- All right, so let's go from here and actually kind of transfer
over to how this relates to what we're doing today, okay?
And the first part of it is that we're actually going
to do kind of a review of how simplifying the expressions.
I know that Abby, you haven't done it before and, Coreese,
you haven't used algebra tiles a lot either, have you?
Okay, so the good thing about it,
I got everybody paired up with actually people that have
done it before so that way they can help you figure it out.
Okay?
The first thing is; somebody explain to me
what you do with algebra tiles.
Pull out an algebra tile and tell me what they are
and what they represent?
Come on, raise your hand, let me know.
- Just one?
- Go ahead.
- So this is Y, this is Y squared
and it just fits all around the edges so it makes Y.
- Okay, so basically she said that Y on one side
and Y on the other side so you have this.
This is Y here; this is Y here, okay?
So basically, now we're going to find the area.
How do you find the area?
- You times.
Multiply the sides.
- Multiply the sides, right, good.
So length times width, right?
So then basically on this is Y times Y.
Y times Y is Y squared. Okay?
So that's why this tile piece is Y squared.
Another piece, Anthony, what do you have there?
- X.
- X? Hold it up, let's see what you got.
- One is positive; one is negative.
- Okay, which one's positive, which one's negative?
- Blue's positive; red's negative.
- Okay. All right, good.
Thank you.
And we got another one from Lamarius. What do you have?
- A Y squared.
- We already did the Y squared.
You piggybacked off it, did you do Y? Yes.
- XY then.
- There we go. All right, good, good.
Flip them around, let's see the colors.
Green is Y I mean, XY.
Now, why is it XY?
Why is it XY?
- I'm just I don't know. I forgot.
It looked like...
- Why is this XY? How did we get Y here?
- You multiplied the two Ys.
- Multiplied the two Ys which is the two what?
- Ys.
- The two sides.
- Yeah, the two sides.
- Okay, all right.
So then what is this here then? What's this telling you?
- Same thing as the one we multiplied the sides.
- Good.
- X and Y.
- X and Y, good.
So that would mean that what, what would be the side lens of this?
- X and Y.
- X and Y, X and Y, good.
So then show me the X tile again,
Anthony. Okay,
wow, so what did you notice?
- One side, it fits on one side.
- Okay.
- Pretty much two sides.
- Does it fit on the top?
- No.
- No. Why?
- Because this side is wide and this one is shorter.
- That one's shorter, the shorter one is the X; the longer one is the Y.
- This one is longer.
- Right, like what Lamarius has,
exactly. Okay,
he did the Y side. Okay,
so we got this one figured out. We got this one.
We got another piece, a couple more pieces that we haven't figured out,
that we haven't discovered. Okay?
Yes. What is that one?
- X squared.
- How is it X squared?
- Because you're multiplying the two sides.
- The two sides.
Coresse, do you see what he's saying? Okay.
Cody, you got it?
Abby, you understand that?
- Yes.
- I like that you're discovering your pieces by looking through them.
That's fine.
And then you have the well, we did X,
XY, Y,
X squared I mean Y squared, excuse me,
and what about these, the small ones?
What do you think?
- Five units?
- Five units, why is it five units?
- Five of these on one of them.
- Yes, and Josh is pointing out that normally we don't use the five units.
- We never do.
- Don't say never but, you know,
we...
- Why today?
- But we haven't been using them, you're right, and the reason
why is that we'd like to use the single unit tiles
instead of using that one, okay?
All right, yes, Anthony, you got a question?
- Is this why like we don't use these because they
don't fit on these, like it doesn't go in one of these?
- No.
The reason why we don't use them because you know how we you'll see
when we start simplifying and splitting;
you can't break those pieces apart.
So if you had to subtract from that five-unit tile
- You had to take all of it away.
- You had to take all of it away
and then bring so you don't have to bring out five unit tiles anyway
or bring out individual unit tiles anyway.
- But seriously, this doesn't fit on any of them.
- It doesn't fit on any, that's a good observation.
Excellent. So you're picking up really quick,
Abby, good.
- But it fit inside of them.
- Inside? What?
- Like
- Elaborate on that a little bit.
- I guess
- Oh wait, I know how.
- But he's saying that you can fit the pieces inside, that's true,
but we don't know what Y squared is worth, right?
But that's a good observation. That's good.
All right, so let's move on to now how do we use the mats.
These right here are equation mats, okay?
Go ahead, explain it.
I'm sorry.
- The equation mats are like these are like the positives
it's like for the plus signs
and these are negatives and then this is like the divide one, right?
And this is the equal like right here, that's equal.
- You're right. So did you get that, Abby?
You get that, Coreese? So what's in the middle?
- The equal.
- Equal, good, good.
And then the positive and we have the negative side, right?
All right, good, good.
So tell me, here,
since you have the mat right there, if I put this equation down, okay?
I'll make it easy for you.
First one, X squared + Y squared + 3X squared.
Remember, do I have an equal sign here? -No.
So am I asking you to solve?
- Simplify.
- Just simplify, good.
So are we doing a simplifying? Everybody look at Amber here.
- Do these go on this side because I get that mixed up sometimes?
- Good question. She's asking,
does she change sides. Now tell me,
you told me what what does that middle mean?
- Equal. Oh, so this all
- There you go.
- Yeah, is that it?
- All right, so what's
- Because there's because you have one X,
here's the one and it's all positive so
- So everybody go ahead and do it at your table.
Work out the same way, do this one on the board.
Hold on, time out just for a second.
Give him a chance to catch up with you.
Everybody got their tiles out? Coreese?
Let Coreese have some of the tiles, too,
that way he can be an active participant. Come on.
Every group is going to have a chance to explain. Are we good?
All right, go ahead, Amber.
- So this is one X squared, so here's your one.
Then plus Y squared so here's this and then your 3X squared
so I'll have three right there. - I get it.
- But none of them are negative so I leave all the color
and I leave them on the positive side.
- Okay. So now,
I want you to, on your expression mat excuse me,
on your expression mat, I want you to write what the new expression is.
On your expression mat, I want you to write what your new expression is.
- Write, what you mean?
- When you're simplifying it.
- With this box?
- Just write. Write down you're going to do a written expression.
You're going to write what this new expression, when you simplify it,
you'll rewrite it, what do you write down here?
Josh, help out your partner.
- We got it. Can I say it because I think I understand it now.
- Okay. Go ahead, Abby, you said you got it.
- Okay.
So you have this one
and then they which one's positive and which one's negative.
- Well, good question.
Which one did you tell, Anthony,
is positive and negative, how did you figure it out?
- Oh, this is positive.
- Why is it positive?
- Because it's purple.
- Because it's purple and what's the negative?
- Red.
- Red. Red,
just think about hot and negative and no, you know,
bad, whatever,
okay?
- And then you have four so 2X and another 2X no, wait.
No, one X and one X is 2X no, wait, what?
- Okay. Keep going,
keep talking.
- And then 3X and I don't know. I don't think that's right.
That's how she explained it.
- Okay, all right.
Somebody help her out. How about Keana?
- 4X, I mean,
four I don't know.
- How many like 4Xs do you have, squares?
- Four.
- So ...
- 4X squares plus ...
- Okay. So she said 4X squared + Y squared.
Okay? So then remember we went back and we said just a quick review,
everybody look up,
that you want to go ahead
and circle if you need to or if you have the tiles,
you bring the like terms together, right?
Remember simplifying, we want to bring like terms together.
So we can circle the X squared, circle the 3X squared and say,
"Well these two come together," right? Right? -Yes, sir.
X squared + 3X squared, is how much?
- Four.
- Four, come on.
- X squared.
- 4X squared. There we go, 4X squared.
Do we have anything else to go with the Y?
-No. -No, plus Y squared.
All we did is simplify, it's that simple,
okay? All right?
Good thing about it,
I gave you some paper towels and you can wipe off your mat.
Let's get started.