>> Hello, mathematicians.

I am so excited to be here with you today.

My name is Mrs.

Correa.

I have been teaching for 17 years for the West New York School District.

Do you know where West New York is?

It's in Northern New Jersey, right across the Hudson River from New York City.

You see?

It's right here.

Did you know that West New York is one of the most densely populated square miles in the United States and worldwide?

Wow.

That means we have a lot of people living in approximately one square mile.

Which brings me to today's lesson.

Today, we're going to be talking all about square units of measurement.

So, what does a square mile mean?

What does a square mile look like?

Today, you're going to learn all about it.

But, first, I want to share a little story with you.

I grew up in West New York, and in West New York, we had a lot of apartment buildings.

I grew up in one of those apartment buildings.

And when I was a little girl, I dreamed of having a flower garden.

But at the time, there was just not enough space for me to have a flower garden in an apartment building.

So when I first moved into my home, I thought, "Wow, this is the perfect place to have that flower garden right here in my side yard."

So I ran out and got some supplies ready to build that garden.

But life got busy.

I started working, and I started taking care of my kids, and I never got a chance to build that flower garden.

So, now that we have been asked to stay home, I thought, "What a perfect time to build that flower garden I always dreamed of as a little girl."

So I found the supplies that I had bought.

I had bought 20 of these.

They're 3 feet each, right, these garden fences.

And I want to finally use them.

So do you think you can help me plan my garden?

What information do you think I'm going to need?

Area and perimeter?

Hmm.

I think you're right.

We can totally do that together.

Mathematicians, you are so smart.

So, for this lesson, you're going to need paper and pencil.

What we're gonna do is I'm going to transition back into my house, and you are going to go grab that paper and pencil.

I'll give you a few -- like 30 seconds, okay?

So, I like to start this class the way I start my class in school.

When I say, "All set," you're going to say, "You bet."

Okay?

So, "All set, you bet."

Ready?

All set?

You bet.

Awesome.

I'm so excited.

See you in 30.

♪♪ ♪♪ ♪♪ Okay, now that you have all your materials ready, let's get started.

Outside, you told me that I would need area and perimeter to help build my garden.

That is correct.

So I figured we'd get started with reviewing what perimeter and what area mean.

Let's start with perimeter.

Let's look at this rectangle.

What can you tell me about this rectangle?

That it has four sides?

Awesome.

That opposite sides are equal.

Very good.

What can you tell me about the perimeter of this rectangle?

That it's the distance around the shape.

Very nice.

And then you add up all the sides.

Very good.

You remember a lot from third grade.

Great work.

Okay, so, let's look at the definition that our vocabulary book tells us.

Here we go.

"Perimeter is a measure of distance around the edge of a figure.

Perimeter is measured in units of length, such as inches, feet, yards, centimeters, meters, et cetera."

Awesome.

You're correct.

So, what if I gave you, then, measurements?

Would you help me find the ca-- Would you help me calculate the perimeter?

Awesome.

So, here we go.

10 inches.

And 7 inches.

The length of this point to this point is 10 inches, and the length from here to here is 7 inches.

Now, you told me opposite sides are equal.

So that means that the distance between this segment is the same as the distance between this segment.

And, likewise, the distance between this length is the same as the distance between this length.

So awesome.

Let's go ahead and calculate the perimeter.

Now, you told me I needed to add up all the sides.

Very good.

Where did that 10 and 7 come from?

That's right.

The opposite sides are equal.

So if this is 10, then this is 10.

And this is 7, then this is 7.

And if we need to calculate all around, then we need to make sure we have four measurements because we have four sides.

Very nice.

So 10 plus 7 is 17.

10 plus 7 is 17.

Here's a double stacked.

17 plus 17 is 34 inches.

Make sure you write the unit of measurement whenever you're solving for perimeter or area.

Is there another way you may have figured it out?

Yes.

Maybe you would have combined the terms that were like together.

Very nice.

So 10 plus 10.

7 plus 7.

Double stacks.

Very nice.

10 plus 10 is 20.

7 plus 7 is 14.

All together, 34 inches.

Great work.

Awesome.

So, here's how you found perimeter.

Thank you for helping me out.

Did you know that perimeter actually has a formula?

Yeah, have you heard of the word "formula" before?

Well, that's okay.

No worries.

I have it right here.

Here's what formula means.

"A formula is a mathematical rule expressed in symbols.

It shows us how things are related to each other."

So, we're going to find that rectangles and, actually, many figures have all sorts of formulas.

There is a formula to find the perimeter of a rectangle and many other shapes.

But, first, let's talk about what does that mean, the word "formula."

See, mathematicians use symbols in math all the time, and all they do is represent something.

So let's look.

What does that digit represent?

Zero.

What does it mean to have zero of something?

Nothing, nada, zilch.

Right?

But instead of writing the word zero, we use this digit.

Other symbols you, I know, are very familiar with... is the operation symbols.

We don't need to write out the word "subtraction."

When we see this symbol, we just know.

You see?

Symbols are everywhere in math.

Some symbols are actual letters like N, X, L, W.

[ Chuckles ] And I know what you're thinking.

"Ms.

Correa, when did the letters get in math?"

Well, don't you worry.

All they mean is that they are variables.

That means that they stand in a place until a value is given to them.

So when we think of a rectangle, we know it has a length and a width, and it uses L and W. Okay?

So, in this particular rectangle, we know what L and W mean, but we may not have known before, so you could have just simply placed an L and a W. And that's what it would have meant.

Length and width.

So, let's try creating a formula, or a rule using symbols, for perimeter.

Okay.

So, mathematicians... instead of writing the word "perimeter" every time, there's an actual symbol for the word "perimeter," see?

And it's a capital P. So we're going to use a capital P. And now what can we say about this perimeter?

We know that there are two lengths.

So instead of writing L plus L, we can actually write it as a multiplication expression.

We can say 2 times L because we know that there's two of them.

And then we can go ahead and add that to the other two measurements, which are known as the width, because there's two of them -- 2 times the 7.

See?

So, here's a formula.

It's a rule that we can use for any rectangle, no matter how big the rectangle or no matter how itsy-bitsy small the rectangle is.

As long as you know its length and you know the width, you can calculate the perimeter using this formula -- if it's any rectangle.

So, let's try it.

We know that P is perimeter.

We have two lengths that are 10.

See, now we're substituting that variable.

That L was just standing in its space until we gave it a value.

Now we've given it 10.

Here, the W represents the width.

So we look at our rectangle.

The 7 is the width.

And then now we have an equation to solve.

We can do 2 times 10 is 20.

And 2 times 7 is 14.

And the last piece right here to simplify, and we get 34 inches, just like we did before when we added all of the sides.

You see, but, this time, we used its formula.

Okay, now let's talk about area.

I want to talk about the area of this same particular rectangle.

But, this time, what's the area mean?

How much space the shape takes up inside?

Yes, very good.

So, you see, this time, we won't be measuring just the edges.

That's perimeter.

Area, we're going to be focused on the inside of this figure.

Right?

Now, you may have done something known as the "area model," so you know a little bit already about what it means to be in the inside of that figure.

Very nice.

Let's look at the definition for area.

Area is measured... [ Chuckles ] "Area is a measure of how many square units are needed to cover the surface.

Area is measured in square units such as square inches, square feet, square centimeters."

And any other measurement.

So, notice the one word that kept coming up in front of the measurement, the word "square."

And you may say, "Ms.

Correa, where are the squares?"

Well, the square are created by these measurements.

You see?

I'm going to change this out.

It's the same figure.

But now I want you to see squares.

See, in order to see how much space that takes up, we have 10 units going this way.

Right?

And then 7 going this way.

So, together, it kind of creates like an array that you learned in third grade.

Right?

There's 10 squares this way.

And there's 7 rows of them.

See?

So, we can solve for area using what?

Multiplication.

Sure.

If we did addition, we would do 10 plus 10 plus 10 plus 10 -- 7 times.

But we know how to make it more efficient by just multiplying, right?

So area equals 10 times 7.

So area is 70.

But it's not just inches.

Because what did we create inside of this shape to see how much space it takes up?

We used squares, right?

So it's square inches.

So, when you do area, you have to make sure that you use the word "square" in front of any unit of measurement that you're using.

Okay?

And it's that simple.

Yeah.

But now I want to use a formula using symbols.

Okay?

Make it a rule.

So, this way, any time you're going to solve for the area of a rectangle, you have a rule in place, a formula.

Okay, so, mathematicians, area is represented with a capital letter A. I bet you knew that.

Now, when we multiplied 10 times 7, what did we actually multiply?

What was the name of that section?

Well, this 10, what do we refer to that as?

The length.

Very nice.

And then we multiplied that by the... width!

Great work.

So, now that we have the formula, no matter how big your rectangle is or how itsy bitsy, if you use this rule, this formula, you will always get the area of that rectangle.

Now, different figures have different formulas, but for a rectangle, that's the one right there.

So let's substitute.

Area equals -- length is 10.

And width is 7.

All together, area is 70 -- what?

-- square inches.

Very nice for remembering that.

Now, remember, students, when we're doing area and perimeter, you have to make sure not to confuse them, because sometimes we confuse them.

[ Chuckles ] But it's okay.

Just know that area needs to fill in this space.

In order to fill in the space, you use little square units.

You see how nicely it fills up that space?

Yeah, but when you're using perimeter, we don't want to know the inside.

We just want to know the distance from this point to this point.

So all we need is that line segment.

So we just need to know the length.

So all you need to know is the unit of measurement as is, but when we're doing area, we need to make sure we do square units because that is what is used in order to show you the inside of the area.

Now, there are many, many situations when you say to yourself, "Well, how do I know when to use area or how do I know when to use perimeter?"

One thing that can help you remember.

I don't know how much TV you watch, but have you ever seen a show when the officers say, "Secure the perimeter"?

Do you know what that means?

That means that they want to make sure that no one comes in this area, so they secure the perimeter.

Sometimes they use tape or whatnot, but they make sure that that area inside is nicely protected.

So "secure the perimeter" is the around, and the area is the inside of the figure.

And that's how you can remember.

Well, let's do an activity just for practice.

We're going to do... You're going to help me out with an activity called a "sort."

I'm going to give you a bunch of situations, and you're going to tell me if you think I need area or perimeter to find a solution for it.

So here are some real-life situations that we can consider.

Here we go.

Fabric to make a quilt.

What do you think I'm going to need -- area a perimeter?

Area.

Very good.

How about a tablecloth for the table?

Area.

Because if you [Chuckles] don't do area and you do perimeter, you're gonna have one big hole in the middle of your table, right?

How about if you want to fence in your yard?

Just the perimeter, because if you put fence all in your yard, you won't be able to play inside the yard.

This is just the perimeter.

How about building a picture frame?

Perimeter.

Yes.

Because if you build the hole in between, you won't have a space for the picture.

How about painting an entire wall?

What do you think?

Area.

Very nice.

How bout rocks around a fountain?

Yeah.

Perimeter.

How about decorative trim for a rug?

Perimeter.

You're getting really good at this.

How about carpet in a bedroom?

Yeah.

You're going to need the area.

Tile for a bathroom floor?

Yes, you're going to need to know the area.

And the last one -- ribbon for the border of a card.

Perimeter.

Very nice.

Wow, that was a lot.

I think we made it just in time for a little brain break.

I don't know about you, but in these times, I've been very encouraged and just so lifted by family.

We've been able to Zoom together and talk on the phone.

Although we can't see each other, we can see each other through Zoom.

So, as a little brain break, I want to you and join me for a family conversation, a little phone call to my brother, and see what he's up to.

And let's just take a break and ease out of all this perimeter and area talk.

Want to join me?

Awesome.

Let's call him.

Hey, big bro.

>> Hey, sis.

What you up to?

>> Actually, I'm teaching a lesson to all the fourth graders in the state of New Jersey.

>> Wow, that sounds awesome.

What's the lesson on?

>> The lesson is in math, but more specifically, we're messing with shapes.

>> Did you say a lesson on getting in shape?

>> [ Laughs ] Well, no, not that kind of shape.

But you know what?

We do have time for a brain break, so maybe we can learn how to get in shape.

Want to help me with that?

>> Of course.

I'm always ready to talk about getting in shape.

>> Awesome.

Let's give these mathematicians just one minute to go get their sneakers, and then we'll be right with you.

>> You got it!

Let's do this!

>> Let's do it.

♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ >> Are you ready for your fitness brain break?

Great.

Here we go.

But before we get started, there's a couple of things to consider, okay?

Exercise is so important.

But in order for us to put everything together in a nice package, we also need to consider eating well, resting, and hydration.

Alright.

So, as far as nutrition goes, a good practice is to follow the food pyramid that we have here.

Okay?

The food pyramid has a whole bunch of different foods from proteins, carbs, and good fats.

Okay, so, now what you need to consider is what options you have in the food pyramid.

And then from there, select something that you like to eat, you enjoy, and put it on the MyPlate.

Okay, the MyPlate is broken up into portions.

That makes it so much easier for you to keep things nice and organized.

All the food that we consume provides us the fuel that we need to tackle our day.

Alright, so, along with eating well, we also need to hydrate.

Hydration is so important.

Okay, our bodies, believe it or not, are composed of 70% water.

Okay?

So a lot of water is required.

Okay?

So we at least should be drinking six to eight glasses of water a day.

And if you're very, very active, maybe you want to boost it up to about 12 or so.

So, now, as far as that goes, now we are going to discuss your rest.

Students are so focused into playing games that we tend to neglect rest.

Rest is a key point, especially at your age.

So you need to least have 9 to 11 hours of sleep a day.

We can't function properly if we're not sleeping well.

Alright.

So, now we got the eating well, hydration, and rest, but now we need to put together our workout program.

So we're going to start off with the wall push-up, okay?

Second, we're gonna go with the body-weight squat.

Third, the wall slide.

Each exercise is gonna be broken down to 30 seconds, each one, with about a 15- to 30-second break before you continue on to the next one, alright?

If you want to do it back to back, then you can.

Sure enough, you can.

Okay, it's all about challenge yourself.

You find what you're comfortable with doing.

As long as your body is moving, you're doing something great for your body, okay?

So those are the three exercises.

Alright, so, each of them are going to be 30 seconds each.

And you're going to do about two rounds, alright?

So it should take you about three to five minutes to complete.

And that should be enough for you to have that energy to get back to your work.

So, here we go.

We're going to demonstrate the three exercises that we want to do for the first program.

The demonstrators are going to be my son, Sebastian, and my daughter, Evelette.

Okay, so, the first one that we're going to do is the pushing exercise, okay, which is the wall push-up.

My daughter, Evelette, will be demonstrating what a wall push-up looks like.

Alright.

So, as she did the wall push-up, this is -- if you've done push-ups before, they could be a little challenging, so this is level one, okay?

My son, Sebastian, is going to demonstrate level two.

You could use a chair, the end of a couch and perform your pushup slightly still elevated, which is a little easier.

Alright?

That was level two.

Level three, if you require a little more, you go on your knees for a modified push-up.

Go down and up.

Now it gets more challenging.

Then you got the plank push-up.

Full plank.

Breathe in as you go down, breathe out as you come up.

Now, that's the hardest one.

Alright, guys.

So, there you go.

You see?

We have four different choices for the pushing exercise.

The first one was a wall push-up, elevated push-up off the couch, modified push-up on the ground, and then a plank push-up.

So, that's exercise one.

My daughter, Evelette, will be showing the tap squat.

Okay?

So, you're going to tap and come back up.

That's level one.

Now, to make it a little more difficult, you're going to go now with the standard squat.

You're going to push your hips back, sit, and come right back up.

Now, if you think that's too easy, you got the single-leg tap.

Tap and just drive with the leg that is flat on the ground.

The other leg, once again, just tap your heel, sit back, and drive through with the leg that's flat on the ground.

That'll give you more of a challenge.

So since the exercise is going to be 30 seconds, you're gonna do one side for about 15 seconds, the other side for 15 seconds, okay -- if you choose the last one, the more challenging one.

Okay?

If you choose the tap squat or the regular squats that Sebastian performed, all you have to do is 30 seconds of that, and you're good.

Exercise number three, the wall slide.

Okay, so, what we're going to do here is come against the wall.

Make sure your feet, your hips, your shoulders are touching the wall, okay?

Stand nice and tall.

And no matter what you do, is I want you bring your elbows to about shoulder level.

Okay?

And now bring it back flat against the wall.

Alright.

So kind of look like a scarecrow, huh?

What we're going to do from this point is we're going to raise our arms up, sliding our wrists and elbows as close as we can to the wall, and then slide them back down a little -- elbows below your shoulders, and keep going up and down for 30 seconds.

Okay, that is your wall slide.

Alright, mathematicians, we're ready to work here.

Sebastian and Evelette are ready to demonstrate each exercise in full time, okay, live for you.

Now, before we get started, though, we want to make sure we establish a perimeter where we can work, right, so we could be inside the area and do all our exercises.

Here we go.

[ Monitor beeps ] So, my kids will be demonstrating every exercise for the duration.

So, as you're pushing, you want to breathe in as you go down, breathe out as you come up.

Don't rush it.

Controlled movement, okay?

You want to maintain proper form throughout the motion.

Keep breathing in as you go down, breathe out as you come.

Good form.

Quality over quantity is very important.

Breathe in.

Breathe out.

[ Monitor beeps ] Great job, guys.

Now we're going to exercise two.

Here we go.

Tap.

Good controlled movement.

Push those hips back.

Breathe in as you go down, breathe out as you come up.

Controlled movements, do not rush it.

Okay.

Breathe in.

Breathe out as you push.

Keep your balance.

Don't rush.

Sit back.

And this is your first variation with the tap.

[ Monitor beeps ] And your second.

Exercise number three, wall slides.

Here we go.

Raise your arms, shoulder level.

Put them back and begin sliding up and down, okay?

Make sure your hips are touching the wall -- your shoulders, your elbows, and your hands, as best as possible.

Stand nice and tall.

And just slide up and down.

Your elbows will come down below your armpit.

Push to the hip to the wall.

Alright?

You can feel it.

It's a little challenging.

This also helps with your posture.

Great job.

We had a fantastic time showing you mathematicians how to get in shape.

It's just as important to train that body as it is the mind.

Back to you, sis.

>> Wow!

That was a great fitness brain break.

Thanks, big bro.

Well, now let's get back to our learning.

So, before we went on break, we were talking about area and perimeter and when we're to use area or perimeter and when to use their formulas.

So, now what I would like to do is give you some examples of rectangles, and we are going to find the area and perimeter and apply the formulas to what we've learned.

Okay?

So, first, you might want to get yourself a calculator or a phone calculator if that works, or if you have this wonderful multiplication chart that your teacher may have given you, you can use that, too.

I will leave the multiplication chart up here on the screen so that you can use it if you need it.

If not, it's okay.

So, let's get started.

I am going to present to you a rectangle.

This rectangle has a length of 2 inches and a width of 8 inches.

Can you find the area and perimeter for me?

Go ahead.

Okay.

How did you do?

Let's see.

We took this rectangle with a length of 2 inches and a width of 8 inches, and we found the area and the perimeter.

Let's see.

Here's the formula for perimeter that we learned.

Instead of an L, we substituted with the length of this rectangle.

And instead of a W, we substituted the 8, the width of this rectangle.

And then we set up the expression, and then we simplified.

Now we ended up with 4 plus 16 because 2 times 2 is 4 and 2 times 8 is 16.

Now we can further simplify, and we have 4 plus 16.

That gave us a total of 20 inches of perimeter all around this rectangle.

Then I asked you for the area.

That's the inside.

How many square units can fill up this space?

Let's look.

So, we substituted the L, for length, for 2 inches, and the W, which is width, with 8 inches.

We continue to simplify, and we get 16 square inches.

Did you remember to label square inches?

It's okay if you didn't.

But don't forget area means little square units.

So you have to make sure to include square inches.

Very nice.

Let's try another one.

What if I gave you this rectangle?

This rectangle has a length of 4 inches and a width of 6 inches.

Go ahead and find the area and perimeter.

I'll give you some time.

Okay.

How did you do?

Let's see.

So, I gave you this rectangle with a length of 4 and a width of 6 inches.

When we substituted the formula, we replaced the length with 4 and the width with 6.

Simplifying it down to 8 plus 12 gave us a total of 20 inches in perimeter.

Then when we came over and did the area, we substituted the length of 4 and the width with 6.

And when we multiplied them, we got 24 square inches.

I bet you remembered to label the square inches this time.

Great job.

What do you notice about these two shapes?

If you look at your work, you saw that our perimeters are the same, yet our areas were different.

So sometimes you may have rectangles that share the same perimeter, but their areas are just not the same.

They create different spaces inside, but the perimeter remains the same.

Pretty cool, right?

Okay, let's look at a different situation.

What if, this time, I told you that you only had 12 square inches to work with and you wanted to create as many rectangles as possible that you could, but the area for each of those rectangles had to be 12 square inches?

Do you think you could find out how many rectangles that could be?

Alright.

Go ahead.

Give it a try.

So, how'd you do?

How many rectangles were you able to create?

Three?

Awesome.

Me too.

I created this space so we can record the length and the width of each rectangle that we were able to create.

So, the first one, what did you get?

Okay, the length of 12 with a width of 1.

Let's see what that would look like.

So, here are 12 square units.

We're going to call them inches for the purpose of this example.

So you're saying it was 12 all together... like this.

Look at that.

You made one long rectangle.

See?

12 units.

That's the length.

And 1 unit up.

There was only 1 row.

So 1 unit made the width.

12 and 1 made an area of 12 square inches.

Very nice.

What's another one that you came up with?

3?

A length of 3 and a width of 4?

Okay, let's try that.

So, if I have 3 -- I'm going to just make sure I have just a length of 3 square units, 3 square units.

Whoa.

I think you're right.

Here we have 3 units.

That's your length.

And 4 rows of them.

That you're width.

Awesome.

Is there another rectangle that you created?

A length of 6 and a width of 2.

Okay.

Let's look at this.

A length of 6.

And a width of 2.

That's what that would look like.

Look at this rectangle.

6 units across -- 6 units -- and 2 units, 2 rows.

So 2 units up.

There you go.

They all made 12 square inches.

Very nice.

So how did you figure it out?

Oh, good work.

You thought of the factors, yes.

What factors... equal 12?

And then, once you know your factors -- which I know you learned earlier this year -- then you can figure out how many rectangles will give you an area of 12 square inches.

So, you may wonder, "When do we use each of these rectangles?"

Well, it depends on the situation.

You see, if you need a rectangle.

If this is a design for something, you may need a certain size -- so, for example, you are creating a doghouse and this was feet, would you really want to create a dog house that was 1 foot wide and 12 foot long?

What if you have a big dog?

1 foot is about this much.

Do you think your dog will be able to get comfy in there?

He may not even fit.

So that wouldn't be a good one.

Maybe you might try a different combination.

Maybe you find that 3 feet by 4 feet is just enough space for your medium-size dog.

And that's the one you would use.

So it all depends on the situation.

Awesome work, guys.

Great job.

Okay.

So, now, what if I gave you a little bit of a different kind of example?

What if, this time, I give you what the area is already and I give you one of the measurements?

In this case, I will give you the length.

How, by knowing the length, can we figure out what the width is?

Do you think you can figure it out?

Here's the formula.

Go ahead.

Give it a chance.

So, how'd you do?

Here's how I set it up.

Here is my formula.

You always want to write the formula.

And you substitute for what you already know.

This time, we already knew that the area was 35.

So right underneath the area symbol, I wrote "35."

I knew what my length was, and I substituted it with 5.

What I was missing was my width.

So, right now, I don't know what that is yet.

So I want you to tell me what number will substitute the W. Well, 5 times what number gives me 35?

7.

You're right!

Awesome work.

Now, what if we change it up a little bit?

What if, this time, I tell you that the area Is 32 square feet?

Okay?

Are you ready?

Go ahead.

Try it.

So, how'd you do?

Let's see.

Help me complete this problem.

So, now the area they gave us was 32.

So I substituted the area with 32.

The length that was given was 8 feet.

And there you have it.

I didn't have the width.

But, this time, I left the variable because we're solving for that variable.

We want to know what is the width equal -- what does the width equal?

Okay.

So, let's see.

8 times what number gives me 32?

4!

Awesome!

So, in this case, the width, the W, equals 4.

4 what?

4 feet.

Now, are you going to square this measurement?

No, you don't have to, because what you're getting here is the width, not the area.

Only the area counts the total square units.

The length and the width are just simple linear measurements.

Wow, that was some great calculating using the formulas of area and perimeter.

That was great.

I think we are ready now to tackle that problem from the beginning of this lesson.

Remember?

I wanted you to help me with my garden.

Now I know you are absolutely ready, mathematicians.

So, what I'm going to do is I'm going to give you the requirements that I have for my garden.

And, based on my requirements, you are going to give me some examples that you think would fit these requirements.

And then we'll see which one best fits the requirements.

So, let's look at these requirements.

First, it must be a rectangular garden.

What does that mean?

It needs to be in the shape of a rectangle.

Also, I want the total area to be 48 square feet.

Now, remember that example we did not too long ago with the little red tiles?

Okay?

Same idea.

What you need to do is find all possible rectangles that will give you an area of 48 square feet, because that's the max I want.

No less.

No more.

48 square feet exactly.

Also, each side has to be greater than 1 because of that same example.

I told you the story of a doghouse.

And if you only made it 1 foot wide, eh, the dog may not be able to get in there.

Same with my garden.

I think -- If it's only 1 foot wide, I think it's going to be a little too small.

So I want all measurements of either sides to be greater than 1.

Okay?

Also, I want the measurements to be in whole numbers.

I'm planning to have my son and my daughter help me with this project, so my son is still little, so I don't want to use any fractions or decimals.

So please stick to whole numbers only.

Also, remember I showed you my garden fencing?

I had 20 of them, and they were each 3 feet wide.

Right?

So, if I had 20 of them, how many do I have?

I have 60 feet for perimeter.

I have 60 feet worth of garden fencing that can be the perimeter of my garden.

So, what I want you to do is, once you find these rectangles, make sure that you choose the rectangle that has the greatest possible perimeter that doesn't surpass 60 feet.

It can't go over, because I don't have any more, and I don't want it to be too little, because is if I don't reach 60, then I don't want to waste any garden fencing, so the closest possible to 60 feet.

So, those are my requirements.

I want you to keep this sentence in mind when you're solving.

This is the final answer.

"The best dimensions for Ms.

Correa's garden are 'blank' by 'blank.'"

So there you'll be your length and your width, okay?

"These are the best dimensions," or, "These are the best because..." And then whatever reason you might have that fits the requirements.

Okay, I'll give you a few minutes to get these problems solved.

Alright.

See you soon.

♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ ♪♪ So, how'd you do?

I set up a table to help me organize your thoughts.

So you want to give me one rectangle that you came up with that gave you 48 square feet?

Okay, yeah, definitely.

A length of 24 feet with a width of 2 feet.

Okay, that's a good one.

Did you come up with another?

A length of 12 feet... with a width of 4 feet.

Awesome.

Did you come up with another?

Ooh, that's a good one.

16 feet... by 3 feet.

Nice.

Is there another?

Okay.

Yes!

That definitely works.

8 feet by 6 feet.

Is there another?

Well, there is the 1 foot by 48 feet, right?

But what was the problem with this one?

Why can't I use the one that's 48 feet by 1 foot?

Because I needed the measurements to be all greater than 1.

So I'm not going to use this one, although it does equal 48 square feet.

Okay.

I think this is all of them.

Let's check.

24 times 2?

48.

Length times width is the formula for area, right?

12 times 4?

48.

16 times 3?

48.

8 times 6?

48.

Awesome.

So, I'm going to label these rectangle A... rectangle B... rectangle C... and rectangle D. So, what I'm going to do now is I'm going to go to my backyard, and I am going to measure these out.

You want to come with me?

Come on, let's go see.

♪♪ ♪♪ ♪♪ ♪♪ Here is the final product.

These rectangles look great.

Thanks for providing the dimensions.

So, let's go down the list of requirements to see which one of these is the best option for me.

They are all rectangles -- first requirement fulfilled.

They all have an area of 48 square feet.

Check.

Each side is greater than 1 foot.

Check, check.

All the the measurements are whole numbers.

Perfect.

Now the last requirement -- which one has the closest perimeter to 60 feet?

Well, let's review.

After calculating the perimeter for rectangle A, we found that the perimeter was 52 feet.

Rectangle B had a perimeter of 32 feet.

Rectangle C had a perimeter of 38 feet.

Rectangle D had a perimeter of 28 feet.

So, which one was the closest to 60 feet?

I think we have a winning design.

Rectangle A. Awesome!

Wow!

That was so much fun.

Let's just recap.

So, rectangle A had a perimeter of 52 feet.

Rectangle B had a perimeter of 32 feet.

Rectangle C had a perimeter of 38 feet.

And rectangle D had a perimeter of 28 feet.

So the one that actually filled all my requirements was rectangle A because it came closest for me to use all of the fencing I had already purchased -- well, maybe not all, because I have 60 feet, but this is the closest to 60 feet.

So, thank you so much for helping me solve my garden problem.

Here's the final answer to this problem.

"The best dimensions for Ms.

Correa's garden are 24 feet by 2 feet.

These are the best because they fulfill all the requirements."

Awesome.

Thank you so much for helping me with that garden problem.

Now, to continue your learning, you can go ahead and maybe create a little scavenger hunt with a loved one.

You can go around and find anything that's rectangular -- a cereal box, a pencil box -- and find the length and the width.

And then solve for area.

Area is length times width for a rectangle.

For perimeter, it's 2 times the length plus 2 times the width.

And maybe you can make a little game of it and see who can find the rectangular shape that has the greatest area or the greatest perimeter or area that's the same or perimeter that's the same.

You are ready to handle any of those situations.

Another game you can play?

You can roll the dice, and those two numbers become the dimensions of a rectangle.

And, again, you could play with a loved one or you can play with yourself.

[ Dice rattle ] It's that simple.

And if you want to further your knowledge on area and perimeter, there are great books in the local library or your school library.

One of my favorites is Marilyn Burns' "Spaghetti and Meatballs for All!"

Such a great book.

So check it out if you have the time.

Anyhow, thank you again so much for this opportunity.

I had so much fun.

I'm ready to go plant that garden with my family.

So stay safe.

Enjoy your time with your loved ones.

Take care.