Math for Grownups
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In Personal Finance

Good Debt, Bad Debt

Today, I welcome Annie Logue, a terrific writer who specializes in business and economics. When she offered to write a guest post about the difference between good and bad debt (with a particular emphasis on student loans), I jumped at the opportunity. We decided that she would write the first half, and I would do the math at the end. If you have questions, she’ll come back and chime in.

Annie Logue

Economists recognize that debt can be good. It smoothes out consumption over a lifecycle, they say; if most people had to save up enough money to buy a house, for example, they would never be able to do it. By taking on mortgage payments while they are working, people can buy a house, live in it, and then pay it off before retirement so that they can live rent-free then. By taking on debt, people have the use of a house while they are paying for it and after it is paid for.

Good debt, then, lets you enjoy the benefits of something before, during, and after the time that you pay for it. It gives you a long-term economic benefit, such as a place to live for the rest of your life.

By contrast, if you run up your credit card to buy a new outfit for a fancy party that you only wear two or three times, and then make the minimum payment on your card, you have bad debt. You took on debt for something that you could enjoy for only a short time – not during or after the years it takes to pay it off. The faster you pay this off, the better!

Student loan debt is usually thought of as good debt: you borrow money to get an education, which is a good thing, and it increases your lifetime earnings power. You can enjoy real personal and economic benefits before, during, and after you pay the debt off.

However, with the rising price of college, the shift in funding toward student loans, and the ongoing recession, many people are asking if college is still enough of a benefit to make the debt worthwhile.

The short answer is yes; the long answer is yes, but.

Georgetown University’s Center on Education and the Workforce has done extensive work on this issue.  What they have found is that the degree matters; people with a bachelor’s degree, on average, make $2,268,000 over a lifetime, while those with a high-school diploma earn, on average, $1,304,000. However, occupation also matters, and many people earn more money than people who have a higher level of education. Someone with a Masters in English Literature is unlikely to earn as much over a lifetime as a police officer or a fire fighter.

We’ve seen the same thing in the housing market, by the way; people who borrowed what they could afford for houses that they intended to live in for a long time aren’t feeling especially pinched by the recent big drop in real estate prices. People who stretched and hoped to flip at a big profit have been suffering mightily.

It’s fine to borrow money for college, but those who do should be practical about it. They need to think about whether they are using that education to enter a field that is likely to make the debt pay off.

Doing the Math

What will a student loan cost in all? To assess whether even good debt will be a good idea, it can be helpful to consider the total cost of the loan and then compare that cost to the average total earnings over a lifetime. Here’s how that can be done.

Chloe is planning to attend a four-year public university. She estimates her tuition, plus room and board to be $15,000 each year. She received a $10,000 scholarship, which will be divided throughout the four years. If she takes out a federal student loan to cover the rest of the costs, how much will her college education cost in all?

First off, she needs to figure out the amount she will borrow each year. Her scholarship is $2,500 each year ($10,000 ÷ 4 = $2,500), which means the annual total that she will borrow is $15,000 – $2,500 or $12,500. She plans to complete her degree in four years, so the total that she’ll borrow is $12,500 • 4 or $50,000.

Remember, this amount is only the principal, or the amount Chloe will borrow. More complex calculations are necessary to find the total amount of the loan, which depends on the interest rate and her monthly payment.

Chloe’s interest rate is 6.8%, and she’d like to pay off her loan in 20 years. Using an online calculator, she finds that her total loan will cost $91,600.68, with a $381.67 monthly payment.

But 20 years sounds like a very long time. What would she need to pay each month in order to pay off her student loan in 15 years? The online calculator spits out $443.84. By paying the loan off earlier, her total cost is only $79,891.81.

So for an extra $62.17 ($443.84 – $381.67) each month, she can save a total of $11,708.87 ($91,600.68 – $79,891.81) in interest over the life of her loan! But even with the second option, she’ll pay a total of $79,891.81 – $50,000 or $29,891.81 in interest.

So how does Chloe’s total student loan debt compare to the amount of money she’ll earn over a lifetime? Let’s take a look. With a college degree, she can expect to earn a total of $2,268,000. If she pays off her student loan in 15 years, she’ll have paid a total of $79,981.81. What percent of her total expected earnings went to her loans?

$79,981.81 ÷ $2,268,000
0.035 or 3.5%

Not a bad return on investment. The trick of course is to get a decent job after graduation and stay on top of those monthly payments.

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In Math Education

Ten Things Parents Wish Math Teachers Knew

We’ve gotten advice from math teachers to parents and from students to math teachers. But parents can also play a big role in how their kids learn math and succeed in school. So, I’ve decided to given them a chance to share their feedback with math teachers. (Besides, when I went looking for students to give me advice, parents just couldn’t help themselves!)

I’ve been on both sides of this equation, so I have lots of empathy for teachers and parents. Neither of you have easy jobs! In case it’s not clear, I wholeheartedly believe that most teachers are in the classroom because they love kids and want to make a positive difference in their lives. But we’re all human, and teachers can always strive to be better at their craft.

Here goes:

Help a parent out.

The language of math is different than it was when most of us learned it the first time. (For example, in subtraction many of us “borrowed.” Our kids “regroup.”) A cheat sheet or a website with information would go a long way in helping parents help their kids with understanding the concepts.

This goes double (or triple) for discovery-based math curriculum, like Investigations or Everyday Mathematics. These programs often don’t rely on the algorithms that many of us are used to using. To be fair, the curricula have parent components, but if the school or teacher doesn’t use them, parents are often left in the dark.

Know the kids.

Parents do understand that there are a lot of big stressors on teachers. Teachers are often told to do things that they wouldn’t choose to do (like teach to a test). They have large classes and short periods of time with the kids. But parents still expect teachers to know each child well. Teachers should know which kids have trouble with memorization and which ones struggle with understanding difficult concepts.

Give parents a homework estimate.

How long should students be working on an assignment? An hour? 15 minutes? Two hours? Kids work at different speeds, and parents need to know when we should be encourage our kids to pick up the pace or investigate whether our children are moving slowly because they don’t understand the concepts.  And while we’re on the topic of homework, parents told me that there was no point in sending home 50 of the exact same problems. One parent said: “Hours of pointless busywork make kids hate math.”

Mean what you say and say what you mean.

This doesn’t have anything to do with classroom management, though this is good advice here, too. Parents told me about very poorly worded questions that confused their kids. “My [child with Aspergers] is very literal,” said one mom. “This sometimes means he actually answers the question correctly but not the way the teacher intended. More than once I have had to ‘correct’ his homework and say, ‘Yeah, I know what you put is accurate, but that is not what the teacher meant by the question.’” One parent suggested having someone who is not an educator look at your materials to be sure that the questions are clear.

Update your materials.

Don’t pull old worksheets from old curricula that doesn’t apply to current pedagogy. And by all means, make sure that what you’re sending home with kids is what they’re learning about in class. It’s really frustrating for parents and kids to see homework that is not jibing with classwork.

Review tests and graded assignments.

Students need to understand where they made their mistakes and why. Parents need to know where students’ gaps in understanding are. Reviewing tests also reinforces the important idea that tests are a means for assessing understanding, not a big, red stop sign for learning. But don’t let students check each other’s work. “It’s demoralizing,” said one parent.

Don’t confuse computational errors with conceptual misunderstanding.

When a student makes a common addition error, that doesn’t mean she doesn’t understand the concepts behind the problems.

Introduce relevant and meaningful application (word) problems.

At the beginning of this school year, my sixth-grade daughter vented about a word problem she was given for homework: Carlos eats 25 carrots at dinner, and his brother eats 47 carrots. How many carrots did they eat in all? “Who eats 47 carrots?” she wanted to know!

If you don’t know what’s relevant to your kids, ask them. Or watch a television program they may like or talk to parents or search the internet. Along with word problems, parents want financial literacy introduced early and often. These problems can be included in a variety of places within traditional curricula.

When a child isn’t succeeding, ask why.

Sometimes this is because of misbehavior, but sometimes misbehavior occurs when a child is bored or confused or just feels unconnected to the class. Some kids give up easily. And others have undiagnosed–or unaddressed–learning disabilities. Get the parents involved as quickly (and often) as possible.

Don’t write our kids off.

Some kids struggle and some kids understand the concepts right away. Parents want teachers to stick with their kid, no matter what. Parents can tell when teachers have decided that a kid isn’t worth their effort. That’s heartbreaking to parents–and students.

Not all parents want or can be intimately involved in their kids’ math education, but I think it’s fair to give each parent a chance. Just as it’s fair for parents to give teachers the benefit of the doubt.

Parents, do you have any additional advice for teachers? Teachers, do you want to respond to any of these ideas? Let’s get a good conversation going!

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In Math Education

Ten Things Students Wish Math Teachers Knew

Two weeks ago, I posted Five Things Math Teachers Wish Parents Knew. Now it’s the teachers’ turn to be on the hot seat. I asked a handful of the middle and high school students that I knew to chime in with some advice or helpful feedback for math teachers. And this is what they came up with:

Make the math relatable.

These kids get it — you honestly like pure mathematics and the State Board of Education has dictated that you cover x amount of material in y period of time. (See what I did there?) But when all students are doing is solving algebraic equations with no connection to the real world, the stuff won’t stick — and eyelids will shut.

Do more “interactive stuff instead of book work.”

Get rid of boring worksheets. Spend a few days applying the material to larger projects. Have the students design carnival games based on probability. Or track March Madness results. Or use special right triangles to find the length of a shadow and compare it to an actual shadow.

Ensure that everyone is ready to move on — before moving on.

Again, these students know that you have some constraints. And I’m willing to bet that most students understand that the class doesn’t revolve around them. (Okay, maybe many students, rather than most.) But if a good portion of the class isn’t following, there’s no point in barreling through to the next concept. I’ll add this: some students won’t tell you that they’re not ready to move forward. Teachers have to get creative in assessing readiness.

Don’t call on the same students all the time.

Everyone knows who the mathy kids are. Don’t let them dominate the discussion. A few days ago, a parent told me that her daughter’s school is really clamping down on “blurters” — kids who get the answers quickly and blurt them out. These blurters can suck all of the life out of a classroom, especially when the majority of students need a little more time and a lot more confidence. And it’s a good lesson for anyone to learn: keep your mouth shut and sit on your hands once and a while.

Don’t refuse to call on a student who usually has the answer.

This one’s personal. In middle school, my daughter was told to stop raising her hand all of the time — and not in a nice, encouraging way. She was crushed by this harsh order. Everyone deserves a chance to participate, at least part of the time. And besides, there are different methods for encouraging participation that don’t require teachers to single out and call on individual students. Learn these methods and use them.

Skip the timed tests.

They freak students out and can bring down a grade in a heartbeat. Fact is, faster isn’t smarter. Speed tests don’t allow different approaches to problems. Besides, what’s more important: automatic recall of the times tables or really understanding where these facts come from? (Please say the latter. Please say the latter.)

Grade as much as possible.

Give students a chance to bring up their grades with graded homework assignments. And give them feedback on their understanding as often as you can. It’s not enough for a student to know that the answer is wrong. Detailed feedback on why is critical for deeper understanding. Kids know this.

Recognize that not all kids learn in the same way.

Remember, the definition of insanity is doing the same thing over and over and expecting different results. If students don’t understand the concept, try explaining it in a different way. Or ask the kids to come up with their own ideas. Discovery is a great tool, and it’s often very engaging.

Stop talking down to students.

Yep, students really said this. And I could wallpaper my bathroom with the number of emails I’ve received from adults who felt shamed by a math teacher. Every adult that a kid meets has the power to make a positive difference in that kid’s life. Belittling, shaming and talking down to kids will have the opposite effect.

And I’ll add #10:

Don’t ever, ever tell students that they’re bad at math.

Want to insure that a kid will never try at math again? Want to smash his confidence? Want to send a lasting message that she won’t be able to balance her checkbook or become an engineer or help her kid with math homework? This is a one-way ticket to that bleek future, and it can happen in a split second with an offhand remark. Remember what it was like to be a student and follow the Golden Rule.

Do you have suggestions for math teachers? Share them (nicely) in the comments section. I’d also love to hear from students and former students who had great experiences with their math teachers. Are you a math teacher? Feel free to offer your feedback, too!

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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!

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In Math for Grownups

I Spy With My Little Eye: Math around us

As you know, this is the first week of Math Awareness Month. But what you may not have realized yet is that I am hosting a contest on the Math for Grownups Facebook page. Each day I give a Math Treasure Hunt clue. The object is to notice that math-related something or concept and then post about it under the clue. At the end of the week, I’ll randomly select one winner from all of the entries. That person will get either a copy of Math for Grownups or a gift card. The details are here.

There were some really cool entries, so I thought I’d share them here.

Monday: A prism — This clue turned out to be a bit tougher than I expected, and that’s because I didn’t consider the different definitions of prism. I meant a polyhedron made up of polygons; in other words, a cube or a box. But the entries really focused on a solid that refracts light. This is often a triangular prism or a polyhedron made up of two triangles and three quadrilaterals. But sometimes these prisms are not geometric prisms at all but may be pyramids.

Tuesday: A percent — Much easier! Here are a few examples that you gave:

I ate 2% of my Daily Total Fat with my shredded wheat this morning.

My daughter is in virtual school and she has completed 77% of her math curriculum for the 2011-2012 school year. We are counting the percent points until summer. 🙂

‎0% chance of precipitation this afternoon means we might get to go to the playground!

Wednesday: A bar graph

Checked out a review of “Mirror, Mirror” online and found the reviews listed as a bar graph by A,B,C,D,F grades. Made it easy to see that the reviews so far give it a pretty average grade. Went to see it and would have given it a B.

I’m teaching about gender work and family in my intro sociology class this month. Here is a link to a bar graph and story that explains class differences in access to parental leave

Thursday: An improper fraction — Yep, this is a toughie. No entries yet — want to be first? In an improper fraction the numerator (the number on top) is larger than the denominator (the number on the bottom). Now can you find one?

Friday (today): Multiplication by a two-digit number — Be the first to enter today!

This week’s chance to win ends at midnight tonight. FAQ:

1. Can you go back and answer questions from earlier in the week? Yes!

2. Can you respond more than once to one clue? Yes!

3. Can you tell everyone you know about the contest? Why yes!

4. Can you make this a project for your home-schooled or classroom kids? Yep! (Just be sure that anyone entering is allowed to be on Facebook.)

Have fun with this contest. Notice the math around you. Learn a couple of things. And share these with everyone.

Do you have ideas for this contest? Drop me a line or share them in the comments section.

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In Math for Grownups

Welcome to Math Awareness Month! Share your math story

Oh, math! How I love thee.

Not.

I like math. I even appreciate math. But I can’t say that I love it. Sometimes I get a little thrill in seeing math around me. Mostly, I just feel comfortable with the math I use everyday and get anxious when I see something I haven’t used in years (like differential equations). Anyone else?

Math is a tool. And just like a hammer or a vacuum cleaner, it probably doesn’t evoke deep emotion in many of us. Still, being aware of math makes sense. Math is everywhere but you don’t have to love it.

To start the month, I thought I’d ask each of you to share your math stories. We all have some sort of feeling about math, whether it’s a deep-seated fear or passion or even indifference. How did you get to that place? What experiences did you have that influenced your feelings and thoughts about math?

You can read my math story here. (Check it out. You might be surprised!) And please share your story in the comments section. I’d love to know how each of you feel about math and what got you there. (Sad and happy stories are welcome!)

Also, don’t forget to enter this week’s Math Treasure Hunt contest on facebook. Each week, you’ll have a chance to win a copy of my book or another cool prize. Get all of the contest details here.

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In Math for Writers

Royalty Math: How many books will you have to sell?

Photo courtesy of Jain Basil Aliyas

So let’s say you got a book deal. Yay! Have that glass of wine or virgin daiquiri — and then it’s time to get down to business. How much can you actually earn from this venture?

If you’re new to publishing, you may not know how you’ll earn a check from a book deal. With the advent of self-publishing and ebooks, there are many different models. Still, many publishers depend on the tried and true advance-royalty model. But how does this work?

First the writer gets an advance. This is a lump sum — sometimes paid in installments — that is paid to the writer before the book is published. This figure can vary widely, from $0 to a seven-figure value. It’s based on the author’s expertise, reader demand and expected sales. That means J.K. Rowling is going to earn a higher advance than a funny, charming math geek.

The advance is exactly what it sounds like — an upfront fee based on what the publisher thinks the book will earn. So you’ll get paid for your time writing the book, even though the publisher isn’t earning anything yet.

Royalties are what you’ll earn from the book sales — usually a percent of the price of the book. But there are lots of things to consider here, like how much a bookstore actually pays for the book.

Here’s the catch: you’ll need to earn out your advance, before you start getting royalties. In other words, you won’t see a dime from your publisher until after your royalties equal the advance you were paid. (And sadly, some books never do this.)

Whew! And you thought all you’d have to do is write the darned thing!

Any experienced writer will warn you: read your contract carefully before signing. I’ll go one step further: do the math. (Surprise!)

What you want to know is the number of books you have to sell before you actually earn some cash. If that number is in the stratsophere — or your advance is really low — you may want to shop around. (Then again, there’s something to be said for taking a risk or enjoying a labor of love.)

Mathematically speaking, there are several variables: the amount of your advance, price of the book, royalty percent and the number of books you’ll need to sell to earn out. The advance, book price and royalty percent are set. What you need to know is the number of books you need to sell.  Let’s look at a simple example:

June has been shopping around Physics for Grownups for several years. She’s convinced that she has a great idea, if she can only find the right publisher. Lo and behold, on her 17th try, she finds a publisher who is interested. The contract offers a $5,000 advance and 5% royalty. The book is priced at $12.99.

Is this a good deal?

June is no dummy. She knows that a physics book isn’t likely to be a best seller. Still, she doesn’t want to spend weeks and weeks writing if she’s not likely to see any profit. Based on the contract, how many books would she need to sell to earn out her advance?

She will earn 5% on each $12.99 book. (That’s assuming that all books are purchased at the cover price.)

$12.99 x 0.05 = $0.65

In other words, June will earn $0.65 per book. To find out her break-even point, she needs to divide her advance by the amount she’ll earn per book:

$5,000 ÷ $0.65 = 7592.3

So, June will need to sell 7,593 books before she will even get a royalty check. That’s a lot of books.

Only June can decide if this is worth it. Some books are like tortoises — they make slow and steady progress, while other books are flashes in the pan. If June plays her cards right, she could do just fine over a long period of time. The math can only give her the cold, hard details.

Have you published a book? If so, what went into your decision to take the leap? Did you do the math or just decide it was worth it regardless? Share your ideas in the comments section.

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In Math for Writers

Overwhelming Word Count? Use math to motivate

November 2011, I knew I had my work cut out for me.  First off, I had never written a book before.  Writing 800-word stories paled in comparison to the 55,000 words I was expected to produce for this book.  Second, I had only 8 weeks to pull off this gargantuan task — and right smack dab in the middle of them were the winter holidays: Christmas, Hanukkah, Winter Solstice and New Years.

Looking back, I think I must have been insane.

But this book wasn’t just any old book. I knew I could crank out the ideas, because they’d been sitting in my head for years and years.  Still, I was nervous.

So what did I do? Well, I turned to my old friend math, of course.

I knew I was probably going to write chapter by chapter. But how many words should each chapter be?  I was contracted to write 10 chapters, plus an introduction.  I also wanted to include a glossary and an appendix with formulas.  Just as a starting point, I figured the introduction, glossary and appendix would be about the same length as one chapter.  So that meant I was dividing the entire word count by 11.

55,000 words ÷ 11 chapters = 5,000 words/chapter

Each chapter needed to be about 5,000 words long.  Convenient, eh? Suddenly those 55,000 words were simply 11 5,000-word “stories.” I’d written 6,000-word stories before, so I knew I could manage this!

Then I had to look at my timeline: 8 weeks.  I didn’t want to write during the week of the Christmas holiday, so I really had only 7 weeks.  But one chapter was pretty much done, since I had to turn it in with my proposal.

Clearly, I couldn’t write one chapter each week.  With 11 “chapters” (if I considered my introduction, glossary and appendix as a chapter), I was going to need to double up.  I had already planned to work 7 days a week, if necessary, so I did some more math to figure out the total number of days I’d be writing the ten remaining chapters.

7 weeks x 7 days = 49 days

And a little more math to figure out the number of days I had to write each chapter.

49 days ÷ 10 chapters = 4.9 days/chapter

To be realistic, I decided to bet on 4 days per chapter.  That would give me a couple of days off here and there.

I did fine with this plan, until mid-December. I slowed down considerably, and by the start of 2011, I was behind. Panic set in.  So I turned to math yet again. This time, I pulled out the big guns: a spreadsheet.

This is an actual screenshot of my book spreadsheet.

I don’t have a screenshot of what my book spreadsheet looked like originally.  The above is how it ended up.  But I can tell you this: when I was really feeling nervous about my progress, I checked my word count and updated my spreadsheet — sometimes several times in an hour — just to see the numbers change.

You see, in some of the fields are formulas that add or subtract to show my word count.  Here’s an example:

I used the SUM function to add up everything in the blue box — in other words, my actual word count for each chapter. When I changed a value in the blue box, the total pages changed as well. Here’s another example:

Here, I’ve subtracted the word count for the chapter on yard work from 5,000 (or my estimate word count for each chapter). Each time I updated my word count for that chapter, the difference changed.

Yeah, this is really, really geeky, I’ll grant you that! And I know it takes a “special” brain to love spreadsheets this much. But I do think it’s an effective way to set goals and get yourself motivated.

So if you’re worried about how you’ll ever finish writing that book or make all of those quilt squares or whatever your big project is, consider how math can help. It just might get you organized enough to get started. (Or it might give you the distraction you need to settle your nerves.)

When have you used math to help you get through a daunting project?  Share your story in the comments section!

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In Holidays

Math at Work Monday: Elana the personal shopper

On the whole, I don’t like shopping.  But I do like shopping for Christmas gifts. Still, at around this time of year, I’m about ready to hand over my list to someone else — say a personal shopper?  And if she can help me find that perfect outfit for Saturday night’s holiday party?  Even better.

Meet Elana Pruitt, a personal shopper in the L.A. area of California.  Elana isn’t just a shopper.  She helps her clients figure out what they need and how to find it. She also writes about fashion at her blog, Good Girl Gone Shopping. Here’s how she uses math in her job.

Can you explain what you do for a living?  

I am a personal shopper and wardrobe consultant. My day-to-day schedule is never the same because the services I carry out are based on the every individual’s needs. I am committed to helping men and women find quality fashion not just for affordable cost, but at their specific budget. My job entails a variety of duties for my clients: re-organizing closets, styling new outfits using the clothes they already own to prove the versatility of their wardrobe, shopping with (or without) the client at particular stores or online, styling new purchases with their existing wardrobe after a shopping trip, and conducting online research.

Although my services are affordable, I realize that hiring a personal shopper and wardrobe consultant is a luxury. So the other half of my job entails writing about fashion. On my blog, Good Girl Gone Shopping, I provide helpful information about shopping and fashion, with references to our culture, entertainment, and the celebrity phenomenon.

When do you use basic math in your job?  

I’ve never been asked this question before – it’s a good one! In thinking about how I incorporate math into my job, I realize that I use it frequently. From counting items in a client’s closet to calculating my gas mileage for a shopping trip to scheduling appointments throughout the month. Everything I do involves the basics of math: addition, subtraction, multiplication, division, and percentages. Most of the time, I don’t consciously think about the fact that math is a natural, necessary, and unavoidable component of my business. The main time when I am aware that I am using math is when there is a transaction of sorts. I charge hourly rates and a commission percentage of purchases, which needs to be clearly defined to the client. In addition, I sell advertising space on my Good Girl Gone Shopping blog. This also needs to be clearly structured for the client to understand (ads can be sold on a 6-month basis or yearly). Those two specific situations are when I am so happy I paid attention in math class throughout college!

Do you use any technology to help with this math?  

I am usually old school – I use a good ol’ pencil and paper most of the time. Then to double check my work, I use the calculator either on my computer or from my phone.

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

For my job, it’s not that it makes it better – it’s just a part of it. Math is that essential to my work as a personal shopper, wardrobe consultant, and fashion blogger.

How comfortable with math do you feel?  

Basic math is second nature to me. Algebraic formulas take more effort. But fortunately, I’m doing something right, because I am able to successfully see my job through, from the consultation with the client to follow-up communication after my service with him or her is complete.  Overall, I feel comfortable with math…basic math.

What kind of math did you take in high school?  

I took Pre-Algebra, Algebra, and Geometry. I do recall struggling with Geometry. I have always respected those who excel in the study of math, because it requires such analytical thinking. I hate to say I wasn’t good at it, but let’s just say I would never choose to enter that field!

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

The skills I use now are pretty much standard. Students everywhere need to erase this thought from their brain, “I don’t know why I’m taking this class, I won’t need it in the real world when I grow up!” The journey throughout adulthood can be amazing if you are knowledgeable and skilled in a multitude of areas. Never say never!

Have you ever wondered how personal shopping works? Now’s your chance to ask Elana.  Post your question in the comments section!

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In Holidays

Talking Turkey

I’m taking it easy this week (ahhh!), and so I’ve brought you an excerpt from my book Math for Grownups.  (Check it out for more great ideas on using math in your everyday life.)  Happy Thanksgiving!

As any experienced cook will tell you, timing is often the most difficult skill to master in the kitchen. Nobody wants to sit down to a meal of overdone fish, cold broccoli, and room-temperature biscuits. (The butter should melt into the flaky layers, you know?)

Figuring out how long a dish should bake, roast, or boil is the first step to presenting a carefully choreographed dinner. And for many novice or not-so-frequent home chefs, a giant turkey is the most daunting of all entrées.

Sure, you can count on the pop-up timer. These come with some turkeys, or you can buy one separately. But you’ll still need to know when to put the bird in the oven—and when to start boiling the potatoes.

And there’s also the thawing time. Buying a frozen turkey means allowing time for it to defrost, which is probably a lot longer than you think!

But you don’t need Julia Child or a semester at Le Cordon Bleu to figure any of this out. Thawing times and cooking times depend on the turkey’s weight.

It’s your first Thanksgiving with your new husband, Tom. And your mother-in-law will arrive just in time for the 6:00 P.M. dinner. She’s bringing pecan pie, stuffing, and homemade rolls. You’re in charge of all the rest—including the turkey. You’ve ordered a 12-pound bird, which you’ll need to thaw in the fridge before roasting. When should you pull it out of the deep freeze?

You know from your sister’s horror stories that you can’t cut corners by thawing the bird on the counter. Unless you want to host the Thanksgiving-dinner-when-everyone-got-Salmonella, your best bet is to defrost the turkey in the refrigerator. The United States Department of Agriculture(USDA) says to allow 5 hours of thawing time per pound. They oughta know, right?

You’ve bought a 12-pound turkey. How long should you allow for thawing?

It’s a simple problem, really. Just multiply the number of pounds by 5—the number of hours needed to thaw each pound.

12 xŸ 5 = 60

So you need to put the turkey in the fridge for 60 hours in order to thaw it. But let’s think a moment. Does this mean 60 hours before dinner is served?  Nope. The USDA also says that serving raw poultry is a big no-no, so you’ll also need to roast the bird.

If your oven is set to 325ºF, the USDA recommends roasting an unstuffed turkey for 2¾ to 3 hours. They’re the experts on avoiding food-borne illnesses, so you decide to follow their recommendations.

With a little time for resting—the turkey, not you—and carving, you estimate that it will take 3 to 3¼ hours to get the bird from the fridge to the table. You’ll need to add that to the thawing time in order to figure out when to pull the turkey out of the freezer.

60 + 3¼ = 63¼ hours

Clearly you’ll need more than a day, but how much more?  There are 24 hours in a day. How many 24s are there in 63¼?  You can use a calculator, but that could be confusing. Instead, try some mental math.

To make things easier, forget about the extra ¼ hour (or 15 minutes). You can add that on to the end. Working with whole numbers is much easier.

It looks like you’ll need at least 2 days. That’s because 24 times 2 is 48, which is less than the total time you have figured out. Will you need a third day?  You can subtract to find out.

63 – 48 = 15

So 2 days and 15 hours (plus the extra 15 minutes) ought to do it. But that doesn’t tell you what time to start defrosting the turkey, does it?

Remember, your dinner starts at 6:00 P.M. Fifteen hours before that is 3:00 A.M., and another 15 minutes before that is 2:45 A.M. So you will have to take the turkey out of the freezer at 2:45 A.M. on the Tuesday before Thanksgiving.

Because you’re doing all the cooking, you decide to let Tom get up to move the turkey from the freezer to the fridge. You set his alarm on Monday night and settle in for the last good night’s sleep of the week.

Do you have any Thanksgiving cooking horrors to share?  Do tell (in the comments section)!

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In Math at Work Monday

Math at Work Monday: Harmony the fabric designer

You may not know this about me yet, but I’m a fabric junkie.  In fact, when I finished my book last winter, my reward was a day-trip to New York City to shop at Mood Designer Fabrics.  I need rehab. 

So when Harmony Susalla contacted me to ask if I’d do a guest post on her blog, I jumped at the chance — and I asked her to do an interview with me.  Harmony is a wonderful textile designer, who works in organic cotton.  

Can you explain what you do for a living?

As a textile designer I create patterns and designs that are printed on fabrics.  Since 2005, I have owned my own organic-cotton fabric company.

When do you use basic math in your job?

For a design to be printable using rotary screens, the design has to fit a particular circumference of the screens.  Typically the circumferences are 25.25″ or 36″.  So I use division on a regular basis because I need the repeat of the design to fit into a number that is divisible into the circumference size.   For example:  If I am using a 36″ screen then, depending on the size of the motifs, the repeat may end up being 18″ or 12″ or 9″ or 6″ or 4.5″ — or even smaller — but it must be a factor of 36.

I remember quite a few years ago I was working for a design firm and we had to do a diagonal stripe that repeated. I was doing it the hard way, meaning I would make manual adjustments, test, readjust, and test again until it eventually worked out.  My colleague and friend at the time, Freya, went home and came back the next day with a formula.   I was VERY impressed and still have that piece of paper with the formula on it.  I still reference it. But it helped me to realize that with the use of basic math skills, I could save a lot of time and effort in my work, and ensure the quality of the final design.

Also, as a small business owner, I am constantly using math to calculate charges, create order estimates, figure out cost and profit margins, determine MSRPs (manufacturer’s suggested retail price), etc.

Do you use any technology to help with this math?

Just last week, I made a spreadsheet of all of the various repeat sizes for the 25.25″ screen size. One of my customers sent me a design she wanted printed, but the design was not created in an appropriate repeat size. I had to use the list I created  in Excel to find the closest repeat-size option for her design and make the necessary adjustments.

I use QuickBooks to generate invoices which does basic multiplication and addition for me.  I also use Excel on a fairly regular basis.

These are only a few of Harmony’s designs. (Photo courtesy of Harmony Susalla.)

How comfortable with math do you feel?

On a scale of 1 to 10, I’d rate myself a 5.   I am really comfortable with simple math.  Work math seems natural. I actually really enjoy having math I learned in school apply to my daily life.  So much of our formal education is forgotten because we just don’t use it, but I get to use math on a daily basis.

What kind of math did you take in high school?

In high school, I was always in the advanced math classes. My senior year, I was placed in calculus.  Until that point, math had been pretty easy for me, but suddenly I was lost.  I think I lasted about 2 weeks before I dropped the class.  It was the first time I can remember truly feeling “stupid.”  I was then placed in regular senior math, and it was so easy that I was held after class by my teacher who believed I had an attitude problem.  While the teacher would go over homework from the day before I would be working on the current night’s homework.  I would finish before class was over, and then stare out the window (because I didn’t need help).  This was the behavior that convinced her I had an attitude problem.  After that, I had to pretend to be paying attention to the lesson being taught, even though it was material I already knew.

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

This is a good question. I think that most of the math I use today I learned in school, with the exception of some of the accounting terminology and applications that were new to me. But because I had a good base in math, it was relatively easy to learn on my own.

This entire week will be devoted to fabrics. Come back on Wednesday to see what I wrote for Harmony’s blog.  On Friday, I’ll show you how I made some gorgeous curtains for my new living room out of Harmony’s Evelyn print.

In the meantime, post your questions for Harmony here. She’s happy to respond!

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In Math at Work Monday

Math at Work Monday: Frank the radiator guy

Photo courtesy of roland

Let’s face it.  We take our heat for granted.  Unless you’ve been without heat for long enough that the charm of it all wears off, you just plain don’t notice that your house is toasty warm.  And if you have radiators, you can thank “the radiator guy” for that.  

I’ve always lived in old house.  (Well, except for those years right after college when I rented circa-1970s townhouses.)  And that means I’ve depended on radiators to keep me warm in winter months.  I love radiators.  Giving up some wall space is worth the even, constant heat.  But until I started renovating my current house, I didn’t understand the calculations required to plan for the right size and number of radiators in a room.

Along came Frank “Steamhead” Wilsey — who has been our “radiator guy” since we moved to Baltimore.  He may not like math, but he does use it in his job.

Can you explain what you do for a living?

I install, service, modify and repair steam, vapor and hot-water heating systems.

When do you use basic math in your job?

I use math for many things–accounting, invoicing, heat-loss calculations, radiator sizes and total amounts, flow rates, pressure drops, pipe and pump sizes and capacities. They’re almost all basic arithmetic- addition, subtraction, multiplication, division.

Do you use any technology to help with this math?

Yes, we use calculators and computers for a good part of it. Accounting and heat-loss calculationprograms save a lot of time, since they store a lot of things we commonly use so we don’t have to memorize them or look them up every time- such as heat transmission factors for various building materials and combinations thereof. Other things, like pump performance curves and oil burner nozzle capacities at different pressures are shown in charts that we keep with us.

These technologies help us work faster and more accurately. For example, most times our accountant doesn’t even have to come to our office- we just e-mail her the proper file. But we try to do the basic stuff in our heads, so we don’t lost the ability.

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

It helps us avoid guessing. It’s way too easy to guess wrong!

How comfortable with math do you feel?

I’ve never really been comfortable with math, but it’s part of my toolkit.

What kind of math did you take in high school?

I took some algebra, consumer math and I think some business types of math. Again, it wasn’t my best subject.

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

Mostly, I had to re-discover things that I forgot I’d learned in school.

So there you go.  The simple quest of warmth requires some kind of math.  Have questions for Frank?  Ask them in the comments section.  And stay tuned to Math for Grownups for more about the math involved in winter heating.

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