FORMULAS Archives | Math for Grownups

In Math at Work Monday

Math at Work Monday: Nate the Restoration Hero

Properties that are damaged by fire, water, storms, smoke, or mold require the services of a professional. This is a job for Nate Dawson, Restoration Hero and President of Sterling Restoration. Read on to see how he uses math to restore damaged properties back to mint condition.

Can you explain what you do for a living?

Sterling Restoration specializes in emergency repair to real property whether damaged by fire, water, storm, smoke or mold. Sterling Restoration is trusted for high quality and comprehensive cleanup, mitigation, and restoration services for both residential and commercial projects. We are a locally owned company based in Springfield, Ohio serving the Miami Valley and Central Ohio areas. We take pride in knowing that our team of professionals and extensive network of resources have the expertise to return any property to its pre-loss condition as quickly as possible.

When do you use basic math in your job?

Basic math is used in all aspects of our business including our accounting, estimating and production departments. Our accounting department uses it to calculate payroll, receivables, and payables. Our estimators use math more than anyone in our business. During the estimating process for reconstruction, we use square footage formulas (L x W) for calculating materials used, for example: subfloor framing, roof framing , insulation, drywall, painting, etc.. We use square yard formulas (L x W/9) for calculating vinyl floors and carpet. Basic algebra formulas are used for calculating rafter lengths based on the rise and run of roof slopes.

One of our most interesting uses of basic math, and one I will focus on going forward is with water mitigation (returning a structure to dry standard). Basically, drying a wet building! Once we determine the affected area we then use a cubic footage formula (L x W x H) along with the extent of saturation to know how much dehumidification is needed. Dehumidifiers are rated based upon how many pints of water they are capable of removing from the air within a specific amount of time (AHAM Rating). Therefore, depending on the type of dehumidification used and it’s rating, we are able to determine the number of dehumidifiers we need to dry a structure within the standards of our industry (S-500 ANSI approved standard). We also use the atmospheric readings to determine whether we are creating the desired conditions required to remove water from affected materials and to determine the effectiveness of our equipment. To do this we use the temperature and relative humidity to determine specific humidity (the weight of moisture p/lbs of air) and dew point (the temperature at which water vapor will begin to condense). The formula we use to determine the number of dehumidifiers needed is as follows:

Step 1 – Determine Cubic feet (CF).

Step 2 – CF/Class Factor(a low grain refrigerant dehu has a class factor of 40 in a class two loss) = # of AHAM pints needed.

Step 3 – AHAM points needed/Dehumidifier rating = number of dehumidifiers needed.

I know! It’s starting to sound a little complicated but it is all basic math.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

Absolutely! Even though we are in the building trade we are not in the dark ages. We use the most advanced estimating system designed specifically for the insurance restoration (property repair) business. After in-putting the dimensions into a sketch type format, this system automatically calculates all the square footages, cubic footages, and linear footages. The next step is to add a specific line item. For example, when you add drywall to your estimate it uses a current square foot price to calculate how much to charge for hanging, taping and finishing the drywall in your project. It will also calculate how many sheets of drywall, how many fasteners are needed , how much drywall tape, and how much joint compound is needed. Finally, it will calculate the material sales tax and any state sales tax on the service.

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

I do not feel it’s a matter of doing my job better. I simply could not perform my job without math! As I stated earlier, we use math in every aspect of our business. I do not feel there are too many moments throughout the day that I am not using some form of math.

What kind of math did you take in high school?

During my high school years I completed algebra and some trigonometry. If I remember correctly, that was all that was offered (yes, I graduated high school 32 years ago). Once leaving high school I furthered my math education in mechanical engineering. In my opinion, the levels of math being taught in high school today are far superior to what was then taught.

Did you like it/feel like you were good at it?

I feel like there are individuals that have an aptitude for math and those who do not. Math will obviously come easy for those who have this aptitude. I would also say that if you are good at something, the chances of enjoying it are far greater than if you are not good. Having said that, I do not believe I had this aptitude. Therefore, I had to work a little harder than others, and, at best, I was average at math. Guess where I’m going with this…no I did not like it.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pick up using the skills you learned in school?

I had to learn how to use the math skills I had already acquired to accomplish the task at hand. For example, if you have the lengths of two sides and the angle of a triangle, you can calculate the length of the third side. It is crazy how much I use this algebraic formula; however, it took some time and experience to learn how many applications this formula has. Having said that, ninety percent of my daily tasks require math learned in high school.

Are you interested in learning more about restoration? Let me know and I will pass your information along to Nate.

In Math for Grownups

Spreadsheets 101: Troubleshooting

This is the third post in a series about spreadsheets, called Spreadsheets 101. Click if you missed the first (Spreadsheets are Powerful. Here’s How) or second (How to Use Formulas) post.

Mistakes happen. But boy they can be frustrating, especially if you’re learning something new or not feeling so confident with your skills. In terms of spreadsheets, these mistakes can show up in one of two ways: a value that doesn’t make sense or an error message. In this post, you’ll get the ins and outs of diagnosing and fixing these problems.

Errors in spreadsheets are almost always user-generated. In other words, you can’t blame the developer or your computer or Mercury rising. This is both good and bad news — and the process for identifying and fixing these issues is very similar to working your way out of a vexing math problem. Don’t let that worry you. Instead, think of it this way: you have a great opportunity to deal with two difficulties at once.

Bad Numbers

When numbers matter, it’s always a good idea to check everything carefully. This might feel like a real drag, but this little habit can save you time, money and heartache in the long run. Take a look at the spreadsheet below. Can you spot the questionable values?

Did you notice the numbers that are out of whack? They’re in E12 and F12: $36,926 and $34,076. It would be awesome to earn that much dough from the sale of 1,000 ebooks, but with a net of $3.69 per book, that doesn’t make any sense at all.

There’s a problem with one of the formulas — probably in E12 or F12. So, let’s take a closer look. If this were your spreadsheet, you could double-click on E12, showing the formula.

Now, this time, I’ve also included the tool bar over the table itself. Notice that the formula is listed to the right of fx. You can also see it in the cell itself. This formula says that you want to multiply the value in D12 by 10,000. (Count the zeros, if you can’t quite read it.) In other words, this is the net, if you were to sell 10,000 ebooks. But what you’re looking for is the net on 1,000 sales. Ta-da! That’s the problem.

Next, you want to fix the error and see if that solves the problem in F12.

Yep, it did. See what happens there? If you make a mistake in one cell, it can carry to other cells. It pays to be diligent.

In this case, I had simply typed too many zeros. Another easy mistake is referencing the wrong cell (typing C12 instead of D12, which would be a tougher mistake to find). It’s also fairly common to accidentally add a cell name to a formula, by clicking the cell before closing up the formula.

Finally, errors in using the order of operations are really easy to make. If you need to add before multiplying, be sure to put the addition step in parentheses. Otherwise, the computer will follow PEMDAS — multiplying before adding. Take a look:

=((D12+E12)*5) means: Add the values in D12 and E12 and then multiply by 5
=(D12+E12*5) means multiply the value in E12 by 5 and then add the value found in D12

Big difference!

The Formula You Typed Contains an Error

Sometimes your spreadsheet program might give you an error message, like the one below.

Of course the error message isn’t helpful at all. But look closely at the formula in the cell. Instead of typing “1000”, I’ve typed “1,000”. And that’s a big no-no. Take away that comma separating the 1 from the 0, and all will be right with the world. Other characters you want to avoid include dollar signs ($) and percentage signs (%). Stick to the symbols outlined in the previous post on building formulas.

The key here is not to ever make mistakes but to identify them, if you do. Review all of your formulas before trusting their outcomes. Check that you’ve included the correct cell names, operations and used parentheses where necessary (so that your order of operations is correct. If you get an error message, look for symbols or letters that shouldn’t be in the formulas.

With a little attention to detail, you can be sure that the data generated by formulas is good to go!

What steps do you take to troubleshoot your spreadsheets? Do you have some advice to share or questions you need answers for? Talk to me in the comments section! There’s one more post coming up soon. Later this week, I’ll teach you how to make pretty graphs using spreadsheets. So easy, you won’t believe it!

In Algebra

It’s Not Tomato Season Yet, But You Still Need Algebra

So I’ve been harping on the fact that math is flexible. And I’ve also said more than once that we do the math that we need to do. (No one here is suggesting that calculus computations are necessary for everyday life.) In fact, because of those first two facts, we often don’t need to write down literal equations at all – we might not even know we’re using a formula.

Here’s an example: Let’s say you need to build a fence around your tomato plants. If you know that the bed is 4 feet by 2 feet, how much fencing do you need? (Yes, I’m ready for spring and summer and fresh veggies. Will this cold weather ever end??)

This is a perimeter problem. Some of you might write down the formula for perimeter of a rectangle: P = 2l + 2w. But I’d be willing to bet that most of us simply add: 4 + 2 + 4 + 2 = 12 feet. No formula needed, right?

But what if we turn the problem on its head? Let say you have 12 feet of fencing, and you’re building a tomato plant bed that must be no longer than 4 feet. How wide can the bed be?

Again, there are tons and tons of ways to approach this problem. One is with literal equations. What do you know about the information you have? The perimeter and the length. What are you solving for? The width.

P = 2l + 2w

The object of the game is to solve the formula for w, in terms of P and l. (Stay with me here. I promise this is easier than that previous sentence made it sound.) To do that, you need to get w by itself on one side of the equation. This is where the algebra comes in.

The most important rule about solving algebraic equations is this: Whatever you do to one side of the equation, you must do to the other. Period. End of Sentence. Amen. Shalom. To do that, you need to undo the operations. It’s like taking something apart. Here’s how it works:

Don’t panic! This is not as messy as it looks. All you need to do now is substitute what you already know, use the order of operations to simplify, and you’ll have w.

So the width of the tomato bed must be 2 feet. My point is not that you must always solve a problem like this one in this way. Nuh-uh. My point is that there’s algebra behind this problem – no matter how you solve it. And whether you like it or not.

How would you have solved this perimeter problem? See if you can spot the algebra in your approach. And share in the comments section.

I am so pleased to be Meagan Francis‘s guest this month on The Kitchen Hour, her 45-minute podcast for parents on the go. We talk about math anxiety, math education and how to encourage our kids to embrace math — while overcoming our own fears. Listen and/or download the podcast at The Kitchen Hour.

In Algebra

Numbers and Letters Together: What is algebra?

A Math for Grownups follower asked me earlier this week to define algebra, and I thought that was an excellent place to start this month-long discussion. I think that most people might be surprised by what is generally found under the algebra tent. The basic definition is pretty broad:

Algebra is a branch of mathematics that uses letters and other symbols to represent numbers and quantities in formulas and equations. This system is based on a given set of axioms.

What does this mean? Well, it’s basically the step beyond arithmetic, where we only deal with numbers. Algebra allows us the flexibility of an unknown — the variable — so that we can make broader statements about situations.

Look at it this way: 8 + 3 is always 11. Always. But 8 + x depends on the value of x. This means we can pretty much substitute whatever we want for x. See? Flexibility. (Of course 8 + x has no meaning without some kind of context. But we’ll get to that later in the month.)

Algebra allows us to discover and create rules. These rules might be formulas or equations that describe a particular situation. Because of algebra, we know that the circumference of a circle is 2πr, where π is the number 3.14… and r is the radius of that circle.

Now, let’s take this definition one step further. What is the circumference of a circle with radius 1?

C = 2πr = 2π(1) = 2π

But what about the circumference of a circle with radius 2?

C = 2πr = 2π(2) = 4π

If you look closely at this, you can draw a conclusion: The larger the radius of a circle, the larger its circumference. When the radius is 1, the circumference is 2π; when the radius is twice as long, the circumference is twice as big.

This points to a critical aspect of algebra: relationships.

Algebra is a branch of mathematics that deals with general statements about the relationships between values, using numbers and variables to describe them.

The formula for the circumference of a circle is a description of the relationship between the circumference and the radius of any circle. When the radius changes, so does the circumference. When the circumference changes, so does the radius. (π is a constant, even though it is technically a Greek letter. Whenever you see π, you know you’re dealing with the number 3.14…)

So that’s it. Algebra is nothing more than a way to describe the relationships between values (numbers, measurements, etc.). In the example of circumference, we’re dealing with two branches of math. The geometry describes why the circumference is twice π times the radius. The algebra is how we describe that relationship in the form of a formula.

Without algebra, we really don’t have ways to describe many things about our lives — from geometry formulas to finding compound interest on a loan. We can fumble around and come to a conclusion, but in the end, algebra can make this process much simpler.

What do you think about these definitions of algebra? Does thinking about algebra in these ways make it a little less threatening? If so, how? Share your ideas in the comments section!

In Holidays

Tis the Season to Give Generously: Do the math first

Yesterday afternoon, I dropped off the gifts I had purchased for a mother and son who are spending the holidays in a women’s shelter. He’s not even three years old, and he’s already had a much rougher life than I. But at least this year, he’ll have a Little People fire truck and new set of ABC and counting board books.

I don’t share this story to toot my horn. Plenty of people do as much or more than that each year. And I’m guessing their motivation is the same is mine — it feels good to give.

At the same time my math brain loves some guidelines. I grew up Lutheran, and I was expected to tithe 10% of my allowance. It was a great practice to get into, but now that I’m not a tithing church-goer, I miss having a formula. How much giving is “enough”? How can I know if I’m pushing myself enough?

Last year, I came across Peter Singer, who developed a really wonderful set of formulas based on a variety of different incomes. I wrote about it last fall, and I thought I point you to it today — in case you didn’t see it or need a reminder.

The Math of Generosity

No matter what holiday you celebrate in December, the month has traditionally marked a time for charitable giving. The weather is growing colder in some areas, making it much tougher on the homeless. The end of the year is creeping up, and with it the deadline for tax exemptions for charitable giving. And holiday cheer often means counting our blessings and remembering those who are less fortunate.
Yes, December is the time for giving. But how much is enough? And what is too much? As we attempt to balance our own needs (especially in these difficult economic times), many of us struggle with our own sense of guilt and generosity. Read the rest of this post.

Do you have a formula for developing your yearly contributions? Share it — or your thoughts about using math to make charitable giving decisions — in a comment.

In Basic Math Review

Formulas: Or is this going to be on the test?

Quick! What’s the formula for finding the circumference of a circle? Do you remember the Pythagorean Theorem? What about the distance formula?

If you’re around my age and not a math geek, chances are the answers are “I don’t know,” “No,” and “Are you kidding me?”

When you were in school, memorizing formulas was required. But as a grownup, that’s not necessary. In fact, you can find all sorts of shortcuts that make formulas unnecessary. Here are two examples:

1. Last week, during spring break, I offered to teach my daughter and four of her friends how to make circle skirts. We bought material, set up three sewing machines and two ironing boards and got to work. I found a really wonderful (and easy) tutorial at Made, which employs a great shortcut for cutting out a circle: fold the fabric into fourths and then trace one-fourth of a circle, which will be the waist. After that, measure the length of the skirt (plus hem allowances) and trace another one-fourth circle.

We needed the radius of the smaller circle, but really all we had was the circumference of that circle — the measure around the waist. Dana at Made has a quick and easy process for this: divide the waist measurement by 6.28. Ta-da! The radius!

But why does this work? Because the circumference of a circle is C = 2πr. 2πr is approximately 6.28r. That means that you can divide the circumference by 6.28 to get the radius. Neat, huh?

2. Yesterday, I was the guest on the 1:00 hour of Midday with Dan Rodricks, Baltimore’s public radio station’s noon call-in program. Dan asked listeners to find the surface area of a cylinder with a radius of 6 and height of 8. A caller reminded me that there is a formula for this: SA = 2 π r² + 2 π r h. But lordy, I didn’t remember that! Instead, I found the area of each base — both circles — and the area of the rest of the cylinder (using the circumference of the base times the height of the cylinder). I added these and got the same answer.

So what’s the point? You don’t need to remember a formula. If you can break the problem down into smaller parts, do that. If it’s easier to remember to just divide or multiply by something, go for it. Unless you’re taking middle school math or have to teach a math course, the ins and outs of the formulas are not critical. What you need to be able to do is use the concepts you understand to solve the problem. Sometimes that means remember the formula, sometimes that means finding a sneaky way around your bad memory.

Don’t forget to enter the Math for Grownups facebook contest! Just visit the page to find out today’s clue (and Monday’s and Tuesday’s). Then post where you’ve noticed this math concept in your everyday life. Good luck!

In Holidays

The Math of Generosity

No matter what holiday you celebrate in December, the month has traditionally marked a time for charitable giving. The weather is growing colder in some areas, making it much tougher on the homeless. The end of the year is creeping up, and with it the deadline for tax exemptions for charitable giving. And holiday cheer often means counting our blessings and remembering those who are less fortunate.

Yes, December is the time for giving. But how much is enough? And what is too much? As we attempt to balance our own needs (especially in these difficult economic times), many of us struggle with our own sense of guilt and generosity.

We’re at the end of our month of nesting here at Math for Grownups, and I wanted to share a little bit about the math of charitable donations. Not much makes me feel better about myself than sharing what I have with others. But finding that perfect balance can be a challenge.

Turns out there are formulas that can help guide these decisions. As we’ve seen in the past, math can remove uncertainty and help us see perspective. Of course what works for one person is impossible for another. And that’s okay. Remember, as grownups we can break the rules — adjust the calculations a bit to suit our personal situations.

Peter Singer, a philosopher who has written about philanthropy, offers an interesting formula. Singer’s suggestion is based on the amount of income a person or household earns. His premise is that the larger a person’s income, the more he or she can afford to give.

This is the table adapted from his “The Life You Can Save” website:

INCOME	DONATION
Less than $105,000	At least 1% of your income, getting closer to 5% as your income approaches $105,000
$105,001 –$148,000	5%
$148,001–$383,000	5% of the first $148,000 and 10% of the remainder
$383,001 -$600,000	5% of the first $148,000, 10% of the next $235,000 and 15% of the remainder
$600,001 –$1,900,000	5% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000 and 20% of the remainder
$1,900,001 $10,700,000	5% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000, 20% of the next $1,300,000 and 25% of the remainder
Over $10,700,000	5% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000, 20% of the next $1,300,000, 25% of the next $8,800,000 and 33.33% of the remainder

Most of us are going to fall in the top bracket — or if you look at your household income, perhaps the second bracket. And that’s where the math is simple.

Let’s say that Antwan and Jeannette bring in $75,000 as a couple. According to Singer, their yearly donations should be between 1% and 5%. They decide that 2% is a good number for them.

2% of $75,000

Just in case you’ve forgotten how to do percents, here’s a little refresher. Two things to know: 1) percents can be written as decimals by moving the decimal point two places to the left. 2) And “of” means multiplication. So that means:

0.02 x 75,000 = 1,500

For Antwan and Jeannette, about $1,500 is a good annual total for charitable contributions.

But for the wealthy, the math gets a little tougher. Let’s look at another example.

Will earns $650,000 each year. According to Singer, he should pay 5% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000 and 20% of the remainder.

One easy way to look at this problem is to first consider four different problems:

5% of $148,000

10% of $235,000

15% of $217,000

20% of the remainder

But what’s the remainder? Add and subtract to find out:

$148,000 + $235,000 + $217,000 = $600,000

$650,000 – $600,000 = $50,000

So he’ll need to find 20% of $50,000.

0.05 x 148,000 = 7,400

0.10 x 235,000 = 23,500

0.15 x 217,000 = 32,550

0.20 x 50,000 = 10,000

Now he just needs to add:

$7,400 + $23,500 + $32,550 + $10,000 = $73,450

According to Singer, a good amount for Will to donate over the year is $73,450.

Of course all charitable giving should be considered in these amounts — from the mittens you donate to the local shelter to the check you send to your United Way.

So do the math yourself — how close are you to Singer’s suggested donation levels? (If you’re a little too nervous to try, read this first.) Are you surprised to give more? Do you think you can stretch? Share your ideas in the comments section.

In Home

Radiator Math: It’s all about the variables

Like most home-improvement projects, figuring out the size radiators that you’ll need for a room hinges on a formula — actually several formulas. Install radiators that are too large, and you’ll burn up. Too tiny radiators? You’ll need that Snuggie that your Aunt Myrtle gave you for your birthday last year. And those formulas depend on variables.

What’s a variable you say? Let me explain.

For all you English majors out there, pay attention to the root: vary. Yep, variables are things that vary or change. So in a formula, the variables are those little letters. And in many formulas — like the ones needed to calculate the number and size of the radiators in your house — there are lots of little letters.

What are the variables that your radiator technician depends on?

Think about the rooms in your house — some are small and some are large. In other words the size of the rooms vary. And any good radiator guy — like our friend Frank — will tell you that the size of a room determines the size of the radiator you need. Small room? Small radiator. Huge room? Probably more than one good-sized radiator.

So, guess what? Your old friend the volume formula plays a role.

V = lwh

where V = volume, l = length, w = width and h = height

(See those variables? Length, width, height? They’re pretty simple to figure out in a room with rectangular walls, floor and ceiling.)

But there are more variables to consider. Typically, you want your bedroom and hallways to be a little cooler than your kitchen and family room. So the kind of room that you’re heating will be another variable.

And rooms with lots of windows and doors — or houses with poor insulation — will lose more heat. Yep, more variables to consider.

Things are getting pretty darned complicated around here.

This is why most radiator technicians often use an online or computer program calculator to determine the size of the radiators needed for each room of a house.

But if you’re renovating an old house, like I am (and your name isn’t Bob Vila), you won’t likely need to find the BTU/hr needed to heat your dining room or the size of the radiator you need for your newly restored downstairs powder room. But knowing a little bit about the math that goes into the process can help you feel confident about the work your radiator guy is doing.

Besides, thinking of radiator heat is a good way to describe variables. Especially in November.

When have you used variables to work out a home-improvement problem? Share your ideas in the comments section.

In Personal Finance

Credit + Debt: A challenging math equation

There may be no more confusing place for math than with credit and debt — and there may be no more important place for A+ math skills than with your money. That’s why I was asked to guest post at credit.com’s News+Advice blog today.

In my post, I discuss three ways that having some math skills — and a little dose of confidence — can help you make better decisions about what you owe and how you’ll pay it off.

Please join me at credit.com, and ask your questions there or in the comments section here!

Math for Grownups: A Simple Approach to Your Debt and Finances

By the way, would you like me to guest post at your blog? Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest. I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow. Get the details here.

In Math at Work Monday

Math at Work Monday: Graham the fish hatchery technician

Graham Laing is my brother, and I don’t think he’d be offended by my telling you that some of us in the family were a little worried that he might not amount to anything. But that’s another story for another day. Today, he’s a fish hatchery technician, which basically means he raises trout — “from eggs to eating size,” he says. That means he moves truckloads of live fish from pond to pond (and raceway and stream) according to their size, and he treats them for parasites and other oogie things. He also does a lot of weed whacking and mushroom hunting.

You might not think that a guy who works outside all day long would use math, but Graham does. And I think his approach is pretty unique. As you read through this, see if you can figure out what he’s not doing. I’ll share my thoughts at the end.

Graham wrestles a snapping turtle. Yes, this is part of his job (but I don’t think the turtle does math).

When do you use basic math in your job?

I use basic math every day. When we load the trucks in the morning, we’re told to load a certain amount of pounds of fish per tank on the truck. Since we can’t load all of the fish at one time, we’re handed a net of fish that usually weighs between 40 and 50 pounds. We have to keep track, in our heads, of how many pounds we have in each tank until it is loaded.

I also use basic math when we treat fish for parasites, using either salt or formalin. Salt baths depend on volume, so I find the volume of the tank in cubic feet and then multiply that by the number of gallons in a cubic foot–to get the total number of gallons to be treated. Then I have to multiply that by the number of pounds in a gallon of water to find the total number of pounds of water to be treated. Since we usually do a 5% salt bath, we find the number of pounds in 5% of the volume and weigh the salt. Finally, we can mix the salt in the water.

When treating with formalin, we have to calculate a gallons-per-minute flow rate. We find this by counting the number of seconds it takes to fill a gallon and then divide that number into 60. (There are 60 seconds in a minute.) So if it takes 10 seconds to fill a gallon, the flow rate is 6 gallons per minute. Since the treatment runs for an hour, I multiply by 60 and then multiply that number by 0.0036, which is the number of grams of formalin needed per gallon. Finally, I multiply by the parts-per-million needed for the treatment, which depends on the water temperature.

Do you use any technology to help with this math?

I use calculators for sampling and for calculating the treatments. If we’re doing a lot of samples at one time, we plug the numbers into an excel spreadsheet that has the formulas we need. Calculators reduce error. One blown sample due to error could cause us to underestimate the number of fish in a raceway. Or it could cause us to underfeed a raceway, resulting in a large size-variation of the fish.

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

Graham is also a master at finding little critters like this toad. Click on the picture to see it up close. (Photo courtesy of Mary Bruce Clemons)

My whole job revolves around math. Without math, the fish would die or become infected with parisites. We would not know how many fish we have on the farm, and we wouldn’t know if we were reaching our stocking goal set forth by the state.

How comfortable with math do you feel? Does this math feel different to you?

I feel very comfortable with math and have since I was a very small child. When I got this job, I had all the skills I needed — it just took a little remembering to become adept at using them.

What kind of math did you take in high school? Did you like it or feel like you were good at it?

I took algebra, geometry, and trig. I was forced to take trig, so I didn’t do so well in it. I slept through trig everyday and was still able to make 40s and 50s on the tests just by intuition.

Trust me. If you met Graham you wouldn’t know he’s a math geek. He doesn’t give a whit about calculus or abstract algebra or fractals. He’s just really good at mental math.

Here’s the interesting thing about Graham’s process: All of the math he describes above can be represented by formulas. And when Graham uses a spreadsheet for the math, he has to use the formulas. BUT when he uses math in the field, he unpacks each formula into a set of steps. (First multiply, then divide, then multiply, etc.) He doesn’t have to memorize a formula to do the work. Instead, he thinks about the process, and he’s attached meaning to each step (“divide by 60 because there are 60 seconds in a minute”), so he doesn’t forget to do something. This is the foundation of mental math — breaking up complicated problems into doable steps.

I’m betting many of you do the same thing. Want to share that process in the comment section? I sure hope you will!

And if you have questions for Graham — whether they’re about huge snapping turtles, tiny toads or wildlife management in general — post them, and I’ll be sure to get Graham to answer them. (I am his big sister, so I can boss him around — a little bit.)