- Hi mathematicians.

My name is Mrs.

Casalunovo.

I'm a fourth grade math teacher at West End Elementary School in Woodbury, New Jersey.

Today, me and my helpers are here to teach you about area and perimeter.

And we're gonna use a toy that we have at home and play with it a lot.

We're gonna start and end this video with some Legos.

So this is Tayla, she's seven, and this is Jessica she's five.

And what we're gonna show you is that if I give you a certain area, you can make rectangles of all different sizes.

So girls, we're gonna make rectangles with an area of 30 inches and each one of these is one inch.

All right.

So we're gonna work on that for a little bit.

You're gonna need a paper and a pencil for some of the work that we're gonna do shortly.

And then we'll check back on these Legos and see how they're working.

We're also gonna do a little fun break between each of the math problems to make sure you're ready to get us a minute.

So the first thing we're gonna talk about is perimeter.

So perimeter is the distance all the way around a shape.

So for example, I drew a rectangle and I gave it a length of eight inches and a width of three inches.

And since it's a rectangle, the two opposite sides are the same size.

So in order to find the distance all the way around the outside, I added eight inches plus eight inches plus three inches plus three inches.

So the total perimeter of the sheet is 22 inches.

So for a little bit, we're gonna work on perimeter.

So we're gonna go all the way around the shape.

I'm ready to save this up here to refer to later.

All right, so you're gonna need your pencil and paper ready.

I'm gonna do some examples.

So the first one is gonna be a square.

So the square has different properties than the rectangle that I showed you earlier.

If I tell you that the length of this square is eight meters, you are able to find the perimeter without knowing the width.

Do you know why?

That's because the square has all four sides of equal length.

So if I know that the length is eight, I also know that the width is eight, so in order to find perimeter, I'm gonna add up all the sides.

So eight meters plus eight meters plus eight meters plus eight meters.

How many total meters is the perimeter of this square?

32 meters.

Good job.

All right.

So I think we should do 32 jumping jacks to celebrate.

What do you think?

All right, here we go.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32.

Woo!

Okay, let's try another one.

So this time you don't, you can find primary of any shape so far, we've done a rectangle and the example, and we just did a square, this time I'm gonna do a pentagon.

Do you know how many sides the pentagon has?

It has five.

So you wanna draw a pentagon.

One, two, three, four, five sides.

And I'm gonna tell you that these two sides are both three inches and the bottom is eight inches.

And the two sides are both five inches.

So remember our perimeter is the distance around the entire shape.

And we get that by adding up all of the length all the way around this shape.

So for this one, We would do three inches, plus three inches plus five inches plus five inches plus eight inches.

How many total inches would that give us?

So three plus three is six, five plus five is 10, add the eight inch, six plus 10 is 16 plus another eight is 24.

So the total perimeter of the pentagon is 24 inches.

All right, this one, we're gonna hold a plank for 24 seconds.

Okay, here we go.

On your elbows and up, up your knees, 24 seconds.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24.

- So, for our next perimeter problem, we're gonna be looking at a word problem.

And a word problem is a way for us to know about how math is used in the real world.

So, in our word problem, we have Alex, who bought some fence for his yard.

So we want it to go all the way around his yard, right?

So he bought 50 feet of fence.

So he thought that was enough.

And the he came home, and he wanted to make sure it was enough before he started.

So, he wants to fence his whole yard.

Did he buy enough fence?

Okay.

So in order to solve this one, we have some information: we know that he bought 50 feet of fence.

But we don't know about his yard yet, so I'm gonna draw and label a picture of his yard.

So his yard is a rectangle shape with a length of 15 feet and a width of 12 feet.

Okay?

So remember, he bought 50 feet of fence, and he wants the fence to go all the way around his entire yard.

If he bought 50 feet, is that enough?

Think back to how we solved for perimeter before.

Okay?

Take a minute and look at the length and the width that Alex has in his back yard, and how could we see what his perimeter is, and then decide if he has enough.

Okay.

So we know that if this length is 15, that this length is also 15 feet.

And if this width is 12, this width is also 12 feet.

So, again, in order to go all the way around, we want 15 plus 12 plus 15 plus 12.

And that will tell us the perimeter of his yard.

Hopefully, 50 feet is enough.

Take a minute and solve.

Okay, what did ya get?

So, 15 plus 12 will give us 27 feet for this part of the yard, and then this part of the yard will also be 27 feet.

So in order to find the whole yard, we wanna add up 27 feet plus 27 feet.

And that gives us 54 feet.

So the perimeter of his yard is 54 feet all the way around.

If he bought 50 feet of fence, did he buy enough?

No, Alex, so close!

You're four feet short.

So, if he bought 50 feet, he would get 15 and 12 and 15, and then he'd only get here to eight feet.

He needs four more feet in order to get to the full 12 feet.

So the perimeter is 54.

50 is not enough.

Sorry, Ale-- Alright, we got 54.

So we're gonna skip 54 times.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54.

Okay.

So we've done a couple of perimeter problems and we're gonna continue, but we're gonna using number lists or problems.

So that means it doesn't have any numbers in it at least to start.

Here's the first part of my problem.

Mrs.

Casalunovo is building a rectangular pool.

The perimeter of the pool is some number of feet, so no numbers, but there is something that I know from reading this problem.

So what I want you to do is we're gonna do a notice and a wonder.

So you split your paper in half, half of it is notice.

And half of it is wonder.

I know this is something that you see or notice from the problem.

It's a statement.

It's something that it ends with an a period.

A wonder is a question you have after reading the first part of this problem.

So something you're still wondering.

So one more time, Mrs.

Casalunovo is building a rectangular pool.

The perimeter of the pool is some number of feet, right down one thing you notice, and one thing you wonder Okay.

So here are some things that you could have put, you could have noticed that I put myself in the problem.

That's very exciting.

And you could know somebody in pool also could be very exciting.

But math wise, you could have noticed that I'm building a rectangular pool.

So even though it's not a number, it is kind of a clue.

So, there is what I know so far, that my pool is rectangular.

I don't know some of the things I wonder, right?

The problem is that the perimeter of the fullest pool is some amount of feet.

I wonder how many feet it is.

I could also wonder what the size of the pool are, because I don't know that yet.

So I'm still wondering, is it a large rectangular pool, is it a small rectangular pool, but did you notice, I do know that it's a rectangle.

All right.

So I'm gonna give you a little more information and I want you to write down something you notice and something you wonder.

Mrs.

Casalunovo is building a triangular pool.

The perimeter of the pool is 112 feet, right down something you notice and something you wonder.

Okay.

So you could have noticed that now I know how much the perimeter is.

The perimeter is 112 feet.

So that could be unnoticed.

I now know that the perimeter is 112 feet.

Is there anything that you're still wondering?

Looking at my picture, I know it's a rectangle and I know the perimeter is 112 feet, but I'm still wondering about the sides, right?

So what does this rectangle looks like whose perimeter is 112 feet?

I don't know yet, because I'm still wondering what are the sides?

All right.

So last one, Mrs.

Casalunovo is building a rectangular pool.

The perimeter of the pool is 112 feet.

The length of the pool is 32 feet.

What is the width?

So, we notice that is a rectangular pool.

The perimeter is 112 feet, but now we have answered our wonder from the last time, which is I need one of those sides, right?

In order to figure out the perimeter.

So I gave you the length.

The length is 32 feet.

What is the width?

So when all the other ones and all the other problems that we did, we knew the two sides, and we had to figure out the perimeter.

But this time we know the perimeter and we know one of the size is 32 feet.

And I need to figure out the other side.

I'm gonna call this side X. X is a variable.

A variable is just a more fourth-grade way of saying, I don't know yet.

Okay.

So instead of saying question Mark, I'm not sure what that site is yet.

I'm gonna solve for it.

You can call it any letter, but X is a very typical mass letter for a variable.

So X is decide that we don't know yet.

It's answering the question, what is the width?

Alright, so I know perimeter is the all the size added up, and I know that this side is 32 feet.

And I also know that our pool is a rectangle.

So which should be our first step?

It's a rectangle.

We did one of these before, right?

A rectangle has opposite sides of the same size.

So if this is 32 feet, that means this is 32 feet.

Okay.

So that's helpful, if this side is X, this side is also X, not that helpful yet because we still don't know what X is.

All right.

And in order to find perimeter, we add up all the sides.

So I know two of the sides are 32 feet plus 32 feet, plus X plus X, two missing sides.

And I know altogether is 112 feet.

So because I already know the answer and I don't know one of the sides, I don't know the size of both of the width.

I have to work a little backwards.

So what I would like to do is add up all the sides and get the area, the perimeter.

But since I already know the perimeter, I'm gonna add up what I already know.

So off to the side, I know that the two known sides are 32 and 32.

So, so far I know that this part and this part of my pool is 64 feet.

And I know that I need some more and some more, and that gives me 112 feet.

So I told you I have to work backwards.

So for adding, we want to do the inverse or the opposite of that.

So the opposite of adding would be subtracting.

So I'm gonna subtract what I already know the total perimeter from what I already figured out, how much I have from the two lengths, which is 64.

So 112 feet minus 64 feet.

So I can do two minus four, right?

Then come over here and make them zero.

And I bring that to a 12, so minus four is eight.

Then I can't do zero minus six.

And the tens place I need to make that a 10.

And I borrow from over here.

And 10 minus six is four.

So that means, if 64 plus 48 equals 112.

So does that mean that X equals 48?

X does not equal 48 because I have two Xs here and both Xs together equal the 48.

So how could I figure out just one X, if I know both Xs together equal 48?

I could devise.

So I know that there are two sides and together they equal 48.

And this split equally because this side and this side are the same.

So this four is worth 40.

And I think about how many times two can go into 40 and they can go in 20 times because two times 20 Is 40.

I subtract, and that leaves me with eight.

Two can go into eight, how many times?

Four, because two times four is eight and no remainder.

And my potion is 24.

So that means that one of these Xs is 24 because over here and this other X would also be 24.

And now if I do that 64 plus 24 plus 24, which is 48, Equals 112 feet.

So the answer to my question of what is its width?

The width of the pool is 24 feet.

I remember we started off with no numbers at all.

We just started off with what we knew.

We knew was a rectangle.

We wanted some more information.

We wanted those numbers, right?

So then we've got the perimeter.

The perimeter was 112 feet.

So we got that.

But then we needed to know the size.

And we figured out we were given a one side and we had to work backwards a little bit.

We had to use some subtraction and we had to use some division, Oh, Nora, to figure out the missing side, which was 24 feet.

Okay, to celebrate.

We're going to do 24 crowd box.

So up on your crabs, here we go.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, Start again.

13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24.

Good job.

So we're gonna continue on with perimeter.

This is gonna be our last perimeter before we move on to area.

And this one has many different answers.

So once I show it to you and I put it up here, if you're able to come up with one very quickly, try and come up with something else, there's more than one way to get this correct.

So, here's your test.

Draw and label a quadrilateral with a perimeter of 24 centimeters.

Okay.

And the reason why this one has so many different correct answers is that this word, quadrilateral here, we haven't used that yet, but we did do some quadrilaterals.

What is a quadrilateral?

It's a four sided shape.

Good.

So not our pentagon that we did earlier.

That was five sides, but our squares or rectangles.

And maybe you can come up with some other quadrilaterals.

So a quadrilateral, whose perimeter is 24 centimeters.

So think about what kind of shapes you could do that have four sides and all the sides when you add them up, equal 24 centimeters.

All right.

Get those papers and pencils, right?

Let me see how many you can do.

(silence) Okay.

So I came up with a couple of examples.

These are not the only correct answers.

But first I started with a rectangle.

So we are gonna draw another rectangle.

I know the perimeter needs to be 24 centimeters.

So I came up with a long skinny rectangle.

So this side is 10 and this side is two.

Okay.

Let's check it.

10 plus 10 plus two plus two, 20, four, 24.

All right.

Next I thought about if I could do with this square, remember we had a square all the way in the beginning, right?

A square has a different property than a rectangle.

So a square, I also wanted the perimeter to be 24 centimeters.

But in a square the sides have to be the same.

So I needed to think about what number could I use four times since it had to be a quadrilateral four sides that gets me to 24 centimeters.

And that will be six because six plus six plus six plus six equals 24.

Alright.

So then I was thinking, did a lot of rectangles and squares.

Is there any other quadrilaterals that I could do?

And I came up with two, we haven't used yet.

So first is this shape.

Do you know what that shape is?

It's similar to a square and that all the sides are the same, but it doesn't have right angles, like a square does.

It has to have a few angles and two have two singles and it's called a rhombus.

But, since a rhombus is similar to the square and that all the sizes, same, I can do the same thing that I did for the square, which is I can make all sides be six centimeters because six plus six plus six plus six.

Lastly, I was really trying to think out of the box.

And I thought this shape.

Did anybody use this shape?

It's a trapezoid.

In a trapezoid, you have two sides that are parallel and two sides that are not.

So I came up with these measurements.

This could be four centimeters.

This could be eight centimeters.

And the two sides could be six centimeters.

Four plus eight is 12 and six plus six is 12 and 12 plus 12 gives us 24.

So those are just four different quadrilaterals whose perimeter is 24.

Good job.

Okay.

So we've learned a lot about perimeter, which remember is the outside of a shape, but now we're gonna move on to area.

So area is the amount of space inside of the shape.

So I have a rectangle here and I labeled one side with eight inches.

And one side with three inches.

But this time I filled in the shape.

So there's my three and here's my eight and if I were to count up all the box, eight an eight an eight which is eight times three I get 24 inches.

So in order to find the area, which is the amount inside of a shape, I multiply the length times the width.

Okay.

So we're gonna do some examples.

So you get your paper and pencil ready.

And we're gonna start with a rectangle.

The length is 10 centimeters and the width is two centimeters.

I wanna find how much is inside.

So I already count all that up.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

I get an area of 20 and a quicker way to do that is multiply length times the width.

So 10 times two equals 20 centimeters where 'cause they did the centimeters and I multiplied them at each other centimeters, Time setting.

Alright.

So we're gonna do 20 hops on our right.

Lets go.

one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

All right, let's see what's that?

Alright, so we're gonna go back to our square that we've worked with a couple of times before in perimeter.

So I'm gonna tell you that this side of the square is five centimeters.

So how could you figure out the length if I don't know how much the other side is?

Right.

Because a square has all sides the same size.

So if this is five, then this is also five.

So five times five equals 25 centimeters squared.

So the area to that square is 25 centimeters squared.

Alright, now we're getting our right foot ready, right foot hops 25 times, here we go.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.

Pencils and papers ready?

Now I have this shape for you and I wanna know what is the area of this shape if it was my garden?

Okay.

Area is length times width.

But I have a couple of different length and a couple different widths and a couple of sides that aren't even labeled.

So let me take this up here and then I'm gonna draw a little bigger for us to work on.

There is my garden.

And here's what it looks like.

So it's not, so it looks like, does it need to be a perfect rectangle to be a garden?

Right?

Maybe my house is in here and I want the garden to be on the outside.

So if you do eight here, three feet and 10 feet.

Okay.

So, so far all I did was just transfer over what I originally know.

So I said that there was a couple sides that weren't even labeled and I need to make sure I know what those sides are.

So one of those sides is over here.

So I'm gonna call that X, right?

Because I don't know what that is yet.

And I also have this side not labeled.

I don't wanna call that X like I did last time when I use my variable, because last time I had an X and an unknown and it was the same number, X plus X, but I have to know that this is the same number.

It doesn't have to be, it's on the other side of a rectangle.

So I'm gonna call this Y. It's just another question Mark.

It just means I need to solve for this side and you decide for this side and I don't wanna give them the same variable because they might not be the same number.

Okay, so let's do X first.

So X is a vertical line is going up and down.

Do you see any other vertical lines in the shape?

They're gonna be helpful for us.

All right.

So I see an eight feet over here.

Do you see any other vertical lines?

I see a six feet over here.

All right, so we're gonna use those to help us out.

Figure out the other vertical side.

So I know that the whole left vertical side is eight feet, okay?

So if I were to make a, if I would have finished this rectangle and draw the all the way down, the whole side would be eight feet but I already have this part which is six feet.

So that means all I really have left to go would be this much.

This is six, this is my X. And altogether it's eight.

So what is this missing side?

And it'll be the same on both sides.

Great.

It's two, because I knew the whole side was eight and I knew this piece was six.

So that means it's missing piece is two because two plus six equals eight.

So since Y is horizontal, I need to find the other horizontal sides that I know to help me find Y the unknown horizontal side.

So I know this whole horizontal bottom is 10 feet, and I know this top part is three feet.

So the Y is this missing piece over here.

If I know the whole thing is 10 feet and this piece is three feet, how much is this piece?

Which is the same as this piece here.

Think about what we did last time with the X, we want to start with the whole bottom 10 and we want to subtract the piece.

We already know, three and that gives us seven.

So this side, Y is seven feet.

All right, so now that we figured out all of the sides, we could figure out the perimeter.

So let's take a quick moment and do that, right.

The perimeter is all the sides.

So we have eight feet plus 10 feet, plus two feet.

We didn't have that before.

We solved for that, plus seven feet.

Also we didn't have before and now you do, six feet and three feet.

Okay, take a moment and figure out the perimeter for the shape.

So eight plus 10 is 18 plus two more is 20 plus seven more is 27, plus six more is 33 and plus the last three is 36.

So side note, perimeter for this garden is 36 feet.

Okay, so let's get back to the original question, which is what is the area?

So area is length times width.

So when we're doing length times width of area, we need to have a rectangle.

And right now we don't have a rectangle.

But look at where I drew this line here when I was using it to help me find the two.

Made a rectangle here and then I made a different rectangle here.

So if I used this to draw a line here, can you see how to mean two rectangles?

So now that I have two rectangles, I could figure out the area of this rectangle and then the area of this rectangle.

And again, how could figure out the area of the garden?

I could add up both of the areas.

All right, so we're looking at this rectangle first.

What is its length?

Eight feet.

what is its width?

Three feet.

So the area of this rectangle is, 24 feet.

All right, now we're gonna do this rectangle.

What is its length?

Remember it's not 10 anymore, it's just this piece which we called seven.

What is it's width?

Two.

So the area for this rectangle is, to find the total area of this shape.

I'm gonna add this together.

So, the area for my garden is 38 feet.

Good job.

Alright, we are going to do 38 arm stretches because we're coming to the home stretch here.

We need to stretch it out before we're done.

Alright.

Stretch your arm.

One, two, three, four, five, six, seven, eight, nine, 10, switch, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

All right, behind my head.

21, 22, 23, 24, 25, 26, 27, switch, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, whew!

All right.

Arms are stretched out.

Here we go.

So we're gonna do another numberless word problem.

So last time when we did that, we started off with a notice and a wonder, someone chooses to take your paper and split it in half.

Because remember I'm gonna give you a word problem, but it's not gonna have any numbers in it.

So we're gonna think about things that we notice.

That's a statement with a period, things that we see in the problem.

And then a wonder is something we're wondering.

So a question, something that we need more information for in order to stop it.

Here we go.

Mr Edmond would like to buy some rugs.

Write down one thing you notice and one thing you wonder Okay.

So we notice that Mr.

Edmond wants to buy some rugs.

We are probably wondering how many rugs, we may be run during the size of the rugs.

Right?

'Cause we're dealing with the size of things.

We might be wondering, are we trying to find the perimeter of the rugs or the area of the rugs?

There's probably a lot you're wondering.

Alright, so here's some more information.

Mr Edmond would like to buy two rugs, a blue rug and a green rug.

For example, one thing you notice and one thing you wonder.

So maybe you know this that he likes blue and green because he wants a blue and green rug.

We definitely now notice that he wants two rugs.

So there was our first number.

We might wonder why he wants a blue rug and a green rug.

We might still be wondering about the sizes and we still might be wondering if we're trying to find an area perimeter.

All right, but we know, two rugs.

Okay, here's what we have now.

Mr Edmond would like to buy two rugs, a blue rug, and a green rug.

The length of the blue rug is four feet and the length of the green is double that.

What do you notice?

What do you wonder?

So he might notice that.

Now we have another number.

We know that there's two rugs and we know the length of one of those rugs.

So the length of the blue rug is four feet.

And we know that there's a green rug and we know the length of the green rug is double that.

That gives us a clue.

What does it mean that the length of the green rug is double the length of the blue rug?

Double is a math word that tells us that we're gonna take the number and multiply it by two.

So four and then four again, so four plus four or four times two means that the length of the green rug is four feet.

Okay, so you know there's two rugs.

The length of the blue rug is four feet and the green rug has a length double that.

Mr.

Edmond would like to buy two rugs, a blue rug, and a green rug.

The length of the blue rug is four feet and the length of the green rug is double that.

The width of the trunk is four feet.

So we may know this, that we have a length for each rug and now we have a width for each rug.

So the width for each rug is four feet.

We may still be wondering if we're trying to find the area or perimeter or what the question is in the problem, but bit by bit, look what we have now.

You know there's a blue rug who has a length of four feet and a width of four feet and a green rug who has the length of eight feet and a width of four feet.

Try this one.

Mr.

Edmond would like to buy two rugs, a blue rug and a green rug.

The length of the blue rug is four feet and the length of the green rug is double that.

The width of each rug is four feet.

What is the total area for both rugs?

That we thought we were gonna do?

All right, so a little area for both rugs.

Okay, so, we want the area for blue rug and the area for the green rug.

And we want the total area.

Okay, what do you got?

All right.

For the blue rug we find area by multiplying the length times the width.

So the area for the blue rug would be four times four which means 16 feet squared.

For the blue rug.

For the green rug it's eight times four so it's 32 feet squared.

And to find the total amount of area, we're gonna take the blue rug and add in the rug and we have a total unknown inside both rugs, of 48 feet squared.

All alright, so we shut your arms.

We're gonna stretch our legs for 48.

Here we go, right leg.

One, two, three, four, five, six, seven, eight, nine, 10, switch.

11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

And we're gonna bend down alone.

21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

We're gonna cross, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, and cross the other way.

41, 42, 43, 44, 45, 46, 47, 48.

All right, mathematician.

I had two final challenges for you.

Alright.

For the first one, you're gonna draw two rectangles with the same area, but different perimeter.

Draw two rectangles that had the same inside space but different perimeters.

(silence) Alright, I'm gonna show you what I came up with, but it's certainly not the only example.

Two rectangles with the same area but different perimeter.

So I came up with, I was thinking of my multiplication facts and I was thinking of a number that has multiple factors, so a number where I can get to it multiple times and 24 is a good one.

So that's what I picked.

So then I need one side be six feet and the measurement unit can be anything.

If you notice, I've used feet and centimeters and inches.

It's just whatever you're measuring by.

And I want it to get in 24 area.

So then the other side needs to be four and I picked 24 because I knew there was another way to get 24.

Write eight feet by three feet and that area is again eight times three is 24 feet.

So both have the same area of 24 feet squared, but I need to make sure they had different perimeters.

So let's check.

This one here is gonna be six plus four, plus six plus four.

Six plus four is 10.

Six plus four is 10, and 10 plus 10 is 20.

So the perimeter for my first shape is 20 feet.

Now my next one is gonna be, eight plus three plus eight plus three, eight plus three is 11, eight plus three is 11 and that gives me a perimeter of 22 feet.

So I did it.

Did you do it?

I have two rectangles that have the same area but different perimeter.

Okay, next.

You're gonna come up with two rectangles with the same perimeter, but different area, same perimeter going around the outside.

But the areas inside are different.

Okay.

Again, there are many different options of rectangles that have same perimeter but different areas.

Here's what I came up with.

I first drew a rectangle and I called it 10, will do meters and five meters.

And because it's perimeter, I need all the sides, so I know this side is also 10 meters and this side is also five meters.

So the perimeter is 10 plus five plus 10 plus five, 15, 15, and 15 plus 15 equals 30.

So this shape has a perimeter of 30 meters.

So I needed another rectangle that also equal 30 but so I thought about different ways that I could equal 15 because you really only need one length and one width and then you're just gonna double it.

So I thought of eight meters and seven meters, because I know eight plus seven is 15 so then if I have another eight and seven I'll have eight plus seven which is 15 and another eight plus seven which is 15 and 15 plus 15 equals 30 meters.

So they both have the same perimeter.

Now we have to check and make sure they have different areas.

So area is gonna be length times width.

So the area for my first rectangle, 10 times five is 15 meters square.

And the area for my second rectangle, it's gonna be eight times seven which is 56 meters square.

So I counted two rectangles that had the same perimeter, 30 meters and different areas, 50 meters squared and 56 meters squared.

I know there's lots of options.

I hope you did a great job.

Hello again mathematicians, we are at the end.

Ready to recap.

So today we learned about area and perimeter.

Perimeter is the outside of a shape and you get the perimeter by adding up all the sides.

Area is the inside of a shape and you get that by multiplying the length times the width.

So we each, if you remember back at the beginning, use our Legos to make a rectangle with an area of 30 inches and each square being an inch.

So Jessica, how many are going across?

- Five.

- And how many are going down?

- Six.

- So five times six equals 30.

So she made a rectangle that is 30 inches.

Kayla, how much is going across in yours?

- Three.

- And how much is going up and down?

- 10.

- And three times 10 is also 30 inches and mine is 15 across and two up and down.

And 15 times two is 30 so we each made a rectangle with an area of 30 inches squares, and they all look very different.

So area and perimeter is lots of fun.

Continue learning.

Bye.

- Bye.