Lesson - Part 2

lesson - part 2

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With the first group, I start by asking them: What is it that we're doing here? What are we talking about? Are we talking about the Y intercept or the X intercept? How do we get started?

lesson - part 2

9th - 12th Grade - Newcomer ELL Algebra - Graphing Quadratics
Carlos Cabana, San Leandro High School, San Leandro Unified School District, San Leandro, California


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00:00 How, Jesus?

00:02 En esta, para encontrar, tenemos que convertirlo en esta forma, para encontrar…

In this one, to find it, we have to convert it to this form, to find…

00:08 Well, lo que estamos, tal vez, pero ¿de qué estamos hablando? ¿Del y-intercept o del x-intercept?

Well, the one we're on, maybe, but what are we talking about? About the y-intercept or the x-intercept?

00:13 Del y.

About the y.

00:15 Okay. Para la primera, ¿verdad?

Okay. For the first one, right?

00:17 Mm hmm.

00:18 Okay. ¿Cómo se encuentra un y-intercept?

Okay. How do you find a y-intercept?

00:22 ¿Resolviendo?

Solving?

00:23 No, how do you start? ¿Para encontrar un y-intercept, como…

To find a y-intercept, how..

00:26 Sabiendo cual es el x?

Do you know which is x?

00:27 Ah ha, y que vas a averiguar del x?

A ha, and what are you going to figure out about the x?

00:29 Para el y-intercept?

For the y-intercept?

00:31 ¿Buscando x y y por 0?

Finding x and y by 0?

00:32 ¿Los dos?

The two of them?

00:33 No.

00:34 Para el y-intercept..

For the y-intercept…

00:36 O! Para reemplazar el x por 0.

Oh! To replace the x with 0.

00:38 Do you guys agree?

00:41 ¿Estan de acuerdo?

Do you agree?

00:42 ¿Seguros?

Are you sure?

00:43 Okay, then do that. Start with that. Remember, you guys, if you show your work in a little t-table, it'll help you keep track of things. Okay?

00:51 Como x son negativos, no mas tambien a positivos, es cuarto, diez es uno.

Because x's are negatives, they can't be positives, in this quadrant, 10 is 1.

00:59 ¿Donde esta la y?

Where is the y?

01:00 A, el y? Aqui esta. Convierte en 0, 0 esta 4 por 2, 4 por 1, 4, como son negativos…

Ah, the y? Here it is. Change it in 0. 0 is 4 by 2, or 4 by 1, 4, because they're negative…

01:10 O sea, es como, como hacer estas.

That is, how, how to do these.

01:13 Ah…

01:14 Es una de las 4..

It's one of the 4.

01:16 That's the perfect question to be asking. So, ¿porque no?

Why not?

01:19 So, wait wait. Eso tiene que decir que no podemos hacer (inaudible) porque ya concocen.

So, wait wait. This means that we can't do (inaudible) because you already know it.

01:23 ¿Cual?

Which?

01:32 Si tenemos un…. Un rectangulo?

If we have a…. a rectangle?

01:35 ¿Para que?

For what?

01:36 Para sacar las…..

To take out the….

01:37 Factores. Exacto. Ok, prueben esto. Asi que, estamos diciendo si factorizan esta expresion, ¿Cómo va a salir?

Factors. Exactly. Okay, try this. So that, we're saying that if we factor this expression, how is it going to turn out?

01:44 ¿Vamos a sacar unos asi?

We're going to take some out like this?

01:45 A ha. Una parecida a esta.

Uh huh. One that looks like this.

01:48 Luego….

Then….

1:50 Vamos a hacer como esta.

We're going to do it like this.

01:53 Aja, y luego tiene la solucion. Muy bien.

Aha, and then you have the solution. Very good.

01:54 Ya ven, cómo se dice, ¿y en estas tambien?

And now you see, how do you say, and in these too?

01:56 Mm hmm.

01:59 Well, este ya está factorizado, ¿verdad?

Well, this one is already factored, right?

02:06 ¿Cómo? Todos hicieron la y? O no?

What? Did you all do the y? Or no?

02:09 No.

02:10 No tienes ya?

You don't have it yet?

02:11 A ver.

Let's see…

02:12 ¿Por qué?

Why?

02:13 La y no les puse el numero.

For the y I didn't put the number.

02:16 La y ya la saben hacer. Ya tienen las respuestas.

You already know how to do the y. You already have the answers.

02:18 La y sí yo la tengo, maestro.

I already have the y, teacher.

02:19 A ver.

Let's see.

02:20 Es x igual a seis.

X equals six.

02:22 No.

02:23 Pero si parecido a este…

But it is like this one.

02:25 Este, aquí.

This one, here.

02:26 ¿Todo va bien?

Is everything going okay?

02:34 En la y los diez problemas son complicados a proposito. Bless you.

For the y the ten problems are complicated on purpose.

02:39 Si no me encuentro, me voy.

If I can't understand them, I'm leaving.

02:40 Por qué escogi esos problemas …

Why did I choose those problems?

02:44 ¡Por gacho, que usted es el maestro!

To be a jerk, because you're the teacher!

02:46 Ya, parte de esto.

Yes, but aside from that.

02:49 ¿Esto es que quieres que aparesca en la camera?

Is this what you want to show up on the video?

02:51 Okay. ¿Por qué escogi 6x + 1?

Okay. Why did I choose 6x + 1?

02:56 Porque… 6 es 60?

Because…6 is 60?

03:01 No.

03:02 A, mas 2.

Oh, plus 2.

03:03 ¿Por que aparece que? ¿Me explique otra vez?

Why does what appear? Can you explain it again?

03:05 Por qué escogi este factor, aqui.

Why did I choose this factor, here.

03:08 Porque quiere que nos quebramos el coco.

Because you want us to break our skulls.

03:09 Pero ya se quebraron el coco una vez.

But you already broke your skulls once.

03:15 No se falte quebrarte el coco por esta.

Don't miss breaking your skull on this one.

03:19 Porque quiere que factorizamos…

Because you want us to factor…

03:20 Wait wait wait….dejarle un chance.

Wait wait wait, give him a chance.

03:23 (inaudible) nada mas que una y no se va multiplicando.

No, it's just that one and you don't go on multiplying.

03:31 Que este numero es como, y el otro, no tiene mas que….

That this number is like, and the other one, you don't have to do more than

03:37 No. Escogi este porque ustedes ya resolvieron este problema. Lo hicieron aqui.

No. I chose this one because you all already solved this problem. You did it here.

03:42 Oh, y okay, ¡es el mismo!

Oh, and okay, it's the same!

03:44 Uh huh, es el mismo factor. Ya lo resolvieron.

Uh huh, it's the same factor, you already solved it.

03:47 Pero no es el mismo resultado.

But it's not the same result.

03:48 ¿Cómo no?

How so?

03:50 ¿O si? Entonces que…

Oh yeah, then what?

03:51 Por eso que va a salir cero.

Because it's going to end up being zero.

03:52 Exacto. Muy bien. Exactamente.

Exactly. Very good. Exactly.

03:54 Porque es uno, con estas, si multiplicas, se va a cero…

Because it's one, with these ones, if you multiply, it's going to zero….

04:00 Wait wait. Dejarlo en forma de fraccion. Tiene razon, en el decimal, pero dejala en forma de fraccion.

Wait wait. Leave it in the form of a fraction.You're right, on the decimal, but leave it in the form of a fraction.

04:06 Un sexto, exacto. ¿Donde esta, Jonathan? Aqui.

One sixth, exactly. Where is it, Jonathan? Here.

04:09 No se falta convertirlo en decimales, trabajo extra, y este resultado es completamente correcto.

Don't miss converting this to decimals, extra work, and this result is completely correct.

04:16 Ahora, agarren esto. Muy bien, you guys.

Now, grab this together. Very good, you guys.

04:20 Nice job.

04:22 Ay, maetro, que me sucedio. Mire.

Ow, teacher, look what happened to me. Look.

04:26 ¿Yo te lastimé?

I wounded you?

04:28 ¡Si!

Yes!

As they move into their groups, no one's supposed to be on the same problem at the same time. They're supposed to be either physically or metaphorically working in the middle. Then if they call me over for a question, it should be a team question. At times I need to interrupt a kid several times to give another student a chance to explain. That is something I'm looking for when I'm circulating around: who's likely to be quiet that needs some invitation or the state of conversation when I'm there.

With this group, I'm trying to get them to ask me questions. Then I'm trying to think of what questions I can ask back that might model for them how they could have perceived this process themselves based on wherever they were. Inherent to that is quickly trying to assess what's smart about the work or the thinking that I see in front of me right now, and asking, "What can I leverage from that they can feel confident about?" so that the fact that they have this question doesn't overshadow what they've done that's positive.

Essentially I'm looking for that glimmer of "Oh" from enough people in the group and sometimes that's one and sometimes it's all four, it depends on who it is and what the concept is that will let you lead.

This is related to something I learned from Phil Tucher, who's the coach in the clips. Years ago when we both talked together he talked about trying to frame a learning agenda for a student. At the time, he was referring to a kid who was desperate, who was starting to fear that he might not be able to learn. What's the one piece of learning that I can ask that kid to focus on, from which achievement and confidence can snowball? It's also true for kids who are just fine; the kids who are superficially really successful are also entitled to a learning agenda. What's the one thing that I want them to attend to that they might gain inspiration from with other students?

I try to never ask questions to which I already know the answer. Those are all the interesting questions, those are all the places where I get to do something with student responses that is affirming, or was a follow-up of some sort, or a call for different ways of thinking.