what is the problem asking me to do? How many tasks and asks are there? How do you know? That's actually number one on the bottom of your page, right? Okay. Ones please talk to twos. Threes please talk to fours.

Students Discuss in Pairs (03:03–03:58)

Student 1: I think the problems are trying me to do is, um. Let me think, let me think. The mistake that he did by one of these two mistakes that are one of them are wrong kind of. What do you think?

Student 2: I mostly kind of disagree, because um uh, it's actually telling us to like find out what in which method Alberto did a mistake in.

Student 1: Okay. Now I agree.

Looking Deeply at Classroom Instruction (03:59–04:11)

Narrator: Watch how the teacher leads the students to justify their mathematical thinking of a solution to a word problem by providing opportunities for them to analyze academic words and build their argument using learn language structures.

Teacher Reviews the Directions (04:12–05:02)

Teacher: Well let's look at the directions. Let's read it together.

Students: Identify the method where Alberto made a mistake and explain what he should do to correct it.

Teacher: What are the two things we need to do? Yeah.

Student 3: Um, we have to identify and explain the, the mistakes that Alberto made.

Teacher: We have to identify and explain. Two things. Right? I want you to think in your head, what does the word “identify” mean?

[Teacher pauses for think time.]

Teacher:  And now I'd like the ones to turn and talk to the twos and the fours turn and talk to your threes.

Students Discuss in Pairs (05:02–05:23)

Student 4: I think “identify” means like find it, discover it, like, just identifying means like something about like what you're finding, like found it, discover it. That's what I think.

Student 5: Same.

Student 4: Same, you agree with me?

Student 5: I agree with you.

Student 4: Thank you.

Whole Group Debrief (05:24–06:15)

Teacher: What does the word “identify” mean? Does anybody else? Xiomara?

Student 4: To search?

Teacher: Okay, to search.

Student 6: To find, like…

Teacher: To find. Hmmm. Well we have the word explain a little bit later, so two different words, right. Leslie.

Student 4: I think “identify” means to discover what the problem is.

Teacher: Okay “identify” means to discover. To find. It's time to start thinking about the math. Right? So, I want you to—with your partners—identify and explain the mistake that Alberto made.

Students Discuss in Pairs (06:16–06:39)

Student 7: She made the mistake in method X because you know what there's… there's a one right there but that's really ten. And then right here they put a one and it's supposed to be a ten because it's in the tenths place. Which one do you think?

Student 8: Yeah, I agree with you.

Student 7: Ok.

Whole Group Debrief (06:40–06:49)

Teacher: He made an error. This is the hard part. Turn and talk to your partners. Where did he make the error?

Students Discuss in Pairs (06:50–06:58)

Student 4: He made an error and he made an error and made an error.

Student 9: Place value.

Student 4: In the place value. I agree.

Whole Group Debrief (06:59–08:53)

Teacher: So, my explanation of my evidence is he made an error in... I don't want to say method X again because we've already said that and I would be repeating. I want to know the mathematical mistake. You two girls. What? Who's gonna talk? Crystal, go ahead.

Student 9: He made a mistake in place value.

Teacher: Hmm, place value.

[students using gestures to indicate they agree]

Teacher: [Teacher writes on the chart.] He made an error in place value. Okay, awesome! I like how Tati filled hers out. Make sure you do the bottom part, and then she left a whole bunch of blank lines after the word “multiply” because she's going to put her numbers in there, right. She's going to go back to the problem and put the numbers in because she has to cite where the mistake is. How do you guys feel?

Students: Good! Smart.

Teachers: Our very first thing we're going to write is the name. Who could tell me what name are we going to put in? Everybody.

Students: Alberto.

Teacher: [Teacher writes on the chart.] Alberto. And now I'm going to use a past tense verb. Think in your mind. What would be a good past tense verb that I could use there? Alberto [fill in the blank] a mistake. Raise your hand. Noelia?

Student 3: Made.

Teacher: Made.

Looking Deeply at Classroom Instruction (08:54–09:13)

Narrator: Watch how the teacher leads the students to justify their mathematical thinking by providing opportunities for them to read and analyze the text to make meaning of the problem. Then watch how the teacher provides them opportunities to speak with peers using learn language structures and vocabulary to build a mathematical argument.

Teacher Gives Directions for Group Work (09:14–09:58)

Teacher: Ones, you're going to be writing the posters. Twos you're going to be the editors looking for mistakes in grammar and spelling and any punctuation. Threes you're going to be giving the ideas. And fours you're going to be reading what is being written out loud for your whole group to hear. You're also in charge of telling the teacher if there's something you need or if there's a problem. We're going to switch these jobs after three minutes. So, we'll have a different job in three minutes. But does everybody know what job they have right now?

Students: Yes!

Teacher: Okay, are you ready?

Students: Yes!

Teacher: Begin.

Students Discuss in Groups (09:59–12:18)

Student 10: In the beginning. [pauses] But when they do the math.

Student 11: Beginning.

Student 10: Yeah, beginning. When, but when they do the math um when when they do the math it shows it shows only a four but not fifteen.

[Students talking in other groups in the background.]

Student 10: And also like that?

Student 4: [Writing and reading from the paper.] It shows that when they do the math.

Student 10: In math it shows. It shows a 4 instead of a 14.

Student 4: [Writing on the paper.]

Student 10: Four instead of a 14. Yeah. Yeah you could put a period. Reader, now you read.

Student 11: Okay. [Student reading from the paper.] Eduardo made a mistake in method X. We know this because in method X it shows that 72 times 14 in the beginning, but when they do the math it shows a 4 instead of a 14.

Teacher: So, the best thing to do is to go back to the original problem and think, okay is that really a two times one or is that a two times [fill in the blank]?

Group of 4 Students: Ten.

Teacher: Ten. And is that really a seven times one or is that a seven times [fill in the blank]?

Group of 4 Students: Ten.

Teacher: Okay, so when you make that comparison, you might see problems—go back to the original math problem, that will help.

[Students inaudible in the background]

Student 10: Made a mistake in.

Student 9: Place value.

Student 10: In. In strategy... Do you think strategy B?

Student 9: Strategy X and place value.

Student 4:  It could be method, strategy, or problem.

Student 10: Yeah. So, which one do you think, place value or strategy? Which one makes a little bit more sense?

[Several students say the same thing.]

Student 4: Place value.

Student 11: Place value.

Student 9: Place value.

Student 10: Yeah, let's put place value.

Student 11: Place value.

Student 4: Place value is...

Student 9: Right there.

Student 10: Yeah, right there.

Student 9: Method X is a place value.

Student 10: Just like what Crystal said.

Reflection and Closure (12:19–12:45)

Teacher:  I'm really excited to see how you guys are building your argument and your justification of your math. And when we're, we're going to put this away for now but let me tell you what our next steps are going to be. Our next steps are going to be, we're going to underline our claims our evidence and our explanation of evidence in our colors. Okay. We'll do that and share our writing with each other. We'll do that next time.

Closing Slides (12:46–13:52)

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 being implemented in this grade four integrated English language development lesson? Number and Operations in Base Ten; Standard 5, English language development Part 1, Standard 1, Exchanging Information and Ideas; and Part 1, Standard 10a, Writing. 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.

[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.