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... 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 packages get delivered to the right place?

How race car drivers are separated just by fractions of a second?

Or how plants are arranged in beautiful patterns with symmetry?

Today, we have a very special episode all about how math helps things move, grow, and stay organized.

First, we'll explore logistics, where math like arrays and multiplication help organize and deliver shipments all over the world.

Next, we're heading to a race track where decimals are used to compare times and determine who is the fastest.

And finally, we'll visit a conservatory, where symmetry and patterns help design and care for plants in beautiful and balanced ways.

From organizing deliveries to racing, to growing plants, you're about to see that math isn't just something you do in school, it's something people use every day to plan, compare, and create patterns in the world around us.

Let's get started.

♪ Doodly doodle doodly doodle, ♪ doodly doodles and digits ♪ ♪ Area, symmetry, fractions, too ♪ ♪ It's all here for you ♪ Every time you buy something online, it goes through a process to land on your doorstep.

The process involves trucks, people, measurements, and multiple types of robots.

There's a ton of math every time you click buy.

Come behind the scenes with me at a distribution center to show How It's Math.

When you order something online, how does it arrive at your house?

This is a warehouse.

So much happens in a warehouse to make sure the product you ordered safely arrives at your doorstep.

It all starts when a truck drops off products to the warehouse.

They come in large boxes or pallets like this.

Math is involved in figuring out how much is in each box, how many boxes fit into one truck, and how many boxes fit on one pallet.

This robot here measures the interior of the truck and unloads all of the boxes.

How cool is that?

Once the pallet is loaded, the items will go into this section of the warehouse.

This section stores the items until they are needed to send to the customers.

This warehouse had to do a lot of math to make sure they had enough storage space.

My name is Meredith Williams and I work for DHL Supply Chain in our Solutions Design Department.

My team works to design warehouses like this, and that is everything from determining how big this warehouse needs to be to how much product goes in.

So, when we figure out how big it needs to be, we look at the length of the facility, the width, and the height, to then determine the size as well as what we can fit in that facility.

So, we really take measurements seriously.

It needs to be exact to ensure that we have the right numbers.

My name is Sean Leedy.

I'm Senior Customer Success Manager here at Locus Robotics.

Our Locus Robots help companies like DHL pick items faster and more efficiently.

So, this is a locus bot.

Down here you'll find we have different lidars and cameras.

This is how the bot navigates and can identify where it's going.

We have safety measures on the bots that will prevent it from colliding with people.

And then, we have the iPad here.

This is what the pickers will use on the floor that tells them exactly where they need to pick from.

A picker is simply a person that picks out the item you ordered and places it on the robot to be packaged, to be sent to your house.

There are a number of different shelf arrays based off of how we're picking the product.

We want to optimize the number of boxes we can fit on a robot.

So, typically, we look at how many items are in an order, and if it needs a large box like that, or if it needs a small box for that order.

If we need small boxes, we then determine that we can fit, say, eight small boxes, four and four, or if it needs a large box, we can fit two large boxes, one and one.

How do you figure out how many people you need to pick?

We look at what people like you are placing in terms of the quantity, the type, the product.

For example, in one hour, we would need 800 hats.

Say a person can pick 100 hats, but we need 800, you take 800 divided by 100 and that's eight people that we would need to pick those hats.

When the product is ready to be picked and sent to the customer, it will go to this section.

This section is really neat, because it uses both human workers and robots to ensure you are getting the exact thing you ordered in your box.

So, let's go back to that fancy hat you ordered.

That order will come to the warehouse, and a robot will drive up to a specific location where your hat is stored.

A worker will then scan the hat and check it's the correct item, then put it in the bin.

The robot will then drive to the next section of the warehouse.

As you can see, there are also arrays involved in this section.

Check this out.

This is an example of a real-life array.

How many rows and columns does this area have?

Not only are arrays used, but large numbers are also used in this section.

Check out how many orders they have filled.

Wait a minute.

Do the robots have to use that?

Our data or dashboards will provide information to the site team, and we have dashboards on the floor that will actually show where the bots are located.

It's a map, it's a real time map that will show the bots navigating the aisles where they're located.

There's graphs, you'll see percentages.

We have dozens of different ways to view numbers based on what you need.

So, you can see a total order count on a day-to-day basis.

We can see how productive the bots are in terms of how many items each bot is picking on an hourly basis.

We also use, for example, fractions with the bots.

Bots have battery life.

So, our dashboards will display if the bot is beginning to die, the battery life, and say it could be down to one quarter, which we consider a critical battery life.

And from there, the locus bot will then go to auto charge, the bot will automatically go to charge, and then return to working once the battery is at an appropriate level.

How do we figure out how many robots we need?

Our solutions design team will initially deploy a specific number of bots based on the numbers, the volume that we're provided, and we'll have a specific bot to work a ratio, a bot to pick a ratio that we'll use to then assign what our recommendation is in terms of how many bots the site could use.

Why is it important to show your thinking?

The importance of showing your work when it comes to working at a -- in a warehouse environment with robots is that if we don't have enough bots on site, it can create problems with fulfilling orders, getting orders out on time and delivered on time.

So, it's important to ensure that we're double checking our work when it comes to numbers that we're reviewing.

Once your hat has been picked up by the robot, it will then go on to a section called the pack station, where they double check your order, place it in the shipping box with your address, and send it on its way.

They will have to know what size box will be required to get the products to your house safely.

When your box is ready to go, it goes on a conveyor belt to then another robot which sorts the box onto a pallet to be shipped.

From there, the boxes will be picked up from the warehouse to be distributed and sent to your house.

Who knew so much math went into clicking Add to Cart.

The warehouse needs to know how many robots they will need during a busy buying season.

They typically need 3 robots per each picker at the warehouse.

They have 18 pickers.

How many robots will they need?

[clock ticking] 54 robots.

18 pickers times 3 robots equals 54 robots.

Did you get it correct?

DHL truly is an essential part of everyday life.

A majority of the products that you have in your home may have come from a DHL site.

We ship cosmetics, healthcare, medical devices, apparel.

I am Sean Leedy, Senior Customer Success Manager here at Locus Robotics, and this is math.

So, this is How It's Math.

All right.

I'm Sean Leedy, Senior Customer Success Manager at Locus Robotics.

I am Meredith Williams, Senior Director of Solutions Design with DHL Supply Chain... -and this is How It's Math.

-And this is How It's Math.

Have you ever wondered how race car drivers know exactly how fast they're going or how winners are decided when cars cross the finish line just moments apart?

At Eldora Speedway, one of the most famous dirt tracks in the world, math plays a huge role in every race.

Drivers and teams use math to measure speed, calculate fuel, and track times down to the 1,000th of a second.

In this segment, we'll meet a former professional race car driver and learn how math helps teams prepare their cars and compete for first place.

Let's head to the race track and discover how racing runs on math.

Hey, I'm Levi Jones.

I'm the General Manager at Eldora Speedway.

We call Eldora Speedway the greatest dirt track in the world.

We race about 24, 26 times a year.

Our core racing is dirt late models and dirt sprint cars.

At Eldora, one lap is a half mile.

The easiest way to think of it is the track at your high school, maybe around your football field.

That's a quarter of a mile.

So, twice as big as that, but it's not flat.

Eldora is bank.

So, you get into the degrees it's banked.

It's banked more up towards the outside wall than it is towards the bottom of the wall.

So, you look at late models, the track record being just over 14.5 seconds.

On a half mile, you're averaging over 120 mile an hour.

A sprint car at 12.5 seconds, you're averaging over 145 miles per hour.

So, top speeds, you know, you're over 150 mile an hour in a sprint car around here.

It's incredible.

How do you use math?

The team that doesn't pay attention to the math on every aspect of the car, they're going to be the ones that finish at the back.

Teams that have all of their engineering and math in order, right, they check all the boxes, have it all covered, eliminate as many variables, they're the ones up front.

But measurements at the race track, it all matters.

Aerodynamics is huge.

So, you think wicker bills or spoilers or front noses, the valence how many inches move left or right, up and down, you're constantly doing that through the night.

Another thing is the tires.

We're going in a circle.

We're turning left, so stagger.

How much bigger is your right-side tire than your left side tire?

So, all those spare tires must be marked, you know, in your trailer or at your pit area.

You know that say that they're 92 inches or 94 inches, or 94.5 and prepared that way.

So, you're -- if there's one thing you're using from the time you get here the time you leave, it's measurements and racing.

What tools do you use when you using math?

When you get to a track a typical event, every car will get three or four practice laps in a group, and then, once practice is over, it's time for what we call qualifying.

So, one car will go out by itself, and you'll be on the watch, right?

So, they time you -- from the start finish line until you get back to the start finish line.

A big event like ours, the difference in first to 20th maybe may only be 3 or 4 tenths of a second.

So, if it's -- you know, 15.2 seconds is the fastest guy, you might go 15.5 and be 20th.

So, those decimals of that qualifying time is really the most critical part of the night, because that places you -- where you're at in your heat races to transfer to the main event of the night.

Why is it important to be precise in your position?

So, we have scales in the pits that your car with you and it has to weigh X amount at the end of the race.

A lot of the series will have a rule, one pound per lap for the fuel.

So, you have to know that, okay, I'm going to use -- I think I'm going to use this much fuel, which is, you know, 6 to 8 pounds a gallon, turned into, you know, depending what type of fuel it is.

And you have to know that I'm going to need to finish with this much fuel to make wait or I get disqualified.

[bell ringing] At Eldora Speedway, race cars are timed to see who is the fastest.

Four drivers have these qualifying times.

Driver A, 15.482 seconds, Driver B, 15.376 seconds, Driver C, 15.429 seconds, and Driver D, 15.401 seconds.

Put the drivers in order from fastest to slowest.

Remember the fastest time is the smallest number.

[clock ticking] To find the fastest driver, we need to look for the shortest time, because less time means the car finished the lap faster.

All the drivers have 15 seconds.

So, we compare the decimal numbers.

Let's start in the tenth's place, 15.376, is the smallest number, so driver B is the fastest.

Next is 15.401, so driver D is second.

Then 15.429 which makes driver C third, and finally, 15.482, so Driver A is fourth.

This shows how race officials use decimals to determine who starts in the best position.

Even tiny differences in math can decide who wins the race.

How did you get to the position you're at today?

My career in racing, I started when I was 6 and go karts, and I just fell in love with it.

I started going to car races in Haubstadt, Indiana, at Tri-State Speedway.

It just got in my blood.

I loved it.

The sound of cars and the roar of the engines, and just the feel and the atmosphere is something that still gets me just as excited today.

So, you know, being in my 40s and still get that same feeling as when I worked at the racetrack the first time, makes it not feel like a job.

That is really cool.

So, I did get to race sprint cars.

I drove professionally for Tony Stewart from 2006 to 2012, then I worked in my dad's family's business for a few years, and then went back to the United States Auto Club to run their racing operation for about 5 years.

Then worked at INDYCAR for 3 years before I came back here to Eldora Speedway.

Do you have any advice for us?

I will tell you that one thing I wish I would have learned and focused on more as a youngster was the metric system as well.

My whole career using inches and feet and miles than my time in INDYCAR were working with mechanics and teams around the world.

Every other country uses metrics, so learning that later in life was always having to convert and make sure instead of just knowing it.

So, I challenge you to learn both and be equally prepared.

Today we learned that math is a powerful tool in the world of racing.

Drivers and teams use decimals, measurements, and problem solving to track speeds, calculate fuel, and make important decisions on the track.

Even the smallest difference in time can determine who finishes first.

The next time you watch a race, remember that math is helping drivers compete at the highest level.

Math isn't just something you learn in school, it's something race teams use every day.

My name is Levi Jones.

I'm a former race car driver and now the General Manager at Eldora Speedway, and this is How It's Math.

Did you know that behind every stunning plant display, every carefully controlled ecosystem and fluttering butterfly at the Franklin Park Conservatory, there's math.

Welcome to How It's Math.

I'm Caroline, and this is my math chicken, and today we're exploring one of the most beautiful places in Ohio, the Franklin Park Conservatory.

But we're not just here to smell the flowers.

We're here to dig into the numbers behind the nature.

From designing the perfect flower bed to the symmetry in every butterfly, math is growing in every corner of this conservatory.

Come behind the scenes with me to show How It's Math.

All right.

What is a conservatory?

A conservatory is a place where we have collections of living plants.

In the word conservatory, you might hear the word conserve, and we know that conserve kind of means to protect or keep something, and that's what we do with the plants.

Sometimes I like to tell students, we're like a zoo, but instead of for animals, we're a zoo for plants.

So, you can come and see plants from all around the world that you wouldn't be able to see otherwise.

Let's talk to the staff at Franklin Park Conservatory to see how they use math.

My name is Katie Speicher and I am the Botanical Gardens Manager here at Franklin Park Conservatory and Botanical Gardens.

I work with a team that takes care of the bed maintenance out in all of the public areas of Franklin Park Conservatory, things like weeding and watering and planting.

What is a plant bed?

So, a plant bed is a area out in a landscape that has different plants in it.

How does a conservatory use math?

So, we use area actually quite a bit when we are doing a design of a space.

Each plant has different spacing requirements.

So, in order to figure out how many plants you need to plant, you would find the overall area of the space, and then take those spacing requirements to determine how many plants you need to fill an area.

When designing a bed, we will use symmetry if the beds are on either side of one another.

If there's a pathway going between the bed, sometimes the beds will match.

What is a line of symmetry?

A line of symmetry is a line that divides a shape into two mirror images.

We also use symmetry when we are doing pruning.

So, when we are shaping a plant, a lot of times we want that to look symmetrical.

Angles are also important in pruning.

When pruning a tree, we would prune at acute angles.

I'm Courtney Billings.

I'm an Exhibitions Designer at Franklin Park Conservatory.

So, at Franklin Park Conservatory, I design their special exhibits, some special exhibits, kind of all throughout the year.

We have an art gallery.

So, I help manage and design all of those exhibits.

So, math is really important in designing exhibits, because you need to know the scale of the space that you design in.

You need to work on paper and in 3D models to design your elements, and be able to then scale it up to the real environment, like the one we have around us.

So, it's really helpful to use multiplication and the vision to be able to scale things up and down to meet the space that you're designing in and the -- so that everything fits.

This exhibit is the Blooms and Butterflies exhibit.

All the signage and interpretation that goes along with the exhibition we design every year.

The content on the butterfly identification signage tells about the size of the butterflies and approximately how many.

So right now, we have around 2,000 butterflies in the garden.

We tally them and keep track of how many we're releasing.

So, we have spreadsheets and tally sheets that help us to keep track throughout the whole season of the exhibit.

What math tools do you use?

Wee using a tape measure to measure spaces and be accurate about measurement is really important.

But I do a lot of my work in 3D models.

So, I use programs like SketchUp, I use the Adobe Creative Suite, like Photoshop, Illustrator.

Those tools help me be able to -- yeah, be as accurate as I can in designing things at the right scale.

My name is Jessie Mace-Froehlich, and I am the Youth Program Senior Manager here at the Conservatory.

If you come here for a camp or nature school or you visit the children's garden, I help make those programs happen.

We try to integrate math into a lot of our educational programming, and sometimes it might be in ways that you wouldn't expect or ways that are a little bit unique.

So, for instance, when we schedule our programs.

So, on a busy day, we can have up to 500 students here on a day to visit for field trips.

When we're scheduling our programs, we have a pretty intricate table that we use that sort of has all of the different times that we can schedule a program.

On one side, all of the different programs that we can do across the top, and then we're able to slot all of our schools into that table.

Another way that I use math is when we're trying to identify different butterfly species or figure out the gender of a butterfly.

We are looking at patterns, so we might be taking measurements to see how far apart different spots or veins or stripes on a butterfly are.

We might be counting those, and that helps us identify those butterflies.

Butterfly bodies are symmetrical.

If we were to draw a line down the center of the butterfly, right through its body, both sides, left and right would be the same.

So, their wings have the same pattern on both sides, they have two wings on each side, and everything should theoretically match up.

The conservatory wants to plant a symmetrical vegetable garden.

They wanted to have reflection symmetry.

What plants are missing on the right side of the line?

[clock ticking] We needed to add some lettuce and a carrot, just like this.

Look, here is the line of symmetry, or this is the spot where if you folded the vegetable garden in half, the two halves would perfectly match.

Did you get it correct?

I've actually been at Franklin Park for 7 years, and have absolutely loved being within the public garden space.

Each day that I work is totally unique, and it's really cool to be able to apply the skills in different ways.

I use math and art together all the time in my career now.

As an adult, if you enjoy math, please stick with it, and don't let other people tell you that you shouldn't enjoy it.

My name is Jessie.

My name is Courtney.

My name is Katie.

I'm an educator.

I'm an exhibitions designer.

And I'm a horticulturalist.

And this is How It's Math.

Wow, look at all the ways math helps things move, grow, and stay organized.

Today, we saw professionals using math to arrange shipments, compare race times, and find the symmetry in butterflies.

Whether it was using arrays, working with decimals, or recognizing symmetry, math helped make sense of how things are organized and how they work.

The next time you receive a package, watch a race, or see a butterfly, 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.

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