Male Narrator: Funding for this program is provided in part by Female Narrator: We believe in getting outside, playing in the yard, growing things, and connecting with the earth.

We believe good can grow anywhere.

That's why we're committed to GroMoreGood, everywhere.

And also by Hi, friends.

I'm Caroline, and this is How It's Math, where we discover the surprising ways math shows up in the real world and in amazing careers.

Have you ever wondered how people designed giant aquariums, built stages for performances, or even understand history through shapes and patterns?

Today, we have a very special episode all about how math helps us measure, build, and understand the world around us, past, and present.

First, we're heading to the aquarium where math helps experts to measure volume and keep massive tanks balanced and safe for marine life.

Next, we'll go behind the scenes with set designers who use area, measurement, and geometry to build stages and bring creative ideas to life.

After that, we'll explore indigenous mounds, where we'll discover how shapes like circles, symmetry, and perimeter were used to design these incredible historical structures.

Finally, we'll visit a pediatrician where line graphs and data help track growth and keep kids healthy.

From water to stages to history to healthcare, you're about to see that math isn't just something you do in school, it's something people use to understand and shape the world around them.

Let's get started.

♪ Doodly doodle, doodly doodle ♪ doodly doodles and digits ♪ Area, symmetry, fractions too ♪ ♪ It's all here for you Welcome to the Greater Cleveland Aquarium, where math plays a big part in keeping the animals healthy.

From measuring the volume of huge tanks to calculating just the right amount of salt in the water, aquarium staff use math every day to create the perfect environment for fish, sharks and more.

Let's dive in and see how math helps keep the water just right.

Have you ever been face to face with a shark or watched a sting ray glide right past you?

At the Greater Cleveland Aquarium, you can do just that.

This aquarium has over 2,700 animals, including sting rays, puffer fish, lion fish, and even sharks, swimming through a 230,000-gallon tank.

You can walk underneath in 175-foot tunnel.

Keeping all these animals safe and healthy isn't just about feeding them or cleaning their tanks.

It's also about math.

Staff here use math every day to measure just the right amount of salt to add to the water, calculate tank volume, and monitor temperatures and pH levels.

They even use graphs and charts to track animal health and water quality over time.

That's a lot of numbers and a lot of responsibility.

Today, we're diving in to see how math helps the team take care of their underwater friends.

Let's find out how they make sure each animal has exactly what it needs to thrive.

My name is Brenton Maille.

I am the Director of Life Support Systems and Operations here at Greater Cleveland Aquarium.

I help oversee all the filtration here at the aquarium, as well as anything else that supports the day-to-day operations to keep everything running.

So, filtration are going to be things like pumps that move the water, filters that are going to make sure that that water is clean, and all of the plumbing to move the water from the habitat where our animals are back into our life support area, where we have dedicated space for all these things, and then back to the habitat.

What does a typical day look like?

Every day is a little bit different.

Some days we are working on upgrading or building new habitats for our animals.

Some days we're doing repairs to a filter that might need a little bit of extra attention.

Typically, we'll be doing things like making salt.

We'll be testing the water.

Water quality is very important here.

So, that's kind of a little bit of a mix of a lot of chemistry, biology, engineering, lots of stuff.

Caroline: How do you use math?

We use math here on a daily basis.

There's lots of engineering that we do here, things like flow rates, and volume, surface area.

What is volume?

Volume is the amount of space a 3D figure takes up and is measured in cubic units.

You calculate volume with an object's height, length and width.

Volume is very important for us here at the aquarium.

Knowing how much water we have in a system will impact things like how much medication we have to put in the water to reach a certain ratio.

It also can impact things that you might not think about, like the weight of water.

Water is very heavy, depending on if it's fresh water, salt water, it might weigh somewhere between 8 to 9 pounds per gallon.

And so, knowing that if we have a really large exhibit, we have to make sure that the structure is able to support that.

So, volume is very important for us, and we are looking at that on a daily basis.

What tools do you use when using math?

Some of the different tools that we use here at the aquarium to make sure that we are doing our math appropriately are going to be things like calculators, scales, pipettes, different thermometers, flow meters.

So, we're looking at how fast the water is moving through different systems, all sorts of different things.

We can even use probes that are actually built into the system.

So, we're getting measurements 24/7.

Here at the aquarium, we actually use a combination of both imperial and metric units.

Here in the lab, we're doing a lot of different things with metric units.

So, we're going to measure things in grams, liters, milliliters, kilograms.

That allows us to talk to people across the world that are doing the same thing that we're doing here in Cleveland, maybe in the UK or Germany or Australia or China.

And so, we can talk the same language back and forth between any water quality lab in the world.

Once we go outside of our water quality lab, we start to use our more customary units, like gallons.

Because when we are talking to the public, they might not have a good concept of how big a liter is, but we all know how big a gallon of milk is, so when we tell them that our exhibits might be 230,000 gallons, they are able to comprehend that.

What's something that might surprise students about your career?

To get salt water here at our aquarium, we are going to make it ourselves on site.

That means we are taking water from the city of Cleveland, just like you would get at your kitchen sink, we're going to bring that into a large vat or mixing chamber.

We're going to add salt into that chamber, and we have to make sure our ratios are correct.

We have to add the right amount of water with the right amount of salt.

Give that a little bit of time to mix up, and then we let that heat up too, because in the winter, we got our city water and very cold.

We want to make sure that is the right temperature for our animals.

And then once it's all blended together, and we have that homemade here in Cleveland saltwater, we're going to be able to send that out to the various habitats here in our facility, including our big shark habitat.

So, saltwater is actually heavier than freshwater because of all the different salt molecules in it.

On average, if it's at ocean salinity, salt water weighed 8.55 pounds per gallon.

Fresh water, meanwhile, is a little bit lighter at 8.34 pounds per gallon.

Did you enjoy math growing up?

I will be honest, when I was in school, didn't really like the math quite as much, because it was always, to me, a problem that just had to be solved.

Now that I do what I do for a living, I know the importance behind it.

I know why it's important to find the volume of a cylinder or a rectangular prism.

I know why doing measurements accurately is important.

So, keep that in mind.

Think about the real-world applications that that math may be able to be used for.

They are designing a new rectangular habitat in the aquarium for some tropical fish.

It needs to be just the right size for the animals.

The dimensions will be 15 feet long by 8 feet wide and 6 feet tall.

What will the volume of the tank be?

[clock ticking] [bell ringing] 720 cubic feet.

I solved this problem by multiplying the length, the width, and the height.

Did you get it correct?

Aquariums here serve a very important purpose across a lot of different areas.

Some of the areas you might think about like are animals and making sure that we are preserving species that might be endangered or might have issues in the wild in their native habitats, but we're also doing things like educating.

So being able to bring people in to see animals that they might not be able to see anywhere else, and we're also doing things like conservation and research.

All of the data that we're collecting on our animals is being shared out with other zoos or aquariums across the world, and what we are able to find out from these animals by being in such close proximity to them 24/7.

I'm Brenton Maille.

I'm the Director of Life Support Systems and Operations at Greater Cleveland Aquarium, and this is How It's Math.

[cock coos] When you think of a play or musical, you might picture the actors, costumes or music, but there's something else that brings the story to life.

The set at Columbus Children's Theatre, set designers use measurement and geometry to build the amazing worlds you see on stage.

From planning the size of a giant book to making sure a staircase is the right height and angle, math helps them turn ideas into real working sets.

In this segment, we're heading backstage to see how math takes center stage and set design.

My name is Brian Altiere.

I'm the Production Manager for Columbus Children's Theatre.

As production manager, I oversee all aspects of the production, so that includes scenery, lights, sound, projection, costumes, all the technical parts of the production, making sure that everything gets done on time and on stage.

When you're designing a set, the first thing you want to do is understand what it is that you're designing, so reading the script or understanding the play, so that you have an idea of the world that these characters are living in.

Then the designer starts making drawings, very accurate drawings to scale, and then, typically, those drawings get handed over to somebody like me, and then we start taking a look at it and actually figure out how to build the things that are in the pictures.

And to me, that's some of the most fun things to do is actually take what's on that piece of paper and bring it to life.

And then once it's all finished and painted, then we'll take it to the theater and we'll assemble it.

How do you use math?

Math is critically important, especially here in the shop and in the theater.

Our drawings are dimensioned, they have measurements right on them, so everybody knows what's on that piece of paper.

The idea that the designer is trying to convey gets built into reality exactly how they expect it to look on stage.

And so, one of the most important aspects is dimensions or measurements, making sure things are going to be precise, because we need to make sure that there's enough space.

Some of the important dimensions that we use in almost every theater is a center line which runs upstage and downstage, and a plaster line which runs across the stage.

We'll use those two lines to transfer dimensions from the designer's ground plan to the stage floor, and that tells us exactly where to put everything.

When we talk about area, one of the easiest ways to recognize that is a square or a rectangle.

We can measure the sides and multiply that out.

We know how much volume it is.

And there is kind of a standard size that we use on stage in theater pretty regularly, a 4 foot by 8 foot, the size typical of a sheet of plywood but we build platforms out of that.

So, being able to look at a drawing and recognize easily how many stock platforms we might be able to use to build an area on the stage is something that we do pretty regularly.

Also, when we think about triangles or perimeter around the side of a triangle, there's a triangle that we use called a 3-4-5 triangle.

And so, that means if the two legs of the triangle, if one is 3 units, one is 4 units, then the hypotenuse or the diagonal part is going to be 5.

That's just a constant.

And we use those all the time.

We might use a multiple of 3-4-5, like multiply it by 2 would make a 6-8-10 triangle.

We would use that if we needed a little bigger space, but that tells us if we have a right angle, if we lay out those measurements, we'll know that we'll have a perpendicular line.

What tools do you use when using math?

We use tape measures all the time, every day.

Being able to use and read dimensions on a tape measure.

That means fractions, too.

So, we're going to be looking for even a 16th of an inch to be able to exactly pinpoint where the set wants to go.

And we also use something called a scale rule, which looks like a regular ruler, however, it's got some different dimensions on it.

This is an actual half inch, and it's broken down into smaller increments.

But there are numbers every half an inch here, and they represent what we would call a foot on our drawings.

And so, we see that it's dimension here, 4 foot 7.

And so, I would turn this to the one-inch side, and I see that, that end lines up with the 4, and over here, it lines up with a little mark just past the 6 that I know is the 7.

If we have a picture of the theater space on our paper, where we want the set to go, or how big we want it to be, we would use a scale rule to be able to measure that if we didn't have a computer regularly available.

They are designing a new platform for the set of an upcoming play.

The platform segments are 4 feet by 8 feet.

They need 4 of these segments to complete the entire platform.

What is the total area of the platform?

[clock ticking] [drum roll playing] [bell ringing] 128 square feet.

I solved this problem by multiplying the length and the width to get the area of one platform segment.

Then I multiplied it by 4 to get the total area.

Did you get it correct?

I was not particularly fond of math in my time in elementary school, until I found out about geometry and shapes, angles, and dimensions and distances, and then I got excited about it.

So, there are just so many different aspects in life where we use math.

I would just suggest to really focus on the type of math that you like, and then branch out from there.

My name is Brian.

I'm a Production Manager, and this is How It's Math.

[cock coos] When someone mentions geometry to you, many might think of the shapes and measurements in the current world around us.

Did you know that humans were using geometry and math 1000s of years ago?

Today, we get to explore the amazing math behind the indigenous people during the Hopewell period.

Come behind the scenes with me, with an archeologist at the Hopewell Ceremonial Earthworks to show How It's Math.

The Hopewell Ceremonial Earthworks are large, geometric landscape architecture that consists of huge squares, circles, and octagons.

Not only are they geometrically precise, they also align with the cycles of the sun and the moon.

Let's talk to a real archeologist who can share some important insights on these sites.

Hi.

My name is Brad Lepper.

I'm the Senior Archeologist for the Ohio History Connection World Heritage Program.

An archeologist is someone who studies the human past, but often without access to a historic record.

I'm currently standing in the gateway of the Great Circle, Earthworks, a UNESCO World Heritage Site in Newark, Ohio.

The Hopewell Ceremonial Earthworks are ancient earthworks built by indigenous people 2,000 years ago, and theye gigantic earthen enclosures in geometric shapes, circles, squares and octagons.

But they all serve a ceremonial function.

These structures are very large in size.

The Great Circle is 1,200 feet in diameter.

This is so large that it can actually fit four entire football fields lined up inside of it.

Well, the Earthworks were first encountered by Europeans.

They just encountered these bewildering, gigantic earthworks that the indigenous people at the time, when asked by Europeans said, they didn't know what they were.

[cock coos] Well, since these are geometric earthworks, math was integrally involved in their design and their construction.

While the geometric shapes are one important aspect to the math that contributes to these great structures, they are also incredibly precise, and when we look closer, they have even more hidden math within them.

For example, the circumference of the Great Circle is equal to the perimeter of the right square.

Reminder, the circumference is the perimeter of a circle.

We don't know why, but these people were studying math and geometry.

They created circles and squares that have the same area.

When you continue to explore the earthworks, you will notice the area of the Great Circle is equal to the area of the hidden square within the octagon.

The distance from the entrance of the observatory circle to the center of the Great Circle is equal to six times the diameter of the observatory circle.

The distance from the center of the octagon to the center of the square is also six times equal.

the geometric concepts present are parallel lines and symmetrical mounds.

As far as we know, this precise geometry on a gigantic scale was laid out by people using poles and ropes.

And so they could put the stake in the ground at the center of where the circle would be built, and stretch out a 600 foot long rope, in the case of the Great Circle, and then just walk around in a circle, just like you'd be using a compass on a piece of paper.

Caroline: As mentioned before, not only are these geometrically precise, these geometric shapes are also in alignment with the moon and sun.

In fact, the octagon aligns with the moon every 18.6 years.

It must have taken incredible planning and precise mathematical work for this to happen.

The Great Circle is 1,200 feet in diameter, while the Observatory Circle is 1,054 feet in diameter.

What is the difference in diameter between each circle?

[clock ticking] The 1,200 minus 1,054 is 146 feet.

Did you get it correct?

This is how I solved it.

I subtracted 1,054 from 1,200 and I got 146 feet.

Did you get it correct?

[cock coos] It's very important to show your thinking, to show your work, so that later people, later scientists that are trying to learn from what you did, know what you did and can build of -- it's a foundation that they can build on.

So, I think all civilizations would require math if they're sort of laying out property boundaries, if they're constructing any kind of architecture.

Math has endless uses, and all ancient societies, all societies throughout the world, would see the value in it.

My name is Brad Lepper, and this is How It's Math.

[cock coos] Have you ever wondered how doctors know exactly how much medicine to give a child or how they make sure kids are growing healthy and strong?

Pediatricians are doctors who care for children, and they use math every single day.

From measuring height and weight to calculating the right dose of medicine, math helps pediatricians make safe and accurate decisions.

In this segment, we'll visit a pediatrician and discover how numbers, measurement, and problem-solving help them take care of their patients.

Let's find out how pediatricians use math.

I am Dr.

Mary-Lynn Niland, and I am a pediatrician.

Many of you may already know what a pediatrician is, because you each likely have a doctor, but a pediatrician is a doctor for kids, and so I get to take care of kids from the time that they are born until they graduate from high school.

How do you use math?

We use math all day long, as a pediatrician, and most doctors use math all day long.

A big part of a pediatrician's job is to measure and follow our patient's growth.

And so, at every visit that you come, when you're coming to be checked for your wellness, we measure your weight and your height and your head size, and we plot those on graphs.

And so that is something that's important, because we have to follow to make sure that kids aren't growing too slowly or aren't growing too quickly, and we follow that and share that with the parents.

We also use math to calculate medication doses, and so we need a child's weight in order to do that.

And then every medicine has a different way that we decide what's a safe dose to give children based upon how much they weigh typically.

What data or numbers do you use in this career?

Probably the most common graphs that we use are the growth curves.

And so, at every well visit, we're plotting weight and height, and under the age of two, we plot head growth.

And so, what I'm looking at for that is a nice, steady curve, as opposed to a curve that's all over the place.

So, a child could be small, but growing at a small, consistent percentage, or a child could be taller and growing at a consistent tall percentage, and that's all normal.

What's worrisome to me is if I see a child who has been tall and growing at a certain percentage and now suddenly has dropped in that percentage and is a little bit smaller.

So, what we like to see is consistency in the graph and not points all over the place.

So, a lot of people ask what the percentiles mean on the growth curve.

And so, if I were to tell you that you were the 60th percentile for your weight and the 70th percentile for your height, that would mean, if you're a boy, for 100 boys your age, you weigh more than 60 of them, and you are taller than 70 of them.

And so that's how the percentiles work on our growth curves.

Is it important to show your thinking?

Our entire note writing process, our documentation process, for when we see every single patient, is us showing our work.

So, that if I were to see that patient again at a later date, or one of my other pediatric partners were to see that patient because maybe they were sick and they're not getting better, they have to look at what I showed as my work in my documentation to Know what I did, what I was thinking, my thought process, the logic and all the things that I considered when I was seeing that patient, so that they review it, and they kind of do their own history and their own planning, but they know at least what I was thinking, and they're not coming into it without any of that prior information.

Why is it important to be precise in your position?

I don't mean this to sound scary, but it can be a case of, if we are not precise in our calculations, in our measurements, we could give a baby or a child too much medicine, and that could be really harmful.

The medicine that we're giving to help them feel better could actually make them sick.

And so, it's super important that we know how to make those calculations and pay attention to the decimal points and pay attention to the details, so that we make sure that we're doing the right thing for our patients all the time.

What's something that might surprise students about your career?

Your pediatrician loves hearing about all the stuff that is going on in your life.

So, not just that you're here and your throat hurts, but how you're doing in school and how you get along with your brother or your sister, and what your favorite fruit and vegetable is.

We love knowing all of those details about our patients and getting to watch those patients grow and change and thrive and excel over time.

Look at this growth chart, which is a line graph.

Based on this graph, is the child growing at a normal rate?

No, the child was at the 50th percentile the last two visits.

But on this visit, the student is only at the 20th percentile.

The doctor might need to investigate why that is.

Today, we learned that pediatricians use math to measure growth, track health, and calculate the right amount of medicine for their patients.

Math helps pediatricians make careful, accurate decisions so children can stay safe and healthy.

The next time you visit the doctor, remember math is helping them take care of you.

Math isn't just something you do in school, it's something pediatricians use every day.

My name is Dr.

Mary-Lynn Niland.

I'm a pediatrician, and this is How It's Math.

[whimsical music playing] Wow, look at all the ways math helps us measure, create, and understand the world.

Today, we saw professionals using math to balance aquarium tanks, design stages, explore history, and track growth in healthcare.

Whether it was working with volume, geometry, patterns or data, math helped make sense of both the world around us and the world before us.

The next time you see a stage, visit a museum, or even go to the doctor, remember, math is helping make it all possible.

Thanks for exploring with us on How It's Math.

I'm Caroline, and I can't wait to discover more real-world math with you next time.

[cock coos] [whimsical music playing] Male Narrator: Funding for this program is provided in part by... Female Narrator: We believe in getting outside, playing in the yard, growing things, and connecting with the earth.

We believe good can grow anywhere.

That's why we're committed to GroMoreGood, everywhere.

Male Narrator: And also by...