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In Math for Parents

Math Secret #3: You can skip the love

When I was a camp counselor after my sophomore year of college, I had a standard response to kids who asked, “Do I have to?” Whether they were complaining about sweeping out the cabin or taking a hike, I’d look them in the eye, smile and say, “No. You get to!”

I wasn’t a teacher yet, but I had this instinct to spin complaints into commendations. Sometimes this worked. The hikes were a good time, and even sweeping sometimes ended in fits of laughter or song.

But the more I think about math and grownups, the more I think that this flip response doesn’t apply. I do think math is fun — well, some math. I love proofs, from the two-column geometry proofs that I did in high school to proving properties of our real number system. I also love doing some kinds of algebra, like solving systems of equations with two variables.

But I don’t love all math. Try as I might, probability still screws with my head. And I honestly and truly despise logarithms. (Those are to solve for x, when the variable is an exponent. More than likely, you haven’t seen logarithms in decades.)

The realization that math doesn’t have to be fun really hit home twice this past year. When I wrote my proposal for Math for Grownups, the publisher offered positive feedback, except for one thing. “Don’t focus on the fun of math,” my editor said. “Focus on the fact that we need it.” That was a real wake-up call for me. I couldn’t say to my readers, “You don’t have to do this math; you get to!”

And this spring, I also served as an instructional designer for two online, high school math courses, Algebra II and Probability and Statistics. This meant that I reviewed the lessons, looking carefully at the pedagogy and mathematics. I could tell when I loved the math. I was ready to work every day and genuinely didn’t want to stop until everything was finished. But when I hit a unit that was less engaging for me, I stalled. I looked for anything else I could be doing — laundry, cleaning out my email, visiting my favorite blogs.

I didn’t love all of the math I was doing. Why should I expect that of anyone else?

That’s why I say that math doesn’t have to be your BFF. It’s like making dinner every night. Some people can’t wait to get their hands into some fresh bread dough or chop up onions or heat up the grill. Others are satisfied with take-out. And then there are plenty of us who are very happy somewhere in the middle.

But we’ve all got to eat, whether we love cooking or not. And we’ve all got to do math. You don’t have to love it, but you can learn to tolerate it.

What do you love or hate about math? Share your ideas in the comments section.

In Current Events

Missing-Persons Statistics: When the numbers don’t add up

I’d like to welcome my first guest poster here atMath for Grownups, Carole Moore. Carole is a fellow writer and the author ofThe Last Place You’d Look: True Stores of Missing Persons and the People Who Look for Them, which hit bookstores in May. Her book is a gripping account of a variety of missing persons cases around the country. A former police detective, Carole knows her stuff.

She also knows how darned scary missing-persons statistics can be. And so she’s offered to take a closer look at these numbers and what story they really tell. This is a critical way that we can use math without even being aware. See, as scared of math as many of us are, we may also be inclined to trust numbers. Unfortunately, without some perspective and context, numbers don’t mean a thing. Keep reading…

When it comes to crime, statistics can be misleading. The truth is in how you break down the numbers. Let’s look at one example: According to the U.S. Department of Justice, 797,500 children under the age of 18 were reported missing in one year’s time. That’s an average of 2,185 kids per day. What’s more interesting is what those numbers don’t say:

First, the category of the report from which they’re drawn (NISMART-2) specifies “reported” missing. That means that some kids who disappeared in the same time bracket were not reported within the reporting period. It doesn’t necessarily mean they weren’t reported at all – although many aren’t. Illegal immigrants often won’t call police out of fear of reprisals, and the children of the mentally ill, transients, the homeless, prostitutes and drug users, as well as foster kids, often escape the count. So, while the figure 797,500 sounds huge, the actual number of missing children in a year well exceeds “reported” missing.

Now, look a little closer at those numbers, starting with family abductions, which account for 203,900 children reported missing, and 58,200 kids classified as non-family abductions. That leaves 535,400 children unaccounted for – of these children only 115 were considered “stereotypical” kidnappings. (Examples of stereotypical kidnappings are usually extreme and include cases such as those of Jamie Duggard and Adam Walsh.) The remaining 535,285 children fit in none of these specific categories.

The children left are grouped miscellaneously. For example, a child reported missing after stopping at a friend’s house following school (and who didn’t notify a parent or caretaker) would now be a reported missing child for statistical purposes. So would a child who becomes lost or hides out whose disappearance is reported – even if the child is really not missing in the truest sense of the word, they would be classified as “reported missing.”

My point is that while the statistics here don’t lie, they also don’t tell the whole story in and of themselves. Many missing children are never reported missing, while many of the reported missing really aren’t missing at all. To truly understand crime stats, it’s important to dig deeper than the numbers.

Carole Moore is a former police detective and current freelance writer, as well as contributing editor and columnist at Law Enforcement Technology. You can learn more about her atwww.carolemoore.com.

Do you have questions about crime statistics? Ask them in the comments section!

In Math Education

Is Math a Foreign Language?

When I was in college, majoring in math education, I learned that math is the language of science. In fact, we called it the Queen of the Sciences. (You’d better believe that gave me a sense of superiority over the chemistry and physics majors!) And yeah, I think that the math I was doing then–calculus, differential equations, statistics and even abstract algebra–is mostly useful for describing some kind of science. [pullquote]We too often think of mathematics as rules rather than as questions. This is like thinking of stories as grammar. — Rick Ackerly[/pullquote]

In some ways, everyday math is also the language of science. Home cooks use ratios to ensure that their roux thickens a gumbo just right. With proportions, gardeners can fertilize their vegetable beds without burning the leaves from their pepper plants. And a cyclist might employ a bit of math to find her rate or the distance she’s biked.

But I think too often we adults get caught up in the nitty gritty of basic math and lose the big picture. This is when many of us start to worry about doing things exactly right–and when math feels more like a foreign language, rather than a useful tool.

Earlier this week, I read a blog post from Rick Ackerly, who writes The Genius in Children, a blog about the “delights, mysteries and challenges of educating our children.” In Why Mathematics is a Foreign Language in America and What to Do about It, he writes:

Why do Americans do so badly in mathematics? Because mathematics is a foreign language in America. The vast majority of children grow up in a number-poor environment. We’ve forgotten that the language of mathematics is founded in curiosity. We too often think of mathematics as rules rather than as questions. This is like thinking of stories as grammar. Being curious together can be a really special part of the relationship in families.

And I couldn’t agree more. For all of you parents and teachers out there: how many questions do your kids ask in one day? 10? 20? 100? 1,000? As Ackerly points out, especially younger children are insatiably curious. They want to know why the sky is blue and what makes our feet stink and how come that ladybug is on top of the other ladybug.

These Stevendotted ladybugs are not wrestling. Photo credit: Andr Karwath

A full 90% of the time, we can’t answer their questions. Or maybe we just don’t want to yet. (“That ladybug is giving the other one a ride.”) With Google‘s help, we can find lots of answers. But how often are we asked a math-related question–by a kid or a grownup–and freeze?

For whatever reason, many people are afraid to be curious about math. Or they’ve had that curiosity beaten out of them. I think that’s because don’t want to be wrong. As fellow writer, Jennifer Lawler said to me the other day:

It’s funny because when I make a mistake in writing—a typo, etc.—I let myself off the hook (“Happens to everyone! Next time I’ll remember to pay more attention.”) But if I misadd a row of numbers I’m all “OMG, I’m such an idiot, and everyone knows I’m such an idiot, I can’t believe they gave me a college degree, and why do I even try without my calculator?”

The same goes for answering our kids’–or our own–calls of curiosity.

So what if we decided not to shut down those questions? What if it was okay to make some mistakes? What if we told our kids or ourselves, “I don’t know–let’s find out!” This could be a really scary prospect for some of us, but I invite you to try.

What’s keeping you from being curious about everyday math? What do you you think you can do to change that? Or do you think it doesn’t matter one way or the other? Share your ideas in in a comment.

In Math at Work Monday

Math at Work Memorial Day: Wendy the television line producer

What is a television line producer, and how long have you been doing this job?

Production companies hire me after they’ve received the “green light” to develop and produce a new television series. The first thing I do is read something called the bible, a document that explains the concept, visual look and tone of the show. My job is to create a production budget based on the amount of money the executive producer has for the entire project. For example, if he or she gives me $6 million to produce 26 episodes, I need to allocate every cent within several dozen categories over the length of the production. I also create the pre-production, shooting and post-production schedules, assist with casting, hire the technical crews and then oversee the whole project from beginning to end. I’ve been doing this work for 23 years.

When do you use basic math in your job?

I have to break everything down in the budget and make sure we only spend what we have! So for example, I have to figure out how many days we need a wardrobe assistant, how much it will cost, and make sure we have some wiggle room for overtime, extra prep days, etc. Sometimes, if I’m working on a smaller budget show, I’m the one who calculates the actors’ and technicians’ time sheets, so lots of adding, multiplication, etc.

Every week or so, I have to do cash flow reports; how much I estimated to spend, the actual costs, and estimated future costs. It all has to balance out, so if we do lots of overtime one week, I need to figure out what needs to be cut over the coming weeks to make up for that shortfall.

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

Oh yes!! Time sheets are now calculated on the computer, but I still check everything with a calculator, as I’ve fallen victim to incorrect formats. Nothing worse than a camera operator coming up to you saying his paycheck is wrong!! Cash flows and budgets are either done on Excel or through special software, often MovieMagic, which has programs for film and television scheduling and budgeting.

I have to admit I also still count on my fingers sometimes

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

It forces me to focus on what is perhaps the most important part of any creative project: the bottom line. Television is lots of fun, but it’s a business, and the executives and broadcasters expect me to deliver a project on budget. Time is money when you’re on-set, so even 15 minutes of overtime can sink you, if you have dozens of cast and crew to pay. Math makes me more organized!

How comfortable with math do you feel?

Today, I’m very comfortable with math, but since I have a tendency to do everything quickly, my challenge is always to slow down and get it right.*

What kind of math did you take in high school?

I hated math all through school, and always excelled at writing, and other creative subjects. I had one fabulous math teacher in tenth grade who finally made math fun. Good thing I was in his class, because I’d always figured I’d never need math to pursue my career goals, but was amazed years later to discover how much math I needed when I started working in television production. I was a script supervisor whose duties included timing segments with a stop-watch, adding things up and making sure we wouldn’t go into editing with too many long scenes. I was terrified of making math errors, and realized quickly to slow down, relax and always double-check my work.

Wendy Helfenbaum is a writer and television producer in Montreal, Canada. Visit her at http://www.taketwoproductions.ca.

*This is perhaps the best advice I can offer anyone who is struggling with math. Only your fifth-grade teacher and the Mathletes coach care how quickly you can do calculations.

Last week’s Math at Work feature was with my sister, Melissa, who is a speech therapist.

In Math Education

Mixing in Math: Teacher Cooks Up Lesson in the Kitchen

So this apparently is big news in Myrtle Beach. A middle school math teacher actually took her kids out of the classroom to teach them math. In the school cafeteria, the students converted decimals to percents and found surface area and volume — as they were cooking up some healthy eats.

Ya’ll, seriously. This is what how we use math as grownups.

(Okay, so the surface area and volume is a bit of a stretch.)

If you think doing math is about chalkboards and protractors, you’re flat out wrong. (Besides schools use dry erase boards these days.)

Math is about getting your hands dirty, sketching a picture on a scrap piece of paper, doing some quick calculations on the iPhone. Most of all, math is about solving real problems — not those silly things that have something to do with trains in Omaha — and coming to these solutions in creative and sensible ways. (There. I said it: creative and sensible.)

Look, I like what this teacher is doing. And so do her students:

“You learn it better because you enjoy doing it,” said Maya Bougebrayel, who made a vegetable chicken stir fry with teammates Allison Klein and Carlisa Singleton. The girls, all 13, agreed that the project put a creative spin on learning and made it easier for those who are visual learners.

But if it wasn’t such a novel idea, wouldn’t grownups be better at math? Feel free to chime in in the comments section.

In Math for Grownups

Preakness Math: What Are the Odds?

This morning at 6:00 a.m., I gave my 10 year old $25 and sent her off to the racetrack.

It’s Preakness weekend here in Baltimore, and just a few blocks from my house, Pimlico Racetrack will host the 136th Annual Preakness Stakes. It’s a half-day at school today, and one of my daughter’s friends is totally into horse racing. Besides, she has adult supervision.

But I probably should have taught her a little bit about odds.

Preakness is the second leg of the Triple Crown, and all eyes will be on Animal Kingdom, the 20-1 long shot who won the Kentucky Derby in early May. Animal Kingdom isn’t a long shot anymore. At the Preakness, his odds are 2-1.

Where do these numbers come from? Betting on horse racing is a popularity contest. In other words, the payoff depends on the bets themselves. People like a winner, and so they tend to bet on the favored horse.

That means that the favored horse will have the best odds — and the lowest payoff. And that’s why Animal Kingdom was such a great win at the Derby. Odds like 20-1 suggest that the horse is not expected to win. It’s the unusual event that every better wants in on.

But while it’s easy to see which horse is favored to win, it’s a little tougher to figure out the payoff. Here’s a quick look at how it will work at the Preakness. To make things simple, we’ll just consider a $2 bet on Animal Kingdom, who currently has 2-1 odds. (Those odds will change as we get closer to the race.)

First multiply the amount of the bet by the first number in the odds ratio:

$2 x 2 = $4

Easy enough, right? Now divide by the second number in the odds ratio:

$4 ÷ 1 = $4

And finally, add the amount you bet, and that’s your payoff:

$4 + $2 = $6

So if you place a $2 bet on Animal Kingdom with 2-1 odds — and he wins — you’ll get a $6 payoff.

Clearly, things get a little more complicated with different odds. So let’s look at another example. What if you wanted to place a $2 bet on Dialed In, another Preakness contender? This horse currently has 9-2 odds.

$2 x 9 = $18

$18 ÷ 2 = $9

$9 + $2 = $11

So placing the same $2 on a horse with 9-2 odds, means a bigger payoff ($11), if the horse wins. How come?

Higher odds have lower payoffs. A long-shot (like Animal Kingdom in the Kentucky Derby) has lower odds, so if they do win, the payoff can be pretty big.

Problem is, it’s not likely that a horse with low odds will win the race. And that’s why Animal Kingdom’s win in the Derby was such a big deal. Still, horses with higher odds have won the Kentucky Derby. In 1913, Donerail won with 91.45-1 odds!

Of course, the more you bet, the more you’ll win — if your horse wins. Take a look at a $150 bet on Dialed In at 9-2 odds:

$150 x 9 = $1,350

$1,350 ÷ 2 = $675

$675 + $150 = $825

Not a bad take. Still it’s a gamble, and that’s why plenty of people lose. To learn more, visit the Preakness website, which includes a great tutorial on betting the horses.

What do you think Animal Kingdom’s chances of winning the Preakness are? Do we have another Triple Crown winner on our hands? Give us your odds in the comment section.

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!