https:/.../Modeling_polynomials_video_lesson_part_1B.mp4

>> Okay. Will you please turn
to your partner and share

your original thinking?

We may come back and revise this
after we do some data collection.

Please turn to your partner and
share your original thinking.

>> I said, “I think the one-cut will maximize
volume of the box because

it will still have a big size,
and it'll only be cut by one square

rather than one or more.”

>> Mine is actually kind of similar,
because I think one cut will minimize

the volume of the box because
it reduces the box size and shape.

>> All right.

>> And you only take off, like, this much.
>> I know what you mean.

>> You know what I mean?
>> So, you can cut the two out right here

on each side,
and then how tall it would be,

and how wide it would be?
You get more.

>> Yeah. Since you're taking out less,
it would, like, have more.

>> Yeah. I know what you mean.
>> Yeah. You know what I'm saying.

>> I mean, I said the
five would, because you take out --

you pretty much take out five units,
and it would be kind of taller.

Know what I mean?
>> Mm-hmm (affirmative)

>> It would be so it could hold more.
That's what I was thinking.

Or like the same width.
>> Okay.

>> Okay, please wrap up those
initial ideas. And I want to remind you,

these are just our
initial ideas.

We have not gathered any data yet.
I want to clarify two things.

One thing is a student asked me,
What did I mean by a size cut?

So, I should have said this
before, if I cut out a square

like this, I'm going to call this
a four-centimeter cut.

Why is it centimeters?
Because we're using centimeter paper.

Okay, so the cut for the square
is a four-centimeter cut.

The second question that I had was,
What did I mean by, "What type of model?"

And so over the past couple of days,
we've been looking at data sets and

using different regression
curves to fit those data sets.

We've looked at a linear model,
we've looked at a quadratic model,

and we’ve looked at a cubic model.
So, that was what I was intending there.

Again, these are our initial thoughts.
Thank you for doing that,

sharing with your partners.

I should have also said that you
may have a camera, like, just

very close on your face, so
I don't want you to be

too startled by that.
We're really trying to capture

what you're saying and what you're doing.
Like if you're pointing at something

or if you're, like,
turning your paper,

even just, "How are students
interacting around this?"

Okay. So, you guys are great.

Thanks for being good sports.
Okay, cool. So, you know what,

we are going to go ahead
and, um — actually,

I'd like to hear, maybe, two
students who would share their

original conjecture with
all of us.

>> I thought of a four-by-four, so I can get

the middle to be wide, but
the size to also be tall.

>> Good. Thank you. Thank you
so much. Alexander.

>> And I said a nine-by-nine
because it's, like, directly half —

or almost directly half of
nineteen, so then you could

use that to spread out the
whole thing, and you have,

like, a big middle base and
then you also have, like,

a wide spread.
>> A wide spread.

Can you say another sentence
about the wide spread please?

>> Like the wide spread on the grid.
So it's like it'd be nine over instead of

just, like, small conjectures.

So then there's longer volume,
a longer base.

>> Thank you. One more.
Thanks. Vincent.

>> I think the one-centimeter cut

will maximize the volume of the box
because we're just

getting rid of four boxes total.

>> Wow. So I just heard
a four-centimeter cut

is going to maximize,

a nine-centimeter cut will maximize
the volume, and a one-centimeter cut.