Photo courtesy of Matt MacGillivray

It’s the last post of June, but we have a lot more summer to go. That means a lot more opportunities to enjoy the outdoors — and expose ourselves to damaging UV rays. Not only is a burn uncomfortable (or downright painful), but it comes with a whole host of other problems, from wrinkles to cancer. Take a look at these facts from the Skin Cancer Foundation:

• More than 3.5 million skin cancers in over two million people are diagnosed annually. That’s more than the combined incidence of cancers of the breast, prostate, lung and colon.
• One in five Americans will develop skin cancer in the course of a lifetime.
  
• Over the past 31 years, more people have had skin cancer than all other cancers combined.
• Between 40 and 50 percent of Americans who live to age 65 will have skin cancer at least once.
• One person dies of melanoma every 62 minutes.
• One or more blistering sunburns in childhood or adolescence more than double a person’s chances of developing melanoma later in life.
• A person’s risk for melanoma doubles if he or she has had more than five sunburns at any age.

So that’s a lot of numbers and statistics. (Believe me, I only shared a fraction of what I found.) But there are other really important numbers to consider: SPF or sun protection factor.

Basically, SPF is the estimate of time that you can be in the sun without burning. This is really easy math. Let’s assume that without sunscreen, you would burn after 15 minutes. If you used a sunscreen with SPF 15, you’d be able to stay in the sun 15 times as long without burning:

15 minutes • 15 = 225 minutes

225 minutes ÷ 60 = 3.75 hours

If you used a sunscreen with SPF 30, you be able to stay out twice as long:

15 minutes • 30 = 450 minutes

450 minutes ÷ 60 = 7.5 hours

But can you add SPF values? In other words, if you put on SPF 15 and then SPF 30, would you have SPF 45? Mathematically speaking, yes. But in actuality, nope. You’re only as good as the highest SPF you applied.

It’s also important to note that SPF ratings are averages. So while these calculations can help protect you from a nasty burn, you can’t count on them for down-to-the-minute protection. (There’s that imprecision-of-math thing again.)

There are also many, many other variables to consider — including time of day (sun exposure is harshest between 10:00 a.m. and 2:00 p.m.), location (water and sand reflect light, intensifying the rays) and activity levels (sweat and water can cause sunscreen to wear off).

The bottom line? You can do all of the calculating you want, but the only sure-fire way to prevent a sunburn — and the health risks associated with it — is to avoid the sun. Protective clothing can help, along with staying out of the sun when it’s at its strongest. And look for new labeling on sunscreen products. Last summer, the Food and Drug Administration (FDA) introduced new rules for these products, which will start showing up next summer.

This is perhaps the most basic math of all, so there’s no need to make it complicated. For once, you don’t need to multiply or do figures in your head. Just follow these simple rules:

1. Wear the highest reasonable SPF levels. (The FDA says SPF 50 is the best you can do.)

2. Everyone needs sunscreen. All skin types can burn or at least suffer from skin damage. So even if you have dark skin, apply sunscreen.

3. Cover up as much as possible, with broad hats, swim shirts and umbrellas.

4. Avoid the sun at peak times, especially if you plan to be on the water or beach.

5. Reapply sunscreen at least every two hours, more often if you’re sweating or getting in and out of the water.

Simple, eh?

How do you manage the sun and outdoor activities in the summer? If you have cool tips to share, post them in the comments section!

On Monday, we’ll take off on a month of travel math. Got questions? Let me know, and I’ll track down the answers.

Photo courtesy of wildxplorer

On Monday, Cristina Santiestevan of Outlaw Garden shared a post about the geometry of gardening, introducing us to the idea of “hexagonal spacing.” This was such a cool idea that I thought I’d explore it further. I wanted to know the math behind it. In other words, why are hexagons so darned special?

Let’s start by with the bees. In research for a magazine assignment, I’ve done some reading about bees lately, and once again, I’m in absolute awe. These little guys are the linchpins of our ecosystem in a lot of ways. Not only does their pollen-collecting insure the reproduction of a variety of plant species (and therefore the survival of critters that depend on these plants), but their colonies are efficient little factories that seem to mirror human manufacturing — from the dance the workers do to relay directions to the best pollen to the efficiency of their job descriptions.

And then there are the hives. If you think of the bees as efficient — and they are — you can deign why the hive is made up of tiny hexagons. (Remember, a hexagon is a six-sided figure.) Not wanting to waste any space whatsoever, the bees figured it out: instead of making circular cells, which leave gaps around the sides, they create a tessellation of hexagons, which leave no empty space at all.

(A tessellation is the repetition of a geometric shape with no space between the figures. Think M.C. Escher or a tile floor.)

The same concept applies to gardening. Why waste space? As Cristina pointed out, choosing a hexagon-shaped planting scheme, you’ll get more plants in your beds.  And if you’ve got an outlaw garden, like Cristina, it’s best to make the most of your space! Here’s how:

In regular rows, you plant 6″ apart in only two directions, getting nice, even rows. But if you consider six directions, you’re replicating the hexagon, instead of a square — and as a result maximizing your space (just like the honey bees). Cristina describes it as planting on the diagonal. Or you can think of each plant at the center of the hexagon.  Then you can plant the others 6″ from the center in six directions — creating the vertices of the hexagon. (If you’ve ever looked carefully at a Grandmother’s Flower Garden quilt pattern, this idea might jump out at you. Not only is each plant the center of a hexagon, but it’s also the vertex of another hexagon.)

Did you see what I did there? Math can be described in a variety of ways! Look at the second diagram carefully, and see what jumps out at you — the hexagons or the diagonal rows?

So there you have it. We can learn a lot from a bee. And I can already think of times when this can be useful in other areas. How many more cookies can you fit on a cookie sheet, if you arrange them diagonally (or in a hexagon shape) rather than horizontal rows? What about kids desks in a classroom?

Where can you apply the hexagon to make your space more efficient? Share your ideas in the comments section!

My thumb isn’t even remotely green. The only plants I have any success with are those that can sustain a tremendous amount of neglect — like hydrangea, hostas and lariope. So I asked fellow write and founder of Outlaw Garden, Cristina Santiestevan to step in with some gardening math. She does not under-deliver! Check out the mad geometry skills she has. Then put her tips to work in your own garden. 

In the garden, math is everywhere. There’s arithmetic and subtraction, which gardeners use to estimate how long it will take for a tomato to ripen or a seed to sprout. There’s multiplication, which helps gardeners calculate expected yields. And, there’s higher math too. Lots and lots of higher math.

Yesterday, for example, I used a measuring tape and a bit of high school geometry to confirm that my tomato trellis would be a nice (right-angled) rectangle, rather than a slightly askew parallelogram. I also used an online calculator, because figuring out the square root of 10,116 isn’t especially easy to do by hand. I knew I’d get a number close to 100, but I wanted to be sure.

Turns out that the square root of 10,116 is 100.57832768544127. I rounded to 100.5, because my measuring tape isn’t quite that fine-tuned.

If you haven’t guessed yet, I was using the Pythagorean Theorem: a² + b² = c². As an avid DIYer, I use this formula a lot. It’s a great way to be sure that your project will be square, with four right angles. That’s essential if you’re building any sort of box, especially if you’ll be adding a door later. A slight skew away from 90° can create all sorts of trouble.

In this case, the motivation is all aesthetics. This trellis could work fine as a parallelogram. The tomatoes wouldn’t even notice. But, I would.

So, here’s how I did it. The trellis is 96 inches tall and 30 inches wide. Those are our a and b sides. Putting them into the equation, we get 96² + 30² = c². That works out to

9216 + 900 = c²

10,116 = c²

This is when I googled “square root,” in hopes of finding an online square root calculator. I knew it would come in close to 100, because 100 • 100 = 10,000. But, I wanted to be as exact as possible. That’s where the online calculator came in handy. The answer — 100.57832768544127 — was more precise than I really needed. 100.5 inches is plenty good enough when building trellises in the garden.

With that number in mind, I measured the diagonal from top to bottom on both sides of the trellis. One side measured about 100.25 inches and the other measured about 100.75 inches. A slight adjustment, and both sides measured 100.5 inches. The trellis was square. Success!

Here’s the plan for the trellis. You can see where the right triangle would go:

(Cristina has a great post detailing the step-by-step process for building her trellis, including a downloadable pdf of her plans. Check it out here.)

Trellises aren’t the only place we use and see geometry in the garden. The Pythagorean Theorem is a great help to gardeners who want to ensure their garden beds and paths are perfect squares or rectangles, for example. And, equilateral triangles — three equal sides — provide guidance when planting the garden. While most books tell us to plant our vegetables in rows that are square to each other, that’s not the best way to maximize our garden space. No. Instead, plant your rows on a diagonal, using an equilateral triangle as your guide, and you will be able to fit more plants into the same amount of space. Like this:

See how a series of six triangles creates a hexagon in the diagonal planting pattern? That’s where the extra space efficiency comes in; you’re basically planting on a hexagonal pattern. And, as bees already know, the hexagon is the most efficient shape.

Even plants have geometry. All members of the mint family have perfectly square stems, like this bee balm:

Sedges — a grass-like bog plant — have triangular stems. Some plants, like dogwood and maple trees, follow a perfect symmetry with their leaves. These are known as opposite plants, because their leaves form opposite one another on their branches. Alternate plants, on the other hand, form their leaves singularly or in groups, on alternate sides of the branch. Other plants grow their leaves and flowers in whorls or rosettes:

The dogwood has opposite leaves.

Virginia Sweetspire has alternate leaves.

The leaves of the culversroot are in a rosette pattern.

And, the Fibonacci Sequence is everywhere:

The pattern of the yellow spirals in this chamomile are based on the Fibonacci sequence

Thank you, Cristina! My advice to you, dear reader: do not miss her blog, Outlaw Garden; it’s funny, informative and really, really clever. Do you spend time in the garden? What kind of math do you use and see while tending your plants? If you have questions, don’t hesitate to ask in the comments section. Don’t worry, I’ll ask Cristina to come by to respond. (It’ll be better that way.)

Photo courtesy of mark roy

Lordy, it’s hot. And the heat makes me cranky. When I saw that the temps were creeping up to the 90s and beyond this week, I vowed to stay in the airconditioning. Trust me; it’s best for everyone involved.

So don’t even tell me what the heat index is. I really don’t want to know. But I have always been fascinated with how it is calculated. What are the variables that affect the heat index? Let’s take a look.

The heat index is how it really feels when the humidity is figured in. (Those of you who live in a climate with dry heat have no clue about this. Count yourselves lucky.) When the humidity is high, the heat index goes up, producing a hot, sticky mess that makes my hair frizzy and sours my otherwise lovely temperament.

The thermometer may say 95 degrees Fahrenheit, but if there’s significant humidity, it might feel like it’s 105. But of course meteorologists don’t guess at this number. There’s an actual formula that’s used to find the heat index.

Before we get to that, let’s consider the variables involved. According to the National Oceanic and Atmospheric Administration (NOAA), there are 20 (yes, twenty) variables that are used to calculate the heat index. These range from vapor pressure to the dimensions of a human to ventilation rate to sweating rate (ew). Because most of these are very specific to each person, a mathematical model was used to determine an appropriate range for each. This allows meteorologists to use a (relatively) simple formula for finding the heat index:

HI = -42.379 + 2.04901523T + 10.14333127R – 0.22475541TR – 6.83783(10^-3T²) – 5.481717(10^-2R²) + 1.22874(10^-3T²R) + 8.5282(10^-2TR²) – 1.99(10^-6T²R²)

Pretty, right? It’s actually not that hard to understand, if you break down the pieces. First, let’s define the variables.

HI = heat index

T = ambient dry bulb temperature (in Fahrenheit)

R = relative humidity (integer percentage)

So there are basically three variables, one being what we are looking for — the heat index. If you were to use this formula, you would need to know two things: the ambient dry bulb temperature (which is merely the ambient temperature as measured by a thermometer) and the relative humidity.

If you put to work the logical part of your brain that notices connections and patterns (yes, you do have one), the math becomes clear. When the temperature and relative humidity go up, so does the heat index. How do you know that? Look at the equation. It’s full of addition and multiplication. In fact, aside from the negative exponents (which actually yield smaller numbers), the equation is based solely on increasing values.

(That is, unless you have negative values for T and R. But in that case, you wouldn’t be figuring the heat index, right? A negative T means a negative air temperature, which is really cold in Fahrenheit. And I’m not sure that relative humidity can be negative at all.)

Now, almost nothing is absolute in weather prediction and measurement, right? And this equation is no exception. As NOAA points out, this equation is created by multiple regression analysis, which means it is not exact. (Basically, in this process, the mathematicians are fitting points to the closest line. Think of a bunch of points on a graph and how you can draw a predictable line or curve that is closest to all of those points.) There is in fact an error of ±1.3 degrees Fahrenheit. But what’s 1.3 degrees when you’re looking at a heat index of 102? Either way, it’s still darned hot.

How do you manage the heat? Do you head inside or hide in a cool, dark place? Share your ideas in the comments section.

Photo courtesy of thebittenword.com

As a child, the only time I ever heard my mother use the f-word was in reference to green beans. It was the summer that my father put in a huge garden at our house, and she was sick of it. When he came home from work one day, asking if she had picked the green beans, she threw down her dishtowel and responded with: “You go out there and pick the you-know-what green beans.”

That was the last time we ever had a garden, but it certainly wasn’t the last time my mother canned. As a little girl, I never had store-bought green beans, canned tomatoes or pickles. These were all preserved in Ball jars and stored in the basement for year-round eating. And while I’ve never canned myself, I am interested in at least pickling a few cukes this summer.

So where’s the math? Well, it’s everywhere in canning. Just like with cooking, preserving foods requires recipes — and then there’s the part about taking a huge pile of fruits or veggies and divvying them up into a series of jars. Yep, math.

See, canning is hot, hard work. In the middle of summer, you need to boil large pots of water, keep the jars warm in a hot dishwasher, the oven or a water bath. The last thing you want to do is run out of jars or lids in the middle of this entire ordeal. Doing the math upfront means you can get in and out of the kitchen without an added trip to the store (or your next door neighbor’s).

Turns out there are easy-to-follow charts and tables for dealing with yield. But if your garden — or trip to the farmer’s market or pick-your-own farm — doesn’t yield the exact amount on the chart, you’ll need to do a little math.

Drew’s humble green-bean patch is overflowing. After convincing the kid down the street to pick all of them (for a small fee, of course), he sits down in front of the television to snap them. (The Olympics and snapping green beans are a perfect combo.) At the end of a few hours, he estimates that he has about 16 pounds of green beans. Whoa.

If he cans all of these beans, how many quart jars will he need? Turning to a trusted web source, he learns that a quart jar will hold about 2 pounds of green beans. Easy math: 16 ÷ 2 = 8. So he’ll need 8 quart jars.

He’s got 15 quart jars in the basement, so the green beans are covered. But he also needs to put away his tomatoes. Will he need to buy more jars?

After canning the green beans (and not using the f-word even one time — such restraint!), he considers those ruby red fruits. This time, he picks them himself, ending up with about 15 pounds. Consulting his yield chart again, he is faced with another decision: crushed or halved/whole? Canning tomatoes is a little more work, since he’ll need to skin them first. He decides to look at the yield for each option before making up a plan.

Crushed tomatoes yield 2.75 pounds per quart, while halving them or leaving them whole yields 3 pounds per quart.

Crushed: 15 pounds ÷ 2.75 pounds= 5.5 quarts (about)

Halved/whole: 15 pounds ÷ 3 quarts = 5 quarts

He’s already used 8 of his 15 quart jars, leaving him with 7. So he’ll have plenty of jars either way. If he crushes the tomatoes, he’ll need a couple of pint jars (because there are 2 pints in a quart). So, he decides to leave the tomatoes whole (or cut them in half, if necessary).

And with two quart jars left over, he decides it’s time for pickles!

Do you have plans to can anything this summer? Share your resources, tips, recipes and more in the comments section. I need inspiration!

A programming note: I am changing my posting schedule a little — at least for the summer. Math at Work Monday interviews will now appear twice a month, rather than every Monday. If you have suggestions of folks I should interview, let me know!

Photo courtesy of Selena N. B. H.

I’m on vacation! (Can you tell?) So this week’s schedule is way off. But when I saw that Lee Doyle, owner of BTO Self Serve Yogurt in Colorado had sent along her Math at Work Monday responses, I decided to spend just a few moments during a delicious hotel breakfast of Cheerios and milk to post the interview. Then I’m back in the car, headed to Cincinnati to my cousin’s wedding.

There’s nothing better than a cool treat on a hot summer’s day, and since I was a little girl, the options have expanded exponentially. From popcicles to snowballs (a Maryland-only experience) to frozen yogurt — ice cream isn’t the only sweet, cold treat available. At the Doyle’s Highland Ranch location of BTO Self Serve Yogurt, you can create your own delicious treat. But first, the math:

Can you explain what you do for a living? 

I am responsible for creating and making all the yogurt at the shop, buying ingredients for recipes and estimating useage of product and toppings weekly.

When do you use basic math in your job?

I use math all day, everyday. Since I create and follow recipes, I use addition, subtraction, liquid and dry measurements, fractions, estimation, equivalency charts multiplication, division, just about every kind of basic math you can think of. For example, if I am creating a new recipe, I use one cup of our basic yogurt and add a teaspoon or tablespoon of various flavors to come up with a new flavor I like. Then I have to write a recipe using a gallon of basic yogurt, because all our recipes are based on one fluid gallon.

Do you use any technology to help with this math?

When I shop for ingredients, I use a calculator constantly to determine price per ounce to be sure the ingredients are within our pricing guidelines.

How comfortable with math do you feel?

I always liked math and feel very comfortable using it. In high school, I took algebra, trigonometry and solids but did not take calculus.

Do you have questions for Lee and Jack? Ask them in the comments section. And of course stay cool with a sweet treat, like frozen yogurt.

Photo courtesy of Patrik Jones

I am not a particularly athletic or physically active person. If given a choice between a hike through the woods or a book and a hammock, the good read always wins out. I start and stop exercise routines at least once a year — usually more. But I do have a bicycle, and once a year, I sit atop that tiny seat and pedal my way through 14 miles of parks in Baltimore.

That was yesterday, and today I’m paying for it, big time. Not only do I have a funny-shaped sunburn on my back (from the one cool exercise shirt that I have), but my legs and feet and rear end are screaming: “What the hell??” Still, I know I’ll do this next year, too. Because it’s the one time a year that it’s worth hoisting three bikes on top of our car and driving 15 minutes away to explore the city parks.

Of course, I think about the math involved. Between birdwatching and listening to my almost 12-year-old complaining, what else is there to do? Here’s what I came up with.

1. I woke up yesterday morning with one thing on my mind: I do not want to spend all day on a bike. But would it be all day? Not likely. So I went to the interwebs to help me estimate the time I’d actually be cycling. Here’s what I found:

For the kind of biking I was about to do, an average speed is about 10 miles per hour. I didn’t even bother with a formula; this information was enough to help me estimate that I’d be pedaling for about 90 minutes or so. (I figured I’m slower than average, we’d have one 5-minute break, and we were biking 14 miles, not 10.)

How did I do with my estimate? Not bad. We pushed off at 9:00 a.m. and were munching hamburgers and hotdogs by 11:45 or so.

2. I once thought that the pedals and brakes and chain were the most important parts of the bike. But it turns out that the seat height has more to do with a comfortable ride than most anything else.

Last year, I spent the first half of the course on a seat that was way, way too low. My thighs were burning by the time we hit the rest spot. Luckily, there was a bike tech there who showed me how to adjust my seat and where. I thought I would fall off the precipitous height when he was done, but the rest of the ride was a breeze, comparatively speaking.

Here’s how it works: The leverage of your pedaling is controlled by the seat height. If your seat is too low, you’ll work way, way too hard to get up even the most modest hill. In other words, when your seat is adjusted properly, you’ll get the most efficient pedal stroke. (And your rectus femoris muscle will thank you.)

There are formulas and online calculators that can help you figure this out. But as a once-a-year biker, I rely on a simple idea. When sitting on my bike, I position my feet at 12:00 and 6:00. If my leg is completely extended in the 6:00 position, my seat is at the correct height.

There’s tons more math in cycling, I’m sure. But as a novice, these little calculations and estimates are enough for me. By next year, I’ll forget how sore I am today — and the trouble it is to get our bikes into the rack — and hit these trails again.

Are you a cycler? What math have you used to help keep your pedaling efficient or manage your rides? Share your ideas in the comments section.

Wait! Isn’t it Monday? Where is Math at Work Monday? It’ll be back, I promise. I had some scheduling problems with some sources, so you may see an interview later this week. Don’t worry!

Photo courtesy of puuikibeach

Whether for graduation or summer camp or a great trip, a memory book or journal can be a nice way to remember a special time. And since I’m currently addicted to Pinterest, I’ve been browsing tutorials–from simple booklets to fancy, bound books. And then there are flower-pressing books and books constructed with homemade paper. The options are endless. (And they’re all so inspiring!)

From my days as my high school yearbook editor, I know that there’s a little formula used to find the number of pages that a book can have. If you need to have a certain number of pages (at least), you’ll need to employ that tidbit of information. But first you must know how many pages you’d like to have in your book.

Your teenager is headed off for a two-week long camp in the woods. She loves to write in a journal, and you’d like to make her a special book to take with her. If she uses three pages per entry, how many pages does her journal need to have?

Let’s assume she’ll be journaling every day of her two-week stay. And let’s assume that she’s leaving on the last day. So that means she’ll journal for a total of 13 days (that’s two weeks, minus one day), and she’ll need a total of 3 • 13 or 39 pages.

But here’s where you’ll need a little book-making insider information. Books are actually made up of signatures, which are sets of folded paper. You can put as many pieces of paper you want in a signature, and you can put as many signatures you want in a book — but the resulting page count will always be a multiple of 4.

(Don’t panic if you don’t remember what a multiple is. Look carefully at the word. You’ll probably notice that multiply is a root, which may cause you to think of multiplication. You’re on the right track. A multiple is a product of two numbers. So the multiples of 4 are: 4, 8, 12, 16, 20, etc. That’s because 4 • 1 = 4, 4 • 2 = 8, 4 • 3 = 12… well, you get the picture.)

In your book, the number of pages must be a multiple of 4, and you need at least 39 pages. Your first question: Can my book have exactly 39 pages? Nope. That’s because 39 is not a multiple of 4.

You need to find a number close to 39 that is a multiple of 4, and you have two obvious choices: 36 (4 • 9) and 40 (4 • 10). Of course, you’re going to chose 40; otherwise, your daughter won’t have enough pages in her book. (Better to have too many than not enough.)

Now you can decide how to create your signatures. I leave those details to the experts. Besides, you need to choose a book style first. Take a look at these great resources I found on Pinterest. Pick one, and have fun!

The Pioneer Woman Makes a Book (from a granola bar box)

Mini Jotter How-To from The Guilded Bee (by way of oh hello friend)

Flower Pressing Book from Family Fun

Teeny-Tiny Leather Spell Book from Ruby Murray

Rainbow Art Book

Have any tips for making memory books? Share them in the comments section!

Photo courtesy of Jason Riedy

I grew up a few miles from the Appalachian Trail in Southwest Virginia and my grandparents lived in the Shenandoah Valley, near Big Meadows a popular stop-off for trail hikers. While I’ve never had any inclination to take the entire trail from Georgia to Maine, I have done a few tiny sections — an hour or two hike each.

It’s way too late in the year to start a thru-hike (doing the entire trail), but a section hike would be perfect for a lazy summer day. These are generally less than 5 miles, though you could string together two or more for a weekend adventure. And if you’re nowhere near the Appalachian Trail, just choose another trail to explore.

But how much time should you allot for your hike? This is an important consideration, since it will determine the time you set out (there are no lights on the trail, so once the sun sets, it’s black as pitch) and what you’ll need to bring (food and water are essentials if you’re planning to be gone more than an hour or so).

Experienced hikers can probably gauge how long it will take to hike a given number of miles. But if you’re like me, you don’t have a clue. That’s where pace counting comes in. The length of your stride will tell you how many steps it will take you to go a certain distance. From that, you can get a good estimate of how long it will take you to complete the hike.

To measure the length of your stride, you’ll need two pens, a tape measure and a long hallway or sidewalk. Place one pen at the end of the hallway or sidewalk and stand with your feet together and hells against the pen. Now, walk 10 steps, taking normal strides. After the tenth step, bring your feet together again, and place the second pen behind your heels. Measure the distance between the pens, using the tape measure. Then divide by 10 to find your stride length. Ta-da!

Another method is to estimate your stride based on your height. There’s a simple formula for this, but you’ll first need to have your height converted to centimeters. If you’re a man, multiply your height (in cm) by 0.415; women will multiply by 0.413.

Once you have your stride length, you can use this to estimate the number of strides you’ll take when hiking a particular distance. Let’s say your stride is 28 inches long, and you’re hiking the Chestnut Knob section in Virginia, which is 2.6 miles round trip. How many steps will you take in that hike?

Ultimately, you’re going to divide the total hike by the length of each stride. But that means you need to have these measurements in the same unit. In other words, you need to convert 2.6 miles to inches. There are 63,360 inches in a mile, so the entire hike is 2.6 • 63,360 or 164,736 inches. Now divide, to find the total number of strides:

164,736 ÷ 28 = 5,883

So on this hike, you’ll be taking a total of 5,883 strides. Still, you don’t know how long the hike will take you, right?

For that step, you need to know how long it takes you to walk a certain number of strides. Let’s go back to the where you found your stride length. If you timed how long it takes you to walk 10 paces, you can easily find the time, right? All you need to do then is use a stopwatch while you take 10 paces. Let’s say that value is 6 seconds. A little bit of math will get you closer to your answer.

First, divide the total paces by 10. Why? Because your time is based on 10 paces, not one.

5,883 ÷ 10 = 588.3

Now multiply this answer by 6 or the number of seconds it takes to walk 10 strides.

588.3 • 6 = 3,529.8

So, it will take you 3,529.8 seconds to hike this section of the trail. It’s probably easier to understand, if you convert this to minutes or hours.

3,529.8 ÷ 60 = 58.83 minutes or just under an hour

Of course this estimate assumes a lot of things: that the terrain is easy to maneuver and that you’re not going to stop to look at the view of Burkes Garden. In other words, you can bet that you’ll be on the trail for longer than an hour, especially if you’re there to metaphorically or literally smell the flowers.

Still, you can use these calculations to estimate the time it will take you to complete any number of hikes. Once you know your stride length and the time it takes for you to walk 10 paces, the math is pretty simple.

What kind of hiking do you love to do? How have you used math to help you plan a hike or other outdoor activity? Share your stories in the comments section.

Photo courtesy of Randy Son Of Robert

Whether a day or sleep-away, camp is a perineal part of summer for many families. So today, I introduce you to Joelle Kelenson, Director of School Age Programming for the Jewish Community Center of Northern Virginia. She uses math, and she doesn’t even run a math camp!

Can you explain what you do for a living?

During the school year I am in charge of managing the before and after school program at the Jewish Community Center of Northern Virginia. The program encompasses 150 children and 30 part-time teenage and college staff. I am responsible for ensuring that our program is up to the health and safety standards of our license, that the children get a healthy snack, training the staff to ensure the well being of all children, that all supplies are purchased, and that all information is communicated with parents. During the summer I switch hats and become the assistant camp director. I develop programming and curriculum for our summer camp, supervise the units heads and specialists and ensure that camp is running smoothly.

When do you use basic math in your job?

I use very basic math in my job like counting how many children are in a room to ensure proper ratios. I also use math to add up staff hours for payroll. In addition I manage a budget of $160,000 so I need to use math to make sure I’m on top it and know where I’m at spending wise.

Do you use any technology to help with this math?

I use a calculator to do my payroll and a formulated Excel spreadsheet to help me manage my budget. I’m also not very good at math so I often use my fingers to count.

How do you think math helps you do your job better?

If I didn’t use math in my job, my program wouldn’t be up par, we would run a defict and our staff would probably get paid more than they actually worked. Math helps me stay on top of things and manage things.

How comfortable with math do you feel?

Over time I’ve gotten better and more comfortable using math. Most of my math is basic, it was the math of managing the budget that at first made me nervous, but now I’m getting better with it.

What kind of math did you take in high school?

I grew up in Montreal and took advanced math called 436 and 536 in my junior and senior year.  I was never good at math. It didn’t come naturally to me and I hated it, but I worked hard and did well in the classes — except that midway through my senior year, I gave up and barely passed my senior math class. As a result I was forced to drop out of the sciences like physics and chemistry and take more social science classes.

Did you have to learn new skills in order to do the math you use in your job?

I did not need to learn anything new but rather refresh myself on the basics. I did however learn the benefits the Excel formulas and how they are helpful!

Thanks, Joelle, for being our Math at Work Monday interview today. If you have questions for Joelle, ask them in the comments section. I’ll make sure she sees them and has a chance to respond.