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MATH

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In today’s world, we’ve all unfortunately been touched by cancer in one way or another.  We may have stood beside a loved one as they battled the disease, or we may have experienced it first-hand.  Rick at First Dayton Cyberknife encounters cancer patients on a daily basis as he assists in their treatment.  I’m thankful for folks like him who use their math skills effectively to help others.

Can you explain what you do for a living?

I am a certified medical dosimetrist at First Dayton Cyberknife. I work in radiation therapy which is used to treat people who have cancer. I make sure the radiation kills the cancer cells without harming the patient.

The medical dosimetrist is responsible for designing a treatment plan and carrying out calculations with mathematical accuracy for the delivery of radiation treatment based on the oncologist’s prescribed course of therapy. This treatment plan takes into consideration tumor pathology, tumor volume, and inherent dose-limiting structures surrounding the tumor. The treatment plan and radiation field-placement techniques are constructed utilizing sophisticated computer equipment and technology. The medical dosimetrist, along with the radiation oncologist and medical physicist, will work to construct a treatment plan that will meet the prescription written by the oncologist, ensuring that the patient will not lose important healthy organ function and that the radiation delivered will not affect healthy surrounding tissue. These treatment plans not only include the use of radiation but also, in many cases, involve the use of radioactive elements during interstitial brachytherapy procedures. Once the treatment plan is complete, the medical dosimetrist will work closely with the radiation therapists in the implementation of the prescribed plan.

When do you use basic math in your job?

My whole job is math related. I wouldn’t be able to do my job without math skills. Most of my job pertains to the physical properties of radiation and its interactions with matter. There are calculations depending on energy, energy type (photon, electron, gamma ray), size of the treatment field etc. Most of these calculations are done using a treatment planning system (TPS). We use Eclipse, which is from a company called Varian. We also use a Cyberknife, which uses a software called MultiPlan.

Do you use any technology to help with this math?

Most of the time I use specialized software for treatment planning but not always. Some plans have to be hand calculated.  

Sometimes I use a hand calculation to basically determine how long the machine needs to stay on to deliver a certain dose to a certain depth. For example, the radiation oncologist will prescribe 2400 cGy (centigray is a unit of absorbed dose) in 10 treatments (240 cGy per treatment) to a depth of 80% or sometimes he will say 2 centimeterss. I will use a simple formula that we call a hand calc, 240 

80% • 1.002 =299cGy
(where 1.002 is the output factor of field and energy)

1 cGy=1 monitor unit on the machine so the machine would be set to 299 mu’s per treatment for ten treatments for 100% coverage of radiation at the 80% isodose line. This is confusing as heck so I won’t get any deeper with this because I will just go on and on and on….

This is a very simple calculation. Most of the time we aren’t this lucky. Actually most of the time everything is calculated with the Treatment Planning System.

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

Math is physics and physics is math, so you can’t have one without the other.

How comfortable with math do you feel?

I feel very comfortable with some math, but with other math I still feel very uncomfortable.

What kind of math did you take in high school?

The highest I took was Algebra II. I barely passed!

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

I have had to learn new calculations for new procedures depending on the type of treatment. Some treatments use a real source of radiation which has different factors. In college, medical physics and radiation physics were totally new to me. I can’t really compare it to normal math class. Lots of formulas, laws and other “math stuff.”

One law that is common is radiation is called the inverse square law: In physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. That is one of the first things you learn.

Want to know more about using math in the fight against cancer?  Let me know, and I’ll be sure to ask Rick your questions.

If you’re used to a completely different Math for Grownups website, hold up. You’re not in the wrong place. For the last two months (or more?), I’ve been working on a redesign of the site. I wanted something fun, punchy and energizing — kind of how I feel about math. And with my newest book, Math for Writers, hitting Amazon last month, this was a great opportunity.

And it’s not just a new book to celebrate! You’ll notice some really cool additions, plus a few old friends. Here’s a quick run down.

Sections for Writers, Parents, Teachers, and All Grownups

If you fall in one of these categories — and unless you’re a kid, you do! — you can zip right over to see the content I’ve developed just for you. Writers will find great ways to develop their craft and manage their writing. Parents will find tips for growing math-confident kids — without losing their minds. Teachers will find resources they can share with parents and students, including the answer to the age-old question: “When will I ever use this stuff?” At the same time, everyone can learn how math can help us make smarter financial decisions, save time and think about math in a completely different way.

OMG, Quizzes!

I can’t tell you how excited I am to introduce original, interactive quizzes. But before you freak out: There is no timer. There are no grades. No one has to know how you did. And that’s exactly how I wanted it. My goals are pretty simple: Show you what kids are learning at various grade levels, and give you a chance to see what you remember (or don’t). I’ll be adding quizzes over time — hopefully one a week or so. And I’ll add some non-math quizzes too, like “Are You REALLY Math Anxious?”

Coming Soon: Online Learning

If reading a blog or a book is not enough for you, I’m gearing up to offer some very targeted online learning. First up will be courses designed just for writers. Over time, I’ll add courses for parents and others. Through Facebook groups, webinars and “homework,” you’ll have a chance to take a deeper dive into the math that you need — but can’t quite grasp. These aren’t college courses, and you won’t be graded on your assignments. The idea is to give you a little special attention, so you can ask specific questions, gain some confidence and learn a few things. Stay tuned!

Math at Work Monday Is Back!

I know that this is a very popular feature on Math for Grownups, and I’ve got a whole series of greatMath at Work Monday interviews lined up. You’ll meet recycling truck drivers and cancer radiology specialists. And if you have a suggestion of someone I should interview, send me a note. I’m always looking for fresh ideas!

Take a look around. Read my new Math for Grownups Manifesto. And let me know what you think. I’m really looking forward to injecting even more energy into math.

Oh, and if you haven’t received my free gift for you, don’t miss out. Just sign up in the bright yellow box to the right, and you’ll get a free copy of Multiply Your Math Moxie: A Painless Guide to Overcoming Math Anxiety. Get comfortable with math, once and for all.

Enjoy!

Real estate appraisers: whether you love them or hate them, they’re a necessity.  Sometimes we may disagree with their figures, but as Tim Lane shows us, the facts are the facts.  And how does Tim get to those facts? Math of course.  This math has a purpose, backed by meaning, and it’s hands-on.  Tim shows us some of the inside scoop in the field of real estate appraisal.

Can you explain what you do for a living?

The job of a real estate appraiser is to determine what the property is that is being appraised: is the property a single family home, a duplex, an apartment building or something else? As well, what is the home in terms of age, size, construction quality, bedroom/bath count, and other features? Once this has been determined, the appraiser’s job then shifts to the task of analyzing the market area. This includes an analysis of the area on a large scale (city wide) relating to economics and the economic base, then a second analysis of the specific neighborhood within the city to determine what is happening in that neighborhood with real estate price trends, supply and demand, and what features or amenities are most important at this time. Finally, all the data comes together into a 30-40 page report in which all the data is given to the client. Contrary to what most people think, appraisers do not set the value of a property, we simply report what is going on in the area, and what a property is likely to sell for based on other recent sales in the area that are as similar as possible to property being appraised.

When do you use basic math in your job?

From start to finish. Initially, we have to use math to determine simple things such as how much time it takes to get from one property to another, what is the distance between them, and how many hours of daylight we have to work with to get everywhere we want or need to be in a day’s time. Math continues when looking at economic statistics to determine market trends ranging from basic issues such as determining if the area has an oversupply of available real state as compared to what the market has demonstrated can be sold in a given time frame, determining how much of a decline a market may see based on different rates of oversupply, using statistics such as regression analysis to determine a market’s reaction in terms of real dollars to different features or lack of a feature in a home. Math is used to determine the living space of a home, the size of the lot, to determine fractional increments of return on the dollar for investments made in a property.  If the property is income producing, we use math to determine an investment rate of return for dollars investments, sinking fund factors, future value of a dollar, and to help determine what type of funds need to be set aside each month for repairs of items such as roofs, HVAC systems, water heaters and other components of a home. Finally, appraisers use math to determine the cost to build a home.

Do you use any technology to help with this math?

We do use calculators and computers heavily. Calculators such as an HP-12C has been the industry standard for the real estate and finance industry for 25+ years. Software providers in the industry do all they can to calculate as many equations as possible so that we can cut down the time it takes to produce a report. Software such as Excel make complex equations much easier. However, if anyone wants to be an appraiser they are still required to be able to do all the math–much of which is very complex–with a simple pencil and paper, in order to be certified by a state and the federal government.

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

Math certainly helps appraisers do our jobs better. Most appraisers are very adept at being able to simply see a property, and know what it is likely to sell for. However our clients such as banks, accountants, lawyers, and tax courts simply will not accept a quick email with a value. Everything the appraiser says has to be backed up with provable facts; this is always rooted in math. Whether it is the size of a room, the size of a home, the size of a lot, the value of an additional bath, or the value of an additional quarter acre of land, it all has to be proven to our clients beyond any shadow of a doubt. Math is the only way to accomplish this level of proof.

How comfortable with math do you feel?

Initially, as I began to get into appraising, I wasn’t comfortable at all. Algebra and geometry play heavily into real estate appraisal, and I was never a standout in math class. Just sitting around doing math problems over and over, with no real purpose to the questions was extremely monotonous. However, once I began to actually see a purpose and a reason to do math, and had a real reason to apply the knowledge to something concrete, it became much easier. Never in my wildest dreams would I have ever believed I would use any math beyond basic addition, subtraction, multiplication and division, but I do every day now.

What kind of math did you take in high school?

I avoided math like the plague. I was forced to take Introduction to Algebra, which was the worst year of my life at the time. I later took Algebra I, which turned out to be even worse! Then geometry, which I loved! But still, math was math and that was all I was required to take, so that is all I took.

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

Yes, I did have to learn some new skills to do my job; and in some cases I had to simply relearn what I had assumed I would have no reason to remember. Real estate appraisal obviously has roots in real estate, and just as much in finance, investments and banking as well. No basic public schooling teaches this type of math. Some math skills transfer well such as word problems, or some geometry, but much of what is needed is more complex financial based math that relates to business math, statistics, projections, finance, and investments.

Questions for Tim?  Let me know, and I’ll see if he can squeeze in an answer between calculations.

Can you imagine being the president of a twenty person manufacturing company–without  math?  Meet Kathy Keel, president of BSF, Inc. and let me tell you, she has to know her math.  In her position, she must keep an eye on profitability, for her own benefit and the benefit of her employees.  But for Kathy, the math goes even deeper. Let’s take a look.

Can you explain what you do for a living?

I am the president and co-owner of a manufacturing company that makes a custom part for the hydraulic industry, called a pump-motor adaptor. My main duties on a daily basis involve managing all of the office employees, designing custom fit pump motor adaptors, editing all drawings done by other designers, costing the part, and processing orders. I also do a lot of customer service as well as troubleshooting problems, processing payroll, and managing human resource duties.

When do you use basic math in your job?

I use basic math while designing the parts to figure dimensions and angles needed for design features. We have to research the dimensions of each component being attached to the adaptor (pump, motor, and coupling usually). Then, we have to design the adaptor to fit those components. This requires fractions and decimals to figure adaptor dimensions and tolerances. I also use math during costing/pricing activities in order to determine what our cost is for manufacturing the part and what our selling price should be on the final part. This involves working with money, percentages, and markups. In addition, I use math when processing payroll.

Do you use any technology (like calculators or computers) to help with this math?

I use a calculator, Microsoft Excel, and design programs such as Solidworks.

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

I could not properly design an adaptor to fit the components without math, and I could not cost and price parts without math. Overall, I couldn’t run a company without math. I use it in almost every facet of my business to make sure that we are profitable.

How comfortable with math do you feel?

I am somewhat comfortable with basic math only. I’m not comfortable at all with more complex math.

What kind of math did you take in high school?

One year of Algebra as a freshman.

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

I had to learn to translate metric to English measurements and to equate fractions to decimals.

Have questions about Kathy’s company, their products, or her use of math skills at work?  Let me know and I’ll be happy to check in with her.

No. I do not have cancer. But in April and May and June of this year, I thought I might.

So that’s the answer to the question in my headline. I’ve been taking a break while I deal with the roller coaster of emotions that come with suspicious mammogram and biopsy results and then surgery. First, the story.

In April, I had an ordinary, run-of-the-mill mammogram. I’m what you call a non-compliant patient, and so I’ve only had one other mammogram in my life. Turns out both of these great experiences ended up with biopsies. My first feeling was to be totally pissed off. I’d had a biopsy before, and let me tell you, they are not fun. And since the first one showed nothing, I expected that this would be more of the same — an exceedingly uncomfortable and nerve-wracking experience that showed nothing.

Except it didn’t. The biopsy showed “atypical” cells. This means I had something called Atypical Ductal Hyperplasia or ADH. This is not cancer. These atypical cells cannot even be called precancerous cells. My amazing surgeon explained: Research shows that women with ADH have an increased chance of those atypical cells becoming cancer. Here are the numbers:

  • Women without ADH have about a 5 percent chance of getting breast cancer.
  • Women with ADH have a 20 percent chance of getting breast cancer.
  • And that means women with ADH have four times the chance of getting breast cancer.

For me, those numbers pointed to a very easy decision: to have the area with ADH removed. On July 5, I had a lumpectomy. Then I waited for the pathology results. I waited for 10 days.

Anyone who has gone through something similar knows the special hell these ten days were. I am not a particularly emotional person. And yet, these ten days were downright terrifying. And here’s why.

There was a 20 percent chance that the lumpectomy would reveal cancer. In other words, there was a slight chance that the biopsy missed any cancerous cells that were already there. Of course, that meant I had an 80 percent chance of no cancer at all.

After the surgery, I updated my friends and family. One physician friend emailed me back: “I hope you find some solace in those stats (ie the 80%).” I assured her that I did. (No lie at that point.) And she followed up with this:

“Glad to hear how you’re taking it. You are right about the stats.  They are often very difficult for patients, because if there is a small chance of something, but a patient has it, that patient has 100% chance of having it, right? But we as physicians use stats all the time, especially in the office setting where you don’t have any and every diagnostic test at your fingertips, and with the cost– psychological and financial– to the patient: what is the chance that this patient with this headache and those symptoms has a brain tumor? What are the chances that this person’s chest pain is a heart attack and not indigestion? It is probability, given symptoms, age, and a slew of other factors, in combination with the implications of a given diagnosis.”

These numbers were supposed to ease my mind. Except feelings + stats + time = complete and utter freak out.

By day nine of my waiting period, I was a total wreck. I cried all day long. I wasn’t sure if I was going to be able to sleep. I was nervous as a long-tailed cat in a room full of rocking chairs.

Happy ending: I don’t have cancer. I know that not everyone gets that amazing news, and I am extremely grateful. I am being followed very closely, because my chances of getting breast cancer are still higher than most women’s. And I’m taking tamoxifen for the next five years, which reduces my chances by half. Those aren’t bad stats either.

I never thought that math was the be all end all, but I have often railed against misinterpreting numbers to incite fears and advocated for the use of statistics to ease worry. Still, feelings don’t always play well with math, I’ve found. When a person is worried — scared, even — a pretty percentage may not be comforting. And that’s okay, too. We all do the best we can with what we’ve got.

What’s your story with health and statistics? Has a percentage ever frightened you to the point of distraction or temporary insanity? Share your story here. You are not alone!

Most of you are probably sick to death of 2012 campaign poll results. But these numbers have become a mainstay of the American political process. In other words, we’re stuck with them, so you might as well get used to it — or at least understand the process as well as you can.

Last Friday, I wrote about how the national polls really don’t matter. That’s because our presidential elections depend on the Electoral College. We certainly don’t want to see one candidate win the popular vote, while the other wins the Electoral College, but it’s those electoral votes that really matter.

Still, polls matter too. I know, I know. Statistics can be created to support *any* cause or person. And that’s true. (Mark Twain popularized the saying, “There are lies, damned lies and statistics.”) But good statistics are good statistics. These results are only as reliable as the process that created them.

But what is that process? If it’s been a while since you took a stats course, here’s a quick refresher. You can put it to use tomorrow, when the media uses exit polls to predict election and referendum results before the polls close.

Random Sampling

If I wanted to know how my neighbors were voting in this year’s election, I could simply ask each of them. But surveying the population of an entire state — or all of the more than 200 million eligible voters in the U.S. — is downright impossible. So political pollsters depend on a tried-and-true method of gathering reliable information: random sampling.

A random sample does give a good snapshot of a population — but it may seem a bit mysterious. There are two obvious parts: random and sample.

The amazing thing about a sample is this: when it’s done properly (and I’ll get to that in a minute) the sample does accurately represent the entire population. The most common analogy is the basic blood draw. I’ve got a wonky thyroid, so several times a year, I need to check to see that my medication is keeping me healthy, which is determined by a quick look at my blood. Does the phlebotomist take allof my blood? Nope. Just a sample is enough to make the diagnosis.

The same thing is true with population samples. And in fact, there’s a magic number that works  well enough for most situations: 1,000. (This is probably the hardest thing to believe, but it’s true!) For the most part, researchers are happy with a 95% confidence interval and ±3% margin of error. This means that the results can be trusted with 95% accuracy, but only outside ±3% of the results. (More on that later.) According to the math, to reach this confidence level, only 1,000 respondents are necessary.

So we’re looking at surveying at least 1,000 people, right? But it’s not good enough to go door-to-door in one neighborhood to find these people. The next important feature is randomness.

If you put your hand in a jar full of marbles and pull one marble out, you’ve randomly selected that marble. That’s the task that pollsters have when choosing people to respond to their questions. And it’s not as hard as you might think.

Let’s take exit polls on Election Day. These are short surveys conducted at the voting polls themselves. As people exit the polling place, pollsters stop certain voters to ask a series of questions. The answers to these questions can predict how the election will end up and what influenced voters to vote a certain way.

The enemy of good polling is homogeneity. If only senior citizens who live in wealthy areas of a state are polled, well, the results will not be reliable. But randomness irons all of this out.

First, the polling place must be random. Imagine writing down the locations of all of the polling places in your state on little strips of paper. Then put all of these papers into a bowl, reach in and choose one. That’s the basic process, though this is done with computer programs now.

Then the polling times must be well represented. If a pollster only surveys people who voted in the morning, the results could be skewed to people who vote on their way home from their night-shift or don’t work at all or who are early risers, right? So, care is made to survey people at all times of the day.

And finally, it’s important to randomly select people to interview. Most often, this can be done by simply approaching every third voter who exits the polling place (or every other voter or every fifth voter; you get my drift).

Questions

But the questions being asked — or I should say the ways in which the questions are asked — are at least as important. These should not be “leading questions,” or queries that might prompt a particular response. Here’s an example:

Same-sex marriage is threatening to undermine religious liberty in our country. How do you plan to vote on Question 6, which legalizes same-sex marriage in the state?

(It’s easier to write a leading question asking for intent rather than a leading exit poll.)

Questions must be worded so that they illicit the most reliable responses. When they are confusing or leading, the results cannot be trusted. Simplicity is almost always the best policy here.

Interpreting the Data

It’s not enough to just collect information. No survey results are 100 percent reliable 100 percent of the time. In fact there are “disclaimers” for every single survey result. First of all, there’s the confidence level, which is generally 95%. This means exactly what you might think: Based on the sample size, we can be 95 percent confident that the results are accurate. Specifically, a 95% confidence intervalcovers 95 percent of the normal (or bell-shaped) curve.

The larger the random sample, the greater the confidence level or interval. The smaller the sample, the smaller the confidence level or interval. And the same is true for the margin of error.

But why 95%? The answer has to do with standard deviation or how much variation (deviation) there is from the mean or average of the data. When the data is normalized (or follows the normal or bell curve), 95% is plus or minus two standard deviations from the mean.

This isn’t the same thing as margin of error, which represents the range of possibly incorrect results.

Let’s say exit polls show that Governor Romney is leading President Obama in Ohio by 2.5 percentage points. If the margin of error is 3%, Romney’s lead is within the margin of error. And therefore, the results are really a statistical tie. However, if he’s leading by 8 percentage points, it’s more likely the results are showing a true majority.

Of course all of that depends — heavily — on the sampling and questions. If either or both of those are suspect, it doesn’t matter what the polling shows. We cannot trust the numbers. Unfortunately, we often don’t know how the samples were created or the questions were asked. Reliable statistics will include that information somewhere. And of course you should only trust stats from sources that you can trust.

Summary

In short, there are three critical numbers in most reliable survey results:

  • 1,000 (sample size)
  • 95% (confidence interval or level)
  • ±3% (margin of error)

Look for these in the exit polling you hear about tomorrow. Compare the exit polls with the actual election results. Which polls turned out to be most reliable?

I’m not a statistician, but I’d be happy to answer your questions or find an expert who can. Ask away!

P.S. I hope every single one of my U.S. readers (who are registered voters) will participate in our democratic process. Please don’t throw away your right to elect the people who make decisions on your behalf. VOTE!

Ever get in one of those organizing moods — looking for ways to save money, save time, save brain cells? That’s so me right now. I haven’t done a good financial audit in a while. Now that my daughter’s in middle school, I’ve got more time to waste (or use wisely). And because I’ve got more work than I’ve ever had in my entire freelancing career, managing my creative energy has become paramount.

For the first time in my life, I’ve hired a business coach. With her help, I’m streamlining my schedule and processes — looking for ways to work smarter, so that I can work less. As a result, I’m on a real savings tear in all aspects of my life — looking to spend less money and carve out more time.

And math has helped. Between considering whether to invest in new accounting software to actively assessing my weekly hours, I’m doing the calculations that help me make these decisions. Especially in this economy, I know that I’m not alone. We’re all looking for ways to cut down on our monthly bills and put more away in savings.

For the month of October, we’ll consider many aspects of savings — money, time, energy, even lives — and how math plays a role. We’ll find intuitive ways to squirrel away these important resources, just in time for a long winter, when we can sit back with a great book and enjoy the fruits (or nuts) of our planning and hard work.

Got questions or suggestions? Please share them in the comments section!

Today’s guest post is from Laura Overdeck, the ingenious creator of Bedtime Math. Don’t know what that is? Keep reading. And then go sign up for their daily email. You won’t regret it!

As kids go back to school, it’s natural for parents to look at their bright-eyed offspring and wonder what they’ll go on to do in life. Chances are they’re hoping their kids will major in something substantial in college to lay the foundation for a great career. Unfortunately, that isn’t what we see happening: According to the National Center for Education Statistics, today more U.S. undergraduates are majoring in “leisure and recreation studies” than in all physical sciences combined (chemistry, physics, astronomy…you get the idea). And there are more than twice as many majoring in leisure studies as in math.

Why does this happen? Why is our next generation running scared from the subjects that involve math? Can we make math the fun leisure activity that kids flock to do?

The problem is that our culture doesn’t view math the way we view reading. Everyone knows to read to children from a young age, and most educated parents do. By the time kids get to kindergarten, even if they can’t read yet, they probably have a warm, cozy feeling about books. To them, reading is a leisure activity, an activity you do for fun when you have free time. Math, by contrast, doesn’t get the same warm, fuzzy introduction as the bedtime story. While there are plenty of magnetic number sets and 1-10 counting puzzles, for most families math at home stops as soon as the children reach toddlerdom. As a result, for a lot of kids their first real experience with math happens in school, with all the associations of homework, drilling and tests. That’s not going to make it feel like leisure. It feels like a chore.

It’s no wonder, then, that kids start off on the wrong foot with their relationship with math.

Kids should view math as fondly as they think about storybooks. While your child plugs away at the usually dry math material from school, it’s good to counter that with fun math at home as an antidote. By the way, that doesn’t mean forced, contrived set-ups where your child can see right through to your intentions. Luckily, there are plenty of fun activities ripe with “stealth” math that may be part of your day already:

  • Baking: Doubling recipes requires multiplying; cutting in half requires dividing; measuring 1/4-cups or 1/4-tsps uses fractions. Any time you bake, you’re quantifying ratios to make magic in the oven. Toddlers can participate by counting out chocolate chips, and of course eating them as a bonus.
  • Building: Anything that involves measuring gets kids counting, adding, and multiplying. Lego and other building toys revolve around numbers, too. And we all see how kids can entertain themselves with a bunch of cardboard boxes, especially if told they’re off limits. Cutting up pieces to assemble a fort all revolves around measurement.
  • Planning: For example, setting up party favors. They’re all sold in different quantities: 10 in one pack, 24 in another, 18 in a third. If there are 16 kids coming over, how many packs of each do you need, and what’s left over? Even putting out breakfast or dinner takes some planning and counting.
  • Sports and exercise: Kids love stopwatches, and watching the seconds tick off gives kids great exposure to counting. Distances and heights require measurement, and even counting jumping jacks, baseball swings, or the kicks to get a soccer ball to the end of a field, can involve numbers.

All of these activities contain a ton of math as a natural part of the process, and this list is just a start. When kids get absorbed in a favorite activity, they don’t even notice they’re learning, just like when they read a bedtime story.

To that point, math can become a part of bedtime as well. Six months ago I founded Bedtime Math, a free website that offers a fun nightly math problem every night – about electric eels, chocolate chips, zip lines into the neighbor’s pool.  Again, the idea is to take kids’ absolute favorite topics and sneak some math in there. After just six months we have over 20,000 people following us through the daily email, the website or Facebook, and parents have written that their previously math-resistant children now ask for Bedtime Math at night, thanks to this new spin on numbers.

Again, it’s all about catching kids while they still think numbers are fun, and building on that mindset. By making math a fun part of favorite natural routines, kids will think of numbers as recreation instead of compulsory drudgery. When they enter school with that new world view, they will have an entirely different, incredibly positive experience with math at school. And with that foundation, maybe they won’t have to sink to majoring in leisure studies when they grow up.  They’ll major in math instead – for fun.

Laura, you’re singing my song! The beauty of Bedtime Math is that it offers three levels of difficulty. Parents don’t have to try to figure out what they should expect their toddler to do or how difficult the math should be for their 2nd grader. And I guarantee — GUARANTEE! — that if you give this a try, you’ll find yourself injecting math all over the darned place.

So what do you think about these sneaky math ideas? Are you ready to throw away the worksheets and flash cards? Have you figured out some easy ways to encourage your kids to do math — without their even knowing it? Share your ideas in the comments section.

In recent months, there’s been a tremendous amount of buzz regarding an educational change called Common Core. And a ton of that buzz perpetuates down-right false information. There’s so much to say about this that I’ve developed a five-part series debunking these myths — or outright lies, if you’re being cynical. This is the fourth in that series (read Myth 1Myth 2 and Myth 3), which will continue on Wednesdays throughout August and into September. Of course, I’ll be writing from a math perspective. Photo Credit: Watt_Dabney via Compfight cc

Myth #4: The Standards Require More Testing

Perhaps the most controversial aspect of the U.S. education system is standardized testing. And for good reason. There are a myriad of problems with these tests–from their links to private companies to their use as teacher evaluation tools.

While I’ve said from the start that it’s not fair to judge the Common Core Standards based on their implementation in individual states, it’s also not fair to pretend that the standards and testing don’t go hand in hand. States aren’t abandoning standardized testing any time soon, so don’t hold your breath.

But what we do know for certain that the adoption of Common Core Standards does not mean more testing–in the long run. In fact, there is no testing requirement inherent in the adoption of Common Core. None!

However, as states move from previous standards to Common Core, there will be some changes in testing. First, student may take two sets of standardized tests–at first. In these situations, one test is the one aligned with the state’s previous standards. And students may take practice tests, based on the Common Core Standards. Usually this translates to more testing during one school year, with only one test score used for student placement or teacher and school evaluations.

Because the Common Core Standards focus on critical thinking, Common Core-aligned tests will probably look a little different than the all-multiple choice tests that we’re all used to. Students are required to show their work and may even be asked to explain how they came to their answers. Here’s a two-part example, which corresponds with the third grade math standards:

A. Fill in the blanks below to make a number sentence that represents the drawing:
________ x ________ = ________
B. Put the dots below into five equally sized groups and write an equation that represents the drawing.

•  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  •  

Answers:
A. 4 x 6 = 24 or 6 x 4 = 24 or 8 x 3 = 24 or 3 x 8 = 24, etc.
B.   •  •  •      •  •  •      •  •  •      •  •  •      •  •  •      •  •  • 
3 x 5 = 15 or 5 x 3 = 15 or 15 ÷ 3 = 5 or 15 ÷ 5 = 3

There’s something going in the above problems that’s difficult (or impossible) to measure with multiple choice questions. First, students are asked to draw as a way of problem solving. Second, there are multiple correct answers.

(Psst. Want to test your third grade or fifth grade math skills? Take one of the Math for Grownups math quizzes. No one has to know your score. Promise!)

So while Common Core does not eliminate testing or prevent test results from being used inappropriately, if the tests are well constructed–and dang, that’s a big if–students have a much better opportunity to demonstrate critical thinking and the open-ended nature of mathematics. That’s not more testing, that’s better testing.

Got a question about the Common Core Standards for Mathematics? Please ask! Disagree with my assessment above? Share it! And if you missed Myth #1, Myth #2 or Myth #3, you can find the herehere and here.

I had the pleasure of speaking with Samantha Volz who has the pleasure of working from her very own home every day. That is one of the benefits of being a freelance designer. In addition to graphic design, this artist also does photography. It seems she is creatively blessed with talent.  I was curious about how she uses math in her work. Let’s take a look at what she had to say:

Can you explain what you do for a living?

I’ve been working as a freelance designer since 2001.  I design marketing/advertising material for companies. In addition, I also design websites and other support files for social media applications. I am a photographer, painter, and artist as well.

When do you use basic math in your job?

I have to use specifications to set up design files. Set up bleed, trim and safe zones so that when the file gets to the printer, it is set up correctly and prints correctly. For instance, if I have a print sheet that is 8.5 by 11 inches for a trifold brochure, I need to divide the paper by three and adjust 1/8th of the 3 panel. Depending on how the trifold folds, I will need to adjust the panels 1/16th of an inch if a panel folds in. Then, on the layout in the software I have to consider set up for a printing press or digital printing if my graphics bleed to the edge I have to add at least 1/8th to 1/4th of an inch of graphics that extends past the actual final layout for being trimmed down to allow for machine error. So my final file that is handed over to the print vendor is 8.5 x11 with bleed 1/8th bleed on all sides. Total graphic coverage is 8.75 x 11.25 trimmed down to 8.5 x 11 and scored for folds indicated on the set up with 3 panels roughly 3.66 ” wide, again depends on the fold design chosen for that tri-fold brochure how it will read, flow and open up to reveal the information being provided.

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

Yes, I use a calculator a lot.

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

I could not do my job without it. It is how everything flows from the client to me, the designer, and then to the printer until it is produced as an end product.

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

I am comfortable with normal addition, subtraction, division, multiplication, and fractions. Nothing too complicated.

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

I took honors math classes.

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?

Yes, what I use now I learned in high school.

Who knew that the creative type still need to know their basic calculations and fractions?  Seems like everywhere you go, even in your home, math is sure to follow. I hope you enjoyed learning a little more about Samantha. Let me know if you have any further questions for her. 

Photo Credit: 55Laney69 via Compfight cc

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

Can you explain what you do for a living?

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

When do you use basic math in your job?

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

Do you use any technology to help with this math?

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

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

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

How comfortable with math do you feel?

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

What kind of math did you take in high school?

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

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

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

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

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.