(upbeat music) - Good morning, my magnificent mathematicians.

I am super excited to be with you this morning.

We're going to have so much fun today learning more about math and growing our brains.

And today, I have two of my incredible kiddos with me.

This is Hayden, and this is Halley, and they're going to help us out today as we investigate perimeter and area.

Now, perimeter is the distance around a shape, and area is the amount of space within a shape.

Let's take a look over at our board.

We've got a good example over here.

So, we've got a rectangle drawn for us, and this is a 2D shape.

That means it has two dimensions.

The first dimension is its width, and the second dimension is its length.

Our rectangle has 16 inches of width, and it has 21 inches of length.

So, to calculate perimeter, we need to think about the outside border of our rectangle.

Kind of like it's a sidewalk.

So, if we were to walk around the perimeter of the rectangle, how far would we walk?

Let's go take a walk.

If we started here, we would walk 16 inches.

And we'll turn that corner and walk 21 inches.

Then we'll turn another corner, 16 more inches, and we'll finish it out with 21 inches.

So to do the math for perimeter you need to add all those numbers together.

So, 16 plus 21 plus 16 plus 21, that gives us 74 inches.

Great job.

Now, let's think about the space inside the rectangle.

Sometimes it helps to think about area kind of like kitchen tiles on a floor.

Since this rectangle is only measured in inches, though, our measurement for area will be in little bitty tiles that are one-inch squares.

That way you can find the area of a rectangle or how many one inch squares it would take to cover the entire area.

And to do that we'll use this formula, area equals length times width.

Okay.

But before I use the formula and get the answer, we're going to investigate the truth of that formula.

So, we have a bunch of one-inch square tiles.

They're actually stickers, and Hayden and Halley are going to tile this entire rectangle.

We're imagining that it's their kitchen, okay?

And the kitchen floor needs new tile.

All right, you all.

How many one inch square tiles do you estimate you would need to go to the hardware store and buy to fill the space inside your kitchen floor?

- I'm guessing there's going to be about 300.

- About 300, okay.

Halley how many do you think?

- No way, definitely 130.

- 130.

Okay.

So, let's switch out.

You all get started, and I'm going to see if the formula for our area gives us the same answer.

Okay.

So, we find the area of a rectangle by multiplying its length times its width.

And our rectangle that represents the kitchen has a length of 21, and it has a width of 16.

Let's plug those numbers into our formula.

We said area equals length times width.

So, I'm going to multiply 21 times 16.

Okay.

So, first let's multiply the six by the 21.

6 times 1 is 6.

2 times 6 is 12.

So, I'm going to write down my 2, and then 1 goes in the 100s place.

Okay.

On the next line we need to put our 0 in for a placeholder.

And now the 1 gets multiplied by the 21.

1 times 1 is 1.

1 times 2 is 2.

So, I have two partial products, 126 and 210.

We need to add those together.

6 plus 0 is 6.

2 plus 1 is 3.

And 1 plus 2 is 3.

That gives me a total of 336 tiles.

Okay.

Let's head over to the board, and see how Hayden and Halley are doing.

How's it coming, guys?

- Hope your formula works 'cause this could take forever.

- Yeah, mom, there's no way we can finish this before Rise and Shine is over.

- I think you're probably right.

It's okay, though.

I think I might have a magic trick up my sleeves.

Let's snap on three.

So, all count to three and we'll snap, and maybe the magic board here will do the tiling for you 'cause I do think you need some help.

Okay, let's try it.

One, two, three.

(laser beeping) - Whoa.

- Awesome.

(Mom laughing) - I'm so thankful that worked.

- Yeah.

- Okay.

So, let's check your number of tiles with the answer that I got using the formula.

- We got 336 tiles.

- Awesome.

That's the answer that I got too.

- Yeah.

Halley, your estimate was way off.

- Okay, yours was too.

And it would look way too weird.

- Okay, you all knock it off, knock it off.

You both did an amazing job.

And this really helps us understand how great it is that the area formula works.

Tiling can get us the same answer, but who wants to do 336 tiles?

- Not me.

- Not me, either.

- How could this help us in the real world with different situations.

Think about things that you tile.

So, it could be the floor at your home.

It could be your roof, maybe the back splash wall in the kitchen or even concrete squares that you could use outside to build a patio.

Now, you could waste a lot of money if you didn't know exactly how many tiles or shingles or concrete squares to buy.

Using the area formula tells you exactly how many tiles it will take to cover that entire inside space.

You all, great job today.

Remember, the difference between perimeter and area is that perimeter is the distance around a shape, like you're taking a walk.

Area is like tiling.

It's that space inside the shape.

Hayden and Halley, thank you again for your help today.

And thank you for joining me this morning.

I hope you have an amazing day, and I'll see you next time on Rise and Shine.