- All right, so Mr. Padgett
is having a program in the library for the parents of Northaven.
for parents at Northaven.
He has purchased brand new hexagon-shaped tables.
He wants to know how many parents can sit around a row of tables
with their edges touching.
The top surface of each table is a hexagon,
and the hexagons are arranged in rows of different shape.
Now that's a lot of words, right?
Did we say a lot of words with this problem?
- Yes.
- All right, now before we even start,
I want to pause for a second, and I want us to think about
what are some things that we do before we even attempt
to solve a problem?
All right, I'm going to give you a few minutes of private think time,
and I just want you to think about,
What are some things that we do in here before we solve a problem?
Let's take a few minutes to think, few minutes to think.
Charles, what do we do?
- Underline important words.
- All right. We begin by doing what to the problem?
Analyze it.
Analyze and then when we analyze we do what?
Break it apart.
We break it apart so that it can make sense.
That's where we're going to start,
but right before we get there,
we've also been learning about some words
and some things that we can do in the classroom
to help us make sense of problems and to help us help each other.
Let's take a look at our mathematical interactions,
and let's make those connections and reminders.
Can someone give me one that you remember that you've been practicing?
Ranaya, which one have you been--which one do you remember,
you connect with?
- Thinking about my thinking.
- Why is that important?
- So when you have a time to think about when you have a question.
- Okay. Because it gives you time to think about,
okay, your question.
All right, let's see.
Let's go to Amaya.
- I've been thinking about private think time
because like if you need private think time,
you can ask your neighbor and say,
"May I have some private thinking time, please."
- Right, because it's very important that we give ourselves time
to think about the problem before we jump right into it
and start talking and interacting with each other.
All right, Gimeria.
- The problem, the words that I've been practicing is thinking
about my thinking because it reminds me of metacognition.
- Okay. What do you know about metacognition?
That's a big word, girl.
- The people think when they could think out loud.
- Okay. It's kind of like thinking it out loud,
thinking about what's in your brain. Okay,
we'll take two more.
We'll take Calicut.
- Genuine communication.
- What does that mean to you and why is that important?
- It's important to me because genuine means wise,
and because if you ask one of your group members a question,
you've got to be wise.
- Okay. And you want to keep it focused on the problem.
All right, we'll take one more from this back group.
Let's see someone who has not--Anisia.
- Share my challenges like if you need help you could ask three
before you ask the teacher.
- Right. And you want to share your challenges
because are we always going to get it right the first time?
- No.
- No. Even Mrs.
Williams, I have to think through and I may have to ask somebody else
and it's okay if we get help from other people.
As we are working and as you begin this process,
I do want you to keep in mind all of these.
Ms. Nacarado is going to hand it to you
because remember filling out a sheet like this?
I'm going to go ahead and put it on your desk
because right before we start the task,
I want you to have it to think about all of these interactions
as you're working through your task
because you'll have to write something about it later on,
and we always have to keep our minds about
how we're interacting with our groups,
and what we're doing when we're working independently.
- All right. So we are going to focus up here.
I want you-- you already have this paper on your desk.
so I'm going to give you two minutes of just private think time.
During this time, all I want you to do Derek,
is I want you to look at your problem that
Mr. Padgett has presented to us,
and I want you in your private think time to underline words
that you think is important,
and words that you think could help you solve this problem.
Are we ready? All right,
begin. Just what do you think is important to solve this problem?
Are you thinking about it in your head? Okay,
you should be underlining those important words.
Finding those math words maybe.
- What's important to you? Oh,
that's a good word. Why did you underline that word?
Okay, do you know something about edges?
What do you remember about edges? Oh,
thinking of a shape and you think that--good.
So you connected that math to it. Very good.
You have about 30 more seconds. Oh,
you underlined arranged. That's a good word.
Why did you underline arranged? Oh,
okay. So it's telling you what it's going to look like,
okay. Yes.
Scoot your chair right here.
- Well, you're going to decide what to use right now
just in this think time
just what words are important
but I'm glad you're thinking.
So you might want to write notes on the side,
something you already are thinking about which you want to use to solve.
You might want to write that down. Good job.
Okay, you have about seven more seconds.
All right. One,
two, three,
all eyes on me. All right,
now that you've had a moment to look through this problem
and begin analyzing it by yourself
deciding what words were really important to help you solve the problem,
Well now I want you to work in your groups.
- When we're working in groups,
what do you all use to speak with each other?
- Talking chips.
- You use your talking chips. So let's take our talking chips out.
Do you guys have enough over there? Okay,
good. Okay,
do we all have our talking chips? No?
You're getting them? All right.
Okay. Let me get your attention again.
Amaya, are you with me?
All right, so you're going to use your talking chips
to share,
you're all with me group?
You're going to share your thoughts with your group
because you could've underlined a word that was
important that maybe someone else missed,
okay.
- You're going to use your talking chips,
and you're going to begin sharing the words that you underlined
that you think will help attack this problem.
All right, I'll give you about two to three minutes to do
this with your group.
Ms. Nacarado and myself will come around to hear what you're
saying to each other.
Begin.
I underlined hexagon-shaped tables because
this will shape the tables.
How many in all can sit around a row of tables?
Okay, what did you underline?
What did you underline? Okay,
all right. What do you know about hexagons?
They have six sides.
Good. So is that something you think is important to solve this?
Is that something everybody could use?
All right, you might want to take your notes
on the side of your paper to remind yourself of that.
That's good. All right,
keep going.
- I underlined hexagon-shaped tables
so I'll know what shape is the table.
- Okay. Can you pick one and tell them why you underlined it?
Why did you think that was important?
- I picked one because it's a different shape than the others.
- Oh, so you're going to see some differences.
Okay. Keep going,
good.
Hexagons are arranged in rows.
Why is knowing the hexagon, why is that important?
- Because so you know what side it is.
- Yes. How many people can sit at the table,
right?
- I underlined hexagon-shaped tables,
and then I underlined row of tables,
and then I underlined edges touching,
and then I underlined hexagons,
and then I underlined hexagons are arranged and rows of different shapes.
- You have about 10 more seconds. Okay,
what did you underline? Did you sort of underline the same thing?
- Yes, ma'am.
- Oh, okay.
Andrew, you already--okay.
Yeah, you do know where I told you Mr.
Padgett was wrong. Clap two times.
Clap two times. Half clap.
Oh. All right.
We've had some private think time to begin to do what to the problem?
- Breaking apart.
- Breaking it apart and making it make sense to us,
and you've also had some time to sort of talk to your group
and begin to tell,
this is what I underlined and why you are sharing ideas.
Thumbs up if you found some important math words
or some important information that you know
you can use to begin solving this problem.
Okay, all right.
Now put your hands down. Well now,
you're going to get the opportunity to use it, okay?
So we're going to go back over the problem again. Mrs.
Williams will read it again. Is that clear?
Can you guys see that?
- Yes.
- All right. Mr.
Padgett, he's having a program in the library
and he wants to invite our parents up.
He's bought some tables and they're in the shape of a hexagon.
And he needs to know how many parents can sit
around a table if their edges are touching.
And I know noticed a lot of you underlined the word edges.
The top surface of each table is a hexagon
and the hexagons are arranged in rows of different patterns.
I also heard you all pointing out how the rows were different what?
- Shapes.
- They were different shapes, very good.
All right, so now,
this is all Ms. Williams is going to give you
because you all are the smart ones.
I'm giving you a table, all right?
Take a moment to look at your table
and the information that I've provide you with.
If you have any questions about that table raise your hand.
Do you have a question about the table?
Yes.
- If it's like a hexagon, only six parents can sit at it?
- I don't know. That's what you're going to figure out for me,
but it sounds like your thinking is in the right way. Okay,
yes, ma'am.
Oh, you all said some great things.
She said, "Well,
wow, Mrs.
Williams, does this have anything to do with input and output?"
Well, guess what,
you are going to tell me. This is all I'm going to give you.
You're going to decide how you would go about finding out--
I have given you how many tables in a row.
What are you going to have to find out?
- The number of parents in each row.
- You're going to find out the number of parents in each row.
And I've heard some really good things.
I've heard some people say,
"This reminds me of input and output"
because we've done some of that before, right?
I've heard some people say, "Ooh,
Ms. Williams,
it's a pattern. I might have patterns." Well,
I want you to decide.
You're going to decide individually and as a group
what you would do to figure out the number of parents in each row.
- Let's look down at the bottom. Let's read this together.
- What is the rules for the table?
- After you figure out the number of parents,
who can sit in each row of table
we know that it follows something and you're going to decide
well what rule did you have to use to figure out
the number of parents of each row.
So at this time, the captains,
let's put our toolbox on the edge of the tables. Okay,
also make sure you have your red and green circles. All right,
who thinks they're ready to begin solving? Who thinks they can help Mr.
Padgett with this problem?
- All right.
So I'm going to allow you all to work together in groups
and you're going to be in teams on the side.
I'll pause one second before you get started, okay?
Make sure you get all of my instruction from me. Now,
you decide what you need to use.
You don't have to say, "Well,
Mrs. Williams,
can I get the markers?" or "Mrs. Williams,
can I get this?"
You're going to decide what you need to solve this problem, all right?
We're just going to be respectful of each other.
- We are going to get the things that's needed and remember,
I want to hear you talking so as I'm coming around,
Ms. Nacarado we may be asking you some leading questions,
but you're going to do the thinking. And notice I didn't say,
"Yes you're going to need this"
because you're going to decide individually and as a group.
Okay. Are there any questions about your task?
- No, ma'am.
All right, you may begin.