Math for Grownups
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In Math at Work Monday

Math at Work Monday: Robert the personal trainer

What does it mean to be an exercise physiologist?

I do exercise testing and personal training at a large, new, state-of-the-art fitness center. The two main tests I conduct are a resting metabolic-rate test, which tells you how many calories your body typically burns at rest (then you can, hopefully, figure out how many you should consume!); and cardiovascular tests, which reveal how cardiovascularly fit you are. Using those results, you can work at the right heart-rate zone to burn fat. I also do strength and flexibility assessments.

And clearly, this requires some mathematical calculations.

I do a little math everyday. Sometimes I’m converting meters to feet or miles. I work a lot with percentages, particularly heart rate percents. Often, I put some raw data into a computer program to get those percentages. Other times it is on the fly with a calculator, always with a calculator. I work with percentages of heart rates for training goals or with disease management cases. I also work in terms of percentages of fat, to weight, and to muscle. Once in a while a computer program doesn’t work and I have to do some algebraic equations by hand, old school. I don’t remember the formulas so I have to look them up.

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

Exercise science is a science, and it should be precise. I measure fitness levels (body composition, strength, flexibility and cardiovascular), prescribe exercise, and try to help clients achieve a certain percent increase in one thing, or a certain percent drop in another, and then measure again. If I get these things wrong, clients are less likely to see results, and in my job, I need to produce results.

How comfortable with math do you feel?

The math I do now I feel comfortable with. I know the basics well. When you throw out numbers to people, when you know numbers, people tend to listen more. When I’m presenting to my department head I always double-check my math.

What kind of math did you take in high school?

I was awful in Algebra. I had to work three times harder than everyone else just to get by. After the basics, math made little sense until I got to study stats in grad school. I found some more purpose in it.

Did you have to learn new skills in order to do this math?

Most of the math that I use at work or shopping at Costco I learned in school.

Want to know more about the math involved in fitness and nutrition? Check out my book Math for Grownups, which will be out on July 18!  And if you know of anyone who uses math in surprising ways in their work, please let me know.

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In Math at Work Monday

Math at Work Monday: Shana the jewelry designer

Art and math are diametrically opposite, right?  Wrong.

Blossom, layering of enamel over silver. Photo credit: Hap Sakwa.

Shana Kroiz is a Baltimore-based, acclaimed jewelry designer and artist, whose work has been shown in the some of the country’s most esteemed galleries and museums, including The Smithsonian and the Museum of Arts and Design in New York City.  She’s kind of a big deal–and she does math!

When do you use basic math in your job?

Most days I contend with a variety of math problems, whether I’m measuring a piece or resizing a ring. I use wax to cast my designs, and so I have to convert the weight of wax into the the specific weight of the metal I am using. I also construct three-dimensional forms out of sheet metal, which requires some geometry. I have to know the sizes and weights of my pieces, so that they are not too heavy to be worn. When scoring and bending metal, I have to figure out the angle of my score lines in order to get the correct angle out of the sheet I am bending. Then there’s the business side of things: calculating the time it takes to make a piece with the cost of materials and the addition of any profit I need to make. Prices also have to be converted into a retail and wholesale values.

Do you use any tools to help with this math?

Yes, I use calculators, calipers, dividers, scales and, of course, computers. They all help with precision and time management.

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

Without math, it is almost impossible to do precision work. I work with a lot of potentially dangerous chemicals, and the math involved keeps me safe.  Plus, if I mix the chemicals incorrectly, the result won’t be what I need.  Being precise with my math means that I can avoid having to do things over again.

How comfortable with math do you feel?

I do most of the same sorts of problems over and over, so I feel comfortable in the studio, and can teach to my students. But there are times when I wish I had a deeper or broader understanding of how to use math. Sometimes I think I take too long to find the answers to calculations.  If I understood how to use a different formula I might get to the answer faster.

Did you have to learn new skills in order to do this math?

Yes, but I had to work it out on my own. When I had a tangible need, I figure things out.

What kind of math did you take in high school?

I went through algebra and some geometry. And I didn’t feel like I was good at it at all! I could follow a problem if I had a model, but I did not have a good enough conceptual understanding of math to work out the formulas on my own. So I would say I was average at best, but I think if it had been taught in a way that I could understand I would have been much better.  I do think if math was taught with more useful applications, students would have an easier time learning, understanding and being engaged in math as a useful tool for life.

Each Monday, I feature someone who uses everyday math in their jobs.  If you would like to be featured (or if you know someone who you think should be featured), let me know at llaing-at-comcast-dot-net.  You can also catch up on previous Math at Work Mondays.

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In Personal Finance

Is Your Boss Ripping You Off?

In last Friday’s Open Thread discussion, Gretchen posted this question:

My husband’s company does not provide health insurance for me and the kids, which is a $12,000 value. In his field, there is a salary scale based on education, number of years experience, geography, etc. The salary scale assumes that the employer provides health insurance for the family. His salary is currently at 79% of the scale, and his employer wants to eventually get him up to 100%. But that doesn’t include the insurance, so it won’t really be at 100% and is not now really at 79%. But I can’t figure out which way to do the math so he can show them the actual percentage. They’re saying he’s at 79 percent. I’m saying it’s lower because they aren’t accounting for that $12K.

All of that boils down to this: What percent of the salary scale is Gretchen’s husband actually making, given that he, and not his employer, pays the $12,000 bill for insurance? There are two steps to this problem:

1. Find the actual salary that is at 100% of the scale.

2. Find the actual percent of Gretchen’s husband’s salary, minus the cost of insurance.

I’m going to tell you up front that we’re going to use a proportion here.  What is  proportions?  A proportion is two equal ratios.  So, if you have two fractions with an equal sign between them, you have a proportion.

And how did I know to use a proportion?  Well, my big clue was that we’re working with percents.  Percent means “per one hundred,” and per one hundred means “out of one hundred,” which just means, “put the percent value over 100.” In other words:

79% = 79/100

The tricky part is figuring out what the proportions should be.

Step 1:

salary/x = 79/100,

where “salary” is Gretchen’s husband’s salary, and x is the top salary on the scale.

That’s because the company assumes that your husband’s salary is 79% of the scale. (Notice this: “salary” and “79″ are in the numerators — or top values of the fractions.)

To solve this proportion, we need to plug in Gretchen’s husband’s salary and then solve for x. In order to make this easy to explain, I’m going to assume that his salary is $100,000.

substitute:   {$100,000}/x = 79/100 cross multiply:   {$100,000*100} = 79x simplify:     {$10,000,000} = 79x solve for x:     $126,582 = x

So if his salary is $100,000, the top salary on the scale is $126,582.

Step 2:

{$100,000-12,000}/{126,582} = p/100,

where p is the actual percent of the scale.

Let’s look carefully at this proportion: The first ratio is just the salary minus the cost of insurance, over the max salary in the scale.  (That’s what we found in step 1.)  The second ratio is just like the second ratio in step 1, except that we don’t know what the percent is.

Now, pay close attention to this.  Check the top numbers to be sure they match. We want to know the actual percent of the scale that Gretchen’s husband is making — and that’s what’s represented in the top number of each ration.

Check the bottom numbers to be sure they match.  Do they?  Why yes!  Yes they do!  That’s because $126,582 is 100% of the salary scale.

(Unlike my 10-year-old daughter’s outfits, math is very matchy-matchy.  Knowing that will help you organize your problems and check to see if they’re set up properly.)

Now all we need to do is solve for p.

simplify:    {$88,000}/{126,582} = p/100 cross multiply:     {$88,000*100} = {126,582p} simplify:       {$8,800,000} = {126,582p} solve for p:       69.5 = p

So what does this mean? If Gretchen’s husband makes $100,000 a year and is paying $12,000 for insurance, he’s earning 69.6% of the salary scale.

If you made it this far, you get a gold star!  Pat yourself on the back, and take the rest of the day off.  This is a complex problem that depends on an understanding of proportions and how to solve for a variable in an algebraic equation.

Never fear!  I’ll unravel some of these mysteries in later blog posts.  And of course, if you have a question, ask it in the comments section!

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In Math for Grownups

My Math Story

The biggest fights my father and I had were about math.  I kid you not.

The year was 1984.  I was a junior in high school, taking Algebra II.  Radicals were kicking my scrawny, little butt.

(Remember radicals?  They look like this: sqrt{24}. In Algebra II, you mostly learned to simplify them, as well as add, subtract, multiply and divide with them.)

My father wanted to help, and he had the patience of Job.  But he was not great at accepting that I didn’t understand.  And I wasn’t great at controlling my emotions.  I hollered, cried and probably threw things.  Somehow, I got the impression that my dad thought I couldn’t do math, and I did what any strong-willed girl will: I dug in my heels.

That’s when I started drinking coffee, actually.  I was so determined to show my dad–and my Algebra II teacher, Mr. Gardner–that I got up at 4:30 a.m., sat in my dad’s easy chair with a cup of coffee and a stack of sharpened pencils, and did problem after problem after problem.

I did every single radicals problem in the textbook.  And then I did them again. I took what Mr. Gardner and my dad taught me and figured the darned things out.  It took time, but I was determined not to give up.

Why on earth would I do this?  Well, I’m stubborn, for one.  But probably the biggest reason is Mrs. Ivey.  She was my geometry teacher the year before, and she changed my perspective about math.  You see, before then, I knew I couldn’t do math.  Mrs. Ivey convinced me that I was wrong.

She and my father are the reasons I majored in math.  I found out I’m a math teacher, not a mathematician. (Sometimes we’re one or the other.)  I’m fascinated by the ways people choose to do math, not by complex computations or proofs.

Math geeks aren’t always born.  Sometimes a teacher inspires us.  Sometimes we’re dragged kicking and screaming. And sometimes we just learn to deal with math–because we have to.

What’s your math story? Share it in the comments section!

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