-Funding for "Doodles and Digits: How It's Math" provided in part by... -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 grow more good everywhere.

♪♪ -Hi.

I’m Caroline from "Doodles and Digits."

And have you ever been curious about how math is used in the real world?

Well, today we get to go behind the scenes of three different industries and see how they use math every single day.

First, we get to go behind the scenes of a bakery and see how they use math when baking these delicious baked goods.

Then, we get to go and see how an architect uses math to build houses.

Finally, we get to go and have a sneak peek of how a dentist uses math every single day to make sure your teeth stay clean and healthy.

Let’s get into it.

♪♪ -♪ Doodly doodle, doodly doodle ♪ ♪ Doodly doodles and digits ♪ ♪ Area, symmetry, fractions, too ♪ [ Bell ringing ] ♪ It's all here for you ♪ ♪♪ -My name is Wendy Miller Pugh.

I am a co-owner of Bake Me Happy, a 100% gluten-free bakery.

We started in 2013.

I believe we moved down here in Merion Village in 2014.

So, do the math on that.

[ Laughs ] In a bakery, we use tons of math, from using measuring cups, doing fractions, percentages, scaling up things, or sometimes if we missed an ingredient, a lot of times we have to do a percentage to try to get back to where we were supposed to be.

Multiplication with counting our cookies.

Like, our trays are always usually the same configuration of cookies.

So, um, you know, we can do like a 4x6.

That’s 24.

We have 10 trays, that’s 240.

So, we do that quite a bit.

There is literally math everywhere.

A lot of people might think that you just start from total scratch with a recipe.

What I do is I start with a base recipe.

So, say we wanted to make a new muffin.

We have a muffin recipe that is pretty solid that we can change it to what we need.

We would change the ingredient by trial and error.

That’s a big thing.

If we want it to be a more dense muffin, we would add more flour to it, maybe more fat, like sour cream.

We want it to be lighter for us, gluten-free.

We have different flour alternatives.

We have different mixes that create different textures.

So, a lighter mix might be lighter grains, like rice and tapioca flour, like starchy things.

Something denser might have more, like, sorghum flour or brown-rice flour.

I remember when I first started, we have a spicy peanut-butter cookie, and that went through a million different iterations to get the right level of spice, so it wasn’t, like, obliterating your taste buds.

-Quick questions with a baker... Why do you love math?

-I did love doing math when I was growing up.

My favorite thing was figuring it out.

Like, I am a lover of puzzles and different tricky word things or math games, and I just felt like I always liked to do math.

There was always a correct answer.

It was never open to interpretation, and there were always different ways to get the correct answer.

So those are the things I really loved about math growing up.

-How do you use fractions?

-I know that a lot of people are scared of fractions.

They’re hard.

The systems with getting the denominators the same -- very frustrating.

We use them a lot.

Measuring our ingredients obviously in the cup, scaling up, a lot of times it’ll be like, "Let’s use a quarter cup more or half a teaspoon more."

But yeah, all the cups are in increments of a third, a fourth, a half.

Knowing that if I need seven-eighths of something I can take out, you know, what is an eighth of cup?

I don’t have an eighth-a-cup measure, but I know an eighth a cup is a half of a fourth of a cup.

So, just knowing those basic things so you can get the guesstimations.

-How important is it to be precise?

-Baking is really a science.

Cooking is more of a creativity-based activity.

Baking, you need to have the right amount of materials and right amount of proportions of your different ingredients, especially a leavener, which is like your baking soda or baking powder.

You do need the right proportions in your recipe, or it won’t come out right.

-What measuring tools do you use?

-We use a lot of rulers with cutting things to make them precise.

We use the cup measures, the teaspoon measures.

We use scales, liquid measuring cups, which are ones that have the handle, which is exactly, you know, a fourth a cup in a cup is going to measure fourth a cup in the liquid.

But it’s just easier.

We have timers.

We have a base time that we have for all of our items.

-How do you figure out the price?

-This is the hardest.

And I think this is where a lot of businesses might fail.

And this is where I do a lot of math, and I kind of like it, but it’s hard to get everything in the right measurements, I think.

So, my spreadsheet, it will have -- I’ll have a recipe I’m using in mind, and it will say butter.

A case of butter is how much?

A case of butter is $100.

So, you put those two measurements in, and then how much do you use in the recipe?

And then it calculates how much money you use in the recipe.

And it creates the price for that.

[ Cash register dings ] So, and we have to keep an account of the labor of someone making it.

So, the labor means, say I’m the person making it, how much I get paid an hour or how much my time is worth, and then how long it takes me to do it.

And then also, if we package it, the packaging price, how long it takes you to package it, any labels you might put on it.

Say a roll of labels cost $200.

There’s a thousand labels on the roll.

How much is one label?

It’ll give you a price of how much money you put into it.

Most people will do a markup of, like, 30% to 50%.

Depends on the product.

And then you kind of compare that to your other products.

Like, does this price of $3 fit with my other products, or is it really low or is it really high?

And sometimes you have to adjust it so it kind of fits within your whole array of your products you have.

It’s a lot of math, especially figuring out, like, say, a 25-pound bag of flour, how much that costs, and then how much does a fourth of a cup weigh, and then how many fourths of a cups are in this 25-pound bag?

How much was my bag?

And so it’s a lot to figure out.

And I think a lot of people starting businesses, they fail to do all that hard work because it’s hard.

It is hard.

It’s time-consuming.

-What is your best piece of advice for math students?

-I think right now, math, as we’ve seen how I did it when I was younger and now seeing where my daughter is, there are more than one way to get to an answer.

You might ask your mom or dad to help, and they’re not doing it like your teacher does.

But there are many paths in math.

If you’re doing it correctly, you’ll get to the same answer.

So, I think that’s the one thing that’s kind of amazing about math.

We all think differently and our brains learn differently.

I always told them that math was everywhere.

You think that you’re working on these problems at school, and you’ll never use them again, and, really, you will use them whether you are a baker or whether you are something that’s math heavy, like an accountant, or whether you are something you think you’re never going to use math again, like, I don’t know, a cosmetologist who colors hair.

She still has to weigh out the hair dye.

So, it really is everywhere.

And calculators are okay to use.

Believe me, I even have to calculate 8x6 sometimes because my brain just isn’t working, and I’m not very good at multiplying my eights for some reason.

[ Clock ticking ] ♪♪ -Wow, that just made me really hungry.

Now that we saw how a bakery uses math, we get to now discover how an architect uses math.

How do you think they use math?

Let’s get into it.

-My name is Jamie Parish, and I’m an architect who specializes in residential architecture.

I have been an architect for about 10 or 11 years and practicing architecture for probably about 20, I would say.

-Okay, so what is an architect?

An architect is a person who designs buildings and advises in their construction.

-Starts with potential clients calling me to see if I am available to do the kind of project that they want to do, and I do custom homes from scratch.

I do addition-and-remodeling projects to existing buildings.

I work on older houses and newer houses, and I kind of like the range that I’m able to do.

Once a client hires me, I will start in the design phase, and that’s where I’m doing everything by hand, sketching out ideas of, you know, we could do the family room here, or we could do it here, and it connects to the kitchen in this way.

So, we look at lots of different options in the design phase of what the possibilities are.

And, of course, what does that look like on the outside?

Once the clients review that and comment on what their likes and dislikes are, then I’ll eventually get into more detailed drawings where I go on the computer and I dimension walls and cabinets and everything else that might need done, any structural work.

I need to think through.

How am I going to add anything to a building and make sure that the weight that’s coming from above is still being dispersed the way that it needs to be.

And that gives us more of an idea of the scope of work of any project.

And then, at that point, I oftentimes bid the project.

So, that means that I will take the design and drawings that we have, and we’ll usually ask a few different contractors to give us prices for my clients.

And that part of my process also includes math, also, because I need to look at all the numbers that they have for all the different parts of a building -- foundation, framing, countertops, cabinets, all of that, and compare to see who’s giving us the best value.

And then once construction begins, I oftentimes will go out to the site to make sure that my drawings were understood properly, because my drawings are in 2-D.

I do a lot of 3-D sketches, but my drawings are very much in 2-D, and so it’s my job to communicate how I want the 3-D structure to look.

-So, now that we know what an architect is, can we have an example of a time that you designed a house using math?

-Before we started this remodel, it was a very small kitchen.

It was probably -- this was probably the edge of it.

So, this was the wall, and this was the kitchen and just your typical 1920's old-home kitchen.

The opening that you can’t see right now, it’s just a door into the dining room.

So, what we needed to do is we wanted to keep the character and the scale of our existing little house but open it up and modernize it for the way that we live now.

I drew all of this out on the computer.

I know to the quarter-inch how much space we have and how I might be able to maneuver things around so that things feel right and look right.

I also do 3-D sketches, too, so not just to show me, but, like, to show my clients this is what the space is going to look like.

This is where the couch is going to be.

This is how it’s going to feel when it’s done.

I measure furniture when I’m designing.

I make sure that every single room, we know exactly how many people we want to sit in that room, what furniture is going to fit, how big or how deep are cabinets?

How deep is this island?

How wide can the island be before it starts to look too long and skinny?

How much walkway space is comfortable?

When you take the dishwasher down, can we still maneuver around it?

There’s so many things that kind of go into making a space feel right and making sure that the functions of the kitchen, even in a smaller kitchen, still move smoothly.

-Quick questions with an architect... Why do you love math?

-I love math because I was able to draw volumes and understand how to do perspective drawings, just really just geometry in general.

-Did you enjoy math when you were growing up?

-I really enjoyed math growing up.

When I was younger, I thought I was really good at it, but as I got older, it got harder, and it was more of a challenge for me.

But I kept working and, you know, and it was fine, but it definitely got harder.

-How do you use area and perimeter?

-I always use area and perimeter when doing designing an addition or doing a custom home.

It’s always important to understand the size of the structure that you’re building -- cost reasons but also just to know exactly how much space you have and how much you need.

-How important is it to be precise?

-It’s very important that measurements are precise, especially when measuring an existing building.

Have to know what’s there and what can be added to that reasonably.

As an architect, I get involved with the structure of a building.

And so it’s important for me to understand how large is a space, how large do beams and structural members need to be because it changes the weight.

-Is it important to show your thinking?

-I show that even from day one.

So, when I’m meeting with a client and showing them the initial designs, which are just hand sketches, it’s important for me to explain to them why I made the choices that I did with their project, because oftentimes when you just look at a space, you’re like, "Well, I think I want to do this."

Well, once you start to dive into the structure and where the load is coming down and how the space actually works now, it might change once I start to look at a project, and it’s important to explain to my client so that they understand exactly why I made the decisions that I did.

And then from us, from contractors, that is important because it’s like I’m taking all the data that I can find, and I will insert that into an Excel sheet on my computer.

I tally up all the information that they’re able to give me to make sure that I am accurate in what I’m expressing to my clients.

-What is your best piece of advice for math students?

-I would say you just have to do what you love.

Find something you’re good at, but find something that you love to do that you can get paid to do and be happy doing it.

And math just happens to be a huge part of what my career is, you know, and I found something that I love and I use math every day.

I use art every day, physics, that kind of thing.

-All right.

Now that we know that architects use area, perimeter, and measurements every single day, now we’re going to discover how dentists use math.

♪♪ ♪♪ -My name is Dr. Joel Richards, owner of Westerville Pediatric Dental, meaning I’m a pediatric dentist, who's a specialist in kids.

-So, how does a dentist use math?

-Oh, yeah, we use math every day, not just the dentist, but also my dental hygienists and my front desk and managers, as well.

Pretty much use it with every single patient.

Oh, we love using fractions.

Actually, every time I do a filling, I use a fraction.

So, say I’m doing a filling.

I use a little bit of numbing sauce.

Right?

The num-num sauce.

So, that num-num sauce I’ll know if I use one full cap that’s, you know, that’s one of the numbing sauce.

But I’ll maybe use a little bit more.

I’ll put in there that I’m using one and a fourth or maybe, you know, one and a half.

So, we use that every time.

And that lets me know, the measurement, how safe we can be, how much we can give that child, as well.

You know, I look at a child and I, you know, generally know their age or what we call when you have certain amount of teeth, it’s called a dentition.

So, you have the baby-teeth dentition, which are called primary teeth, and then the permanent teeth with the permanent dentition.

And when you’re in between there and you’ve lost a couple baby teeth and now you some permanent teeth coming in, it’s called the transitionary dentition.

So, I can look at a child and know, you know, if they’re younger than five or so, they’re probably just going to have 20 teeth, which is what we would expect.

Or if we have about a year, a baby or an infant that’s about a year old, you know, they might have anywhere from, you know, two to eight teeth on average.

It's just kind of interesting because there’s, you know, there’s the clinical stuff, where we’re counting teeth.

But I think a lot of people don’t know.

As a kids' dentist especially, we find missing teeth, extra teeth.

And sometimes we call those extra teeth supernumerary teeth.

I like to call them, like, super-power teeth.

And sometimes I can an X-ray.

I can kind of estimate when those would come in.

So, it’s kind of cool.

So, some people have extra teeth that they don’t know.

And it’s very common that it runs in a family.

So, I always ask questions about if it runs in families, you know, did they have super-power teeth, too?

So, I think that’s really fun.

And sometimes teeth are fused together.

So, when I count, my number might be off because those fused teeth that kind of grew together and they kind of are like cuddling a little bit closer, they, um, you know, now I know the numbers.

So, then I would take X-rays to verify those numbers.

As time, I mean, most obvious one is we try to schedule our, you know, patients a certain allotted time.

So, some appointments may take 20 minutes, some kids might need 30 minutes.

So, we kind of know how to, you know, properly schedule those patients.

So, throughout the day you know, we start at 8:30.

Our lunch is generally 1:00 to 2:00.

So, then in between all those times, you know, I’ll have many patients, sometimes 10, sometimes 15.

I generally know that my hygienist will have about 30 minutes at least to spend with their patients.

So, generally, they will have 15 patients during that day.

We actually do do the metric system.

So, we generally measure things in millimeters.

So, you know, that’s really small.

So, one centimeter is just ten millimeters.

We know that different averages of teeth, though.

So, that’s a really, really good question.

So, when I know like that tooth cavity or sugar bug goes into it, it might go in a millimeter or two.

Sometimes it’ll be a few more millimeters.

And that’s how I can kind of guess or approximate how close we are to the nerve of that tooth, because we want to keep that tooth safe and healthy.

-Quick questions with a dentist... What was your favorite part of math?

-My favorite thing about math?

Definitely not the times tables.

Those were always kind of stressful, and I just know some kids are really super fast at them.

Probably like all you guys, like super good at first, but, um, you know, maybe doing some word problems and throwing in some words in there.

-How do you know what supplies to buy?

-I mean, it depends on the month, because sometimes we, you know, the growing we get more patients that want to come see us and we want to see them.

And then we kind of have averages.

So we actually can set up those averages with our companies.

So, our representatives maybe from Oral-B or whoever is supplying our toothbrushes, they’ll actually know, "Okay, you ordered this much this time.

Maybe we’ll order more this time."

Yeah, yeah, we have a spreadsheet on Excel.

So by keeping track of all that, we can be very prepared because you don’t want to over- or under-buy stuff because then you don’t have it when you need it, or you buy too much and then you don’t have enough to have lunch that day.

-How important is it to be precise?

-Oh, yeah.

Measurements, to be precise, is very critical, especially as a dentist.

We’re working with, you know, a hard tooth, but we’re also working with a live entity of that tooth, which is called the nerve.

And the blood vessels are the pulp.

So, when we want to be really precise with something, we need to know exactly how that looks like.

So, I will take X-rays.

We have seen, you know, millions of these so that we can kind of look at them and we can kind of see how close are we to that nerve if we’re filling a cavity, which is really gentle, and we kind of, um, we'll know if we have the exact measurement.

We know exactly the width of our burrs.

So, the burrs is that toothbrush piece that goes and cleans out the soft part of the sugar bug.

And if it’s getting closer and that tooth bug has kind of turned into a dinosaur egg, we might want to get a little closer, might even put a special medicine.

So, we’re going to be very precise.

We’re actually, believe it or not, in dentistry we can actually kind of measure, even kind of with our eyes a little bit, to the tenth of a millimeter sometimes.

We practice that in dental school, and we still practice that every day.

-Did you enjoy math growing up?

-Um, it wasn’t my favorite, you know, doing math.

But, you know, I’m a science guy for sure.

So, I always love science and history, reading.

But you know what?

Now I realize I use it every day.

Like, it’s kind of phenomenal.

It’s really, really kind of cool how it helps me provide good care to my patients, you know, setting up appointments, and working with my whole team and staff to make the whole appointment safe and fun.

-Do you need to show your thinking?

-Dentists, especially kids' dentists, you know, I work with parents and the child, so I think it’s really, really important to be a good teacher, and to be a good teacher, we’ve got to kind of show things of what we do.

So, I’m really big on pictures.

So, I love, you know, when parents maybe have a toothache, a bump, they can send pictures to me.

Well, I also have little forms that I’ll show them.

And then I’ll kind of review that.

Same thing when I have X-rays.

We don’t just say, "There’s cavities there."

We want to show you.

We want you to understand and see the cavity process.

And sometimes they’re little baby ones, little shadows.

We can maybe monitor them and see what happens over six months and then take new X-rays, or radiographs is what we call them.

But it’s really good to be able to look at those, look at those X-rays, teach and show them, and kind of explain the process.

-What is your best piece of advice for math students?

-I would say I think repetition.

Everything we do, I think in life I always learn better by repetition.

I think someone said that maybe you have to do something 12 times before it becomes a good or like a habit or something.

But when I want to practice something or be really good, you know, it’s repetition.

Perfect practice makes perfect.

-Remember, you can pause to take your time and solve.

[ Clock ticking ] 3 x 1/2... That's the same as... ...which equals three halves or 1.5 hours.

♪♪ Wow, that was a lot of math.

Did any of it surprise you?

Did any of the things that they mentioned you do in math class yourself?

♪♪ -Funding for "Doodles and Digits: How It's Math" provided in part by... -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 grow more good everywhere.