Math for Grownups

Category: Math for Grownups

Math at Work Monday: Stephen the Realtor

When we moved to Baltimore almost seven years ago, my family and I found amazing friends in our next-door neighbor Stephen Sattler and his partner Neil. So, it is really no surprise that Stephen has now found his calling as a Realtor, working primarily with relocation. Here’s how Stephen uses math in his work.

Can you explain what you do for a living?

Basically, I help my clients find shelter–which includes the buying, renting, selling, and ferreting out of places to live, after listening and then understanding what they’re trying to tell me.

When do you use basic math in your job?

The whole idea of proration is key to the real estate industry. At the settlement table, the property’s monthly taxes, utilities, interest, and other financial considerations must be equitably split between both buyer and seller, as of that date. The same thing holds true if you’re renting a house, especially if you’re beginning your term in the middle of a month. Leases typically call for a yearly total of rent due, which means you just multiply the monthly rent by twelve. But calculating the first month’s rent can be tricky if you don’t know how to calculate the daily rate. It sounds complicated, but all you have to do is divide the yearly rent by 365. Then you can multiply that by the days left in the month.

Stephen Sattler

Do you use any technology to help with this math?

I do have a fancy real estate calculator that helps with the more complex things like finding a monthly amortization amount at a given interest rate over a set period of time, but for the most part I hand-calculate the math I tend to use from day to day.

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

I wouldn’t really have a job unless I could apply math at its most basic levels: settlement costs are a typically a set percentage of the sales price, prorated bills are due as of the date the property is transferred, and my income is always a percentage of the total sales price–which can change at each and every transaction. I feel like I’m always taking quick, armchair calculations to figure out where things generally stand at the end of any given week.

How comfortable with math do you feel?

I was one of those students in school who tended to excel more in the creative arts–writing, languages, history, and the like. I have horrible memories of feeling I was the last person in math or science class to even generally grasp the problem being discussed, from algebra to geometry to even basic chemistry. I don’t think I ever quite figured out how to balance a chemistry equation!

I turned 50 this year, which meant I could finally let go of what hasn’t worked for me in the past. With GMATs and all the other truly stressful mathematical events I’ve had in my life, I was convinced that my brain just wasn’t wired the right way, or that I even had some sort of math disability. Put me in a job I absolutely love, however, and help me see how math can help my clients find and then settle into the home of their dreams, and I’m astonished at how mathematically competent I now feel!

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

I took everything mathematical a good properly-educated, college-bound boy was supposed to take, but my God was it absolute torture. There were so many rules to understand and follow, and you couldn’t really reason or write your way out of a problem–like you could in an essay question in, say, English class–unless you knew how to manipulate the underlying mathematical formulae (which of course my feeble brain could barely even understand let alone memorize and apply). It also didn’t help that all the math teachers at my school seemed to double as coaches for various sports teams in their after-school lives, and using the same motivational threats they used on the field (Yo– what the &*^%$ were you #@!) thinking!) didn’t quite have the same result in the classroom with those of us who were not quite as macho about math.

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

Actually, successfully using math as much as I do now in my everyday job has finally helped me feel I’m not the complete and utter dolt I always thought I was when it came to dealing with figures.

Do you have questions for Stephen about the math of real estate? Please ask them in the comments section. He can responded there or I’ll write another post addressing more complex issues.

May 14, 2012
Math at Work Monday: Jameel the financial organizer

Welcome back to Math at Work Monday! (We took time off from this regular feature, so that we could spend more time celebrating Math Appreciation Month.) If you’re new here, each Monday I post an interview with someone about how they use math in their jobs. I’ve interviewed Maryland’s Commissioner of Health, one of my former students who is a glass blower and my sister who is a speech therapist.

Because we’re focusing on personal finance this month, I thought it would be a great idea to reintroduce you to Jameel Webb-Davis, a financial organizer and budget counselor who helps people get realistic about their finances.

Can you explain what you do for a living?

I help people get their finances organized. Sometimes that involves actual bookkeeping work – going into people’s offices, balancing their checkbook, organizing their mail, entering stuff into a computer, generating checks for them to sign, and then making little spreadsheets for them to look at telling them when they’re going to run out of money. This brings a bit of money which provides time for me to be a budget counselor.

The Budget Counseling is much more fun. That’s where I sit with people one-on-one, have them tell me how often they get paid, how much they make, and what their bills are, amount due and due dates. I plug everything into a spreadsheet (it takes about 30 minutes) and then I counsel them around whatever money issues they may have. Some people are struggling and don’t know how to pay their bills, but most are making good money and don’t understand why it disappears on them. Most sessions turn into therapy sessions rather than a discussion about making or saving money.

People with a lot of money are just as bad, if not worse, at managing their money as people with a little money. In fact the amount of money and education you have has nothing to do with how well you manage your day-to-day money life. It just takes arithmetic and subtraction, but many people find this hard to believe.

When do you use basic math in your job?

I use it every day. Addition and subtraction. Easy stuff, but people run from it screaming. The spreadsheet I designed looks basically like a checkbook register (see it here). I use it for my own personal finances. I plug in how much money a person has today. Then I list all the times the person will have to spend money in the future (date, reason, amount). Then I list all the times the person is expecting money in the future (date and amount). Then I sort the list by date. I’ve basically created a checkbook balance for the future. This way they can know exactly how much extra money they have or when they’re going to run out of money.

Read the rest of the post here. If you have questions, feel free to ask them here or in the original post. I’ll see them in both places, and I’ll be sure to let Jameel know.

May 7, 2012
Saving Lives with Math

Math Appreciation Month has finally come to a close. And I thought I would end with some math that could save your life. This is serious — and I think really interesting — stuff.

If you’re seen a recent “best college degrees” list, you probably wondered two things: Why the heck is Applied Mathematics on the list, and what is it? First off, applied mathematics is not about crunching numbers. Instead, these folks use higher level mathematics — from abstract algebra to differential equations to statistics — to solve a myriad of problems in a myriad of industries. And that, my friends, is why it’s on the list. In industries like energy, cell phone technology and medicine, math modeling and statistical analysis have been applied to solve really big problems.

Math modeling is one branch of this field that has become a very big deal. Let’s say a city planner wants to know how many snow plows to buy so that the city isn’t paralyzed by a winter storm. Modeling this problem using mathematics is one way to address this problem. The way I look at it, math modeling helps us understand things we can’t see — because they’re part of situations that haven’t occurred or are too far away or are too tiny and hidden.

That too tiny and hidden part that is what math modelers are honing in on with medicine. In this field — sometimes called bioinformatics or computational biology — mathematicians help medical professionals address problems that are under the skin. Here are two examples:

Fighting Cancer: Researchers at University of Miami (UM) and University of Heidelberg in Germany have created a math model that will help oncologists predict how a tumor will grow, and even if and how it will metastasize. There have been other math models that look at tumors, but this one is different. Instead of looking at each cell or all of the cells has a big group, this model creates a kind of patchwork quilt of areas of the tumor to examine. As a result, the doctor can create a tailored plan for treating the disease that is very specific for each patient. The promise is that with specialized (rather than generalized) treatment plans will offer patients a better chance at survival.

Treating Acetaminophen Overdoses: When a patient comes into the emergency room having overdosed on acetaminophen, the ER staff is faced with a really complex decision. Often these patients are hallucinating, unconscious or comatose. And since it’s relatively easy to overdose on the drug (it takes only five times the daily safe dosage, and acetaminophen is in many different over-the-counter and prescription medications), it’s sometimes impossible to determine when and how much of the drug was ingested. There is an antidote, but at a certain point, the doctor needs to skip that step and put the patient on the liver transplant list immediately. The trick is accurately identifying that point. University of Utah mathematician, Fred Adler, developed a set of differential equations that can better pinpoint the critical information needed to make these decisions.

In both of these cases, the math is pretty darned complicated, depending on a branch of calculus called differential equations. This approach is a step up from statistical analysis, which compares patient data to data collected from other patients. In other words, it assumes that tumors grow in the same way in all patients — which we know isn’t true. These dynamical math approaches allow doctors to offer treatments that are customized for each patient, based only on the information collected from the patient.

And the best part is that the doctors don’t have to know the math. If future studies bear out these new discoveries, a simple app can be designed for smart phones or tablets, allowing physicians to make diagnoses and treatment plans bedside.

I suspect these applications will continue to grow, as the medical community turns to mathematicians for insight into what we can’t see. That’s great news, because these advances can save lives.

I hope you’ve enjoyed what we’ve put together here for Math Appreciation Month. If you have questions, please ask them below. I’m always open to ides for future blog posts, so please share them!

April 30, 2012
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!

April 25, 2012
Ode to Special Numbers

There are numbers, and there are special numbers. Okay, so just like children, all numbers are special. But a few of these numbers have qualities that make them stand out from all of the rest. Some of them you’ll recognize right away, because they’re used in everyday math. Others may be completely new to you — or at least you haven’t thought about them for years!

Let’s take a look.

Zero
It may look pretty ordinary, but 0 is one of the most important numbers in the entire system. It’s called the additive identity, because when you add 0 to any number, you get that number back. As a digit, it is used as a placeholder in the decimal system. Without 0, 4.32 equals 4.032, which would really shakes things up!

It may seem strange, but zero is an even number. That’s because it is evenly divisible by 2 (0 ÷ 2 = 0). But dividing any number by 0 is undefined; you can’t do it! Zero is neither negative nor positive, and it’s neither prime nor composite. When you raise 0 to any number (square, cube, etc.), you get 0.

One
Another ordinary number, 1 is called the multiplicative identity. In other words, when you multiply any number by 1, you get that number. As a result, 1 is it’s own square, cube, etc. It’s often called the unity, and it’s the first odd number in the natural numbers. Like 0, it is neither prime nor composite.

i
Remember the rule that says you can’t take the square root of a negative number. Well, this is where i comes in. In fact, i is the square root of -1. It’s known as the imaginary number, but believe me, it’s very real. (Okay, it’s not real in the sense that it’s not part of the real number system.) That means that the square root of -25 is ±5i. The square of i is 1.

Imaginary numbers aren’t used in everyday math, but they’re a big deal in electromagnitism, fluid dynamics and quantum physics.

Φ
Phi is another number that you might not be very familiar with, but many mathematicians would say that it’s the most beautiful of all numbers. That’s because it represents the Golden Ratio. Two numbers are in the golden ratio if the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller quantity. Whew! That complicated definition boils down to the irrational number 1.6180339…

The golden ratio is found in art, architecture, music and even finance. The proportions of the Parthenon are said to mirror the Golden Ratio or Φ, and Salvador Dali’s The Sacrament of the of the Last Supper employs Φ. Stradivari used the Golden Ratio to place the f-holes in his violins. And it seems that the financial markets mimic the Golden Ratio.

Nature abounds with the Golden Ratio. If you divide the number of male bees by the number of female bees in a hive, you’ll get 1.6180330… Measure of the distance from your shoulder to your finger tips and the distance from your elbow to your finger tips. Divide the longer measurement by the shorter, and — yep, you guessed it — you’ll get Φ.

e
Like i and Φ you may not be very familiar with the number e. Quite simply, e is the base of the natural logarithm. It is equal to the irrational number 2.71828…

Computer geeks love e. When Google went public, the company’s goal was to raise $2,718,281,828 or e billion dollars to the nearest dollar. In further homage to the special number, the company put up a mysterious billboard designed to attract potential employees, who were also enamored with e.

π
Of course no list of special numbers would be complete without π or pi, which is equivalent to 3.1415926… But do you know where π comes from and why it’s so important? The number is the ratio of the circumference of a circle to its diameter. In other words, if you divide the circumference of any circle by its diameter, you’ll get π. Cool huh? Pi helps us find the area and circumference of a circle. It’s also useful in trigonometry.

More importantly, π has it’s own day: March 14 (or 3/14), when eating pie is encouraged, as well as celebrating the most famous constant in all of mathematics.

Do you have any additions to this list? Share your ideas in the comments section.

April 23, 2012
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!

April 18, 2012
Journey from Math Loser to Math User

Today, I’ve asked Siobhan Green to share her math story with everyone. As the CEO Sonjara, Inc., a woman-owned technology firm, she is a huge proponent of increasing women and men’s math skills worldwide. But she hasn’t always felt confident in her math skills. As she told me, “I think my story is not that unusual in how many of us, especially girls, too easily believe that math is hard and only for super smart math geek types.” Amen!

I was considered a smart kid. I learned to read early, knew my numbers and letters before age 3, entered first grade early and did well in school. However, when I got to third grade, I and my teachers started noticing a discrepancy between my math scores and the rest of my school work. I would regularly get poor grades on timed math tests — two- and three-digit addition and subtraction problems — which predominated our math education. I easily mastered the concepts presented, but when given a timed test, I would run out of time and/or make a lot of odd mistakes.

This pattern continued in elementary school. The result was that I was either yelled at by teachers for being lazy or intentionally not focusing on my math work, or the teachers just assumed I was “bad at math.” I vividly remember one teacher saying “Yeah, girls are better at verbal skills, boys at mathematical/spacial ones. Just stick to what you are good at.”

Things got better in seventh grade when we moved to pre-algebra. I was excellent at pre-algebra and routinely got As and Bs on tests. But I also managed to make the teacher mad when a group of students was interviewed by a local paper and I made a disparaging comment about him (I had no idea what I was doing). As a result, he recommended that I NOT move into Algebra as my grades would warrant but rather into pre-algebra/algebra, for kids who struggled. No one — not my guidance counselor, nor my parents, nor even me — remarked on this fact, as we all had agreed by that point that I was “bad at math.”

This decision had huge implications. Math is tracked; students take algebra, then geometry, then algebra II and then trig, and only then can you take calculus. By not allowing me to go into algebra in eighth grade, I would not take calculus in high school — something that excluded me for many science (especially computer science) learning opportunities.

The rest of my educational history with math was similar – I excelled in algebra (go figure), did fine in algebra II and trig and did surprisingly well in geometry, but my heart wasn’t in it. I also took some basic computer programing courses — BASIC and Pascal. I enjoyed these but never associated them with math, and the overwhelmingly geeky-boy atmosphere of the computer lab turned me off to more experimentation in these fields. By the time computer science camps started becoming popular in high school (in the mid/late 80s), many programs expected that students would be in advanced math classes.

My college degree was in international affairs, which required two years of economics. I was NOT good at economics, and because I didn’t know calculus, and my antipathy for anything involving numbers, was a big part of it. I excelled in the social sciences and went onto a career in international development.

However, over the years of my career, I noticed that I was good at technology — I was the person in the office who figured out the printers, who set up macros and templates in Word, and who taught herself basic HTML. I was also a whiz with developing databases and excel spreadsheets and was often the person who tracked expenses and invoices. I became more and more interested in using technology for international development; I did my masters’ dissertation on the Internet in Africa in 1997. Falling in love with a software developer didn’t hurt, either.

It was actually through my husband (the math/computer science major and total math geek) that I realized I am NOT bad at math. I am in fact pretty darn good at it, and a lot of the tasks I enjoyed “count” as math!

Andy recognized that I have a mild learning disability — dyscalculia. I transpose numbers, have a hard time retaining numbers in my head, don’t memorize numbers well (I still don’t know my 7 and 8 times tables by heart — and by now, I will never memorize them), and often misstate numbers when going from listening to writing. (Trying to capture a number left on a voicemail is torture for me.) And this is true after years of learning coping skills! He was the one who said “Your calculation mistakes are not normal. And they have NOTHING to do with your math abilities.”

See, remember those timed tests? Thinking back, I would think one number and write down another one. Now, I always take a second to double check, but in a timed situation at age 8, I would panic and just move on to the next one. Many of the mistakes I made in the early years were down to calculation errors. When the math was based in patterns (like algebra) or depended on calculators, I did much better. But by that time, my math ability had become a self-fulfilling prophecy. The research is clear about the impact of low expectations on ability; I never pushed myself and accepted lower scores as evidence of my innate lack of talent.

I didn’t realize that my strong abilities in building relational databases, especially to track quantitative data, counts as math! I absolutely love building databases, especially related to financial management. Those spreadsheets I use to track finances? They speak to me and tell me a story in numbers. I had no idea that my ability to create and read those numerical pictures of my firm also counted as math.

Andy also taught me how to program, and while I will never be a full blown developer (mainly because I don’t have time to gain in-depth programming experience), he found that I grasped the key pattern processes quite easily. This skill has been invaluable in my role as business process analyst for web application development. It helps me translate between user needs and programming architecture, which helps with figuring out edge cases and pricing.

Today, my job as CEO of a web application company involves a lot of math. For example:

* Pricing work, especially figuring out hourly rates for specific roles/individuals based on salary, benefits, and overhead plus profit. It is very easy to “win” enough work for bankruptcy (win the work but price it so low you don’t cover your costs). We are always repeating the joke “yeah, we lose $1 per widget sold but we will make it up in volume.” (The explanation is at the bottom.)

* Overseeing projected and actual utilization of my staff. If our rates are based on this person being at 80% billable, and they are regularly at 75% billable, that 5% difference will eat into my profit.

* Understanding the difference between the profit and loss statement, the balance sheet, and a cashflow statement. This is omething that every business owner must understand in order to figure out how the business is doing. You can have huge paper profits but still be in serious trouble if you cannot make payroll, or you could be cash rich but slowly going under because your easy access to credit is masking the fact you are spending more than you are earning.

* Making decisions about how to spend money. What investment will make a bigger impact? For example, should I hire another person or pay down a loan? Should we purchase this new computer now on credit or wait until the next check comes in?

Oh, and here’s the explanation of the above joke: “Yeah, we lose $1 per widget sold but we will make it up in volume.” Assuming that your costs do not scale (decrease per widget based on volume), if you sell 100 widgets, you have now lost $100. And if you sell 1,000,000 widgets, you have now lost $1,000,000. It is astonishing the number of business people I meet who do not get this concept. Usually, they are not in business for long.

Can you identify with Siobhan’s story? Share yours below.

April 16, 2012
The Math of Poetry (Yep, there’s a connection)
```
anyone lived in a pretty how town
(with up so floating many bells down)
spring summer autumn winter
he sang his didn't he danced his did
```
So goes my very favorite poem, written by e.e. cummings. In my senior year of high school, I wrote a term paper explicating the verse, and I fell in love. At the same time, I was taking two math classes, and somehow the process of solving a system of equations was similar to understanding cummings’ strange syntax and playful turns of traditional poetic forms.

April is not only Math Awareness Month but also National Poetry Month. In a facebook conversation with another writer, I found myself offering to show the connections between math and poetry — a task that is surprisingly simple but (if similar articles and blog posts are any indicators) could be very contentious. I like a challenge and a good intellectual fight, so here goes:

Symbols

I’ve long asserted here that mathematics is a language that describes the physical world. Without mathematics, we cannot describe physics. And mathematical models allow us to predict the future or see the invisible. Math also depends heavily on symbols — variables, Greek letters and characters that represent operations like addition and division.

Clearly, symbolism is the very basis of poetry. When Robert Frost writes, “Two roads diverged in a yellow wood, / And sorry I could not travel both” he doesn’t mean that he is literally sorry that he cannot literally travel two literal roads. Nope. The yellow wood represents the later years of the poet’s life when he’s considering the choices (roads) he could have made (taken). (For sure, there are many versions of this interpretation.)

The same is true for the symbolism in math. When you graph a curve that represents the steady increase of your take-home pay over several years, the curve is a symbol of your financial (and perhaps professional) success. But you can interpret or apply the curve in a variety of different ways, and the curve doesn’t tell the entire story.

[laurabooks]

Patterns

You can’t deny the patterns found in mathematics. All you need to do is list multiplication facts for a certain number, and a structure will jump off the page or computer screen. (Eventually.) Then there are a variety of sequences and series, like Fibonacci’s Sequence (1, 1, 2, 3, 5, 8, 13, …) or a geometric series (like 1 + 2 + 4 + 8 + …).

The patterns in poetry are often found in meter and rhyming schemes. So the first line of Shakespeare’s Sonnet 73 is in iambic pentameter: “That time of year thou mayst in me behold.” We know this because it features five two-syllable feet that are expressed as non-stress, stress. (In other words: “That time of year thou mayst in me behold.”) Along with iambic, traditional poetry may follow trochaic, spondaic, anapestic or dactylic meters — but there are endless more styles. Cummings’ “anyone lived in a pretty how town” is generally considered to be a ballad, which, when you know the key that unlocks the poem’s meaning, makes perfect sense.

Symmetry

The idea that two halves are symmetric is not mandatory in mathematics or poetry, but oftentimes it takes center stage. In math, we have symmetric shapes, like circles or isosceles triangles. Symmetry is also critical in solving equations, as you must do the same thing to both sides of the equation.

And in poetry, symmetry is often found in the ways that verses and stanzas are structured. “The Road Not Taken” features four stanzas with five verses each.
```
Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

Then took the other, as just as fair,
And having perhaps the better claim
Because it was grassy and wanted wear,
Though as for that the passing there
Had worn them really about the same,

And both that morning equally lay
In leaves no step had trodden black.
Oh, I marked the first for another day!
Yet knowing how way leads on to way
I doubted if I should ever come back.

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I,
I took the one less traveled by,
And that has made all the difference.
```
Many mathematicians and poets have pointed out even more similarities (some that, in my opinion, suck the life and art out of both math and poetry), but these are some basic ideas. I’ll leave you with what Einstein said on the matter: “Pure mathematics is, in its way, the poetry of logical ideas.” To which I say: math and poetry are designed to give the illogical some kind of logical shape.

There are some really interesting everyday life math examples in my books. Visit this page and buy the book today!
April 13, 2012
$Formulas: Or is this going to be on the test?$

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!

April 11, 2012
Parlez-Vous Mathematics? Math as a foreign language

In redesigning my blog, I’ve read a lot of the posts I’ve written over the last year. In fact, take a look at this math: On average, I’ve written 13 blog posts each month or 164 posts (counting this one) since last May. And so I decided to repost this one, in honor of Math Awareness Month, which addresses the language of math.

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.

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.

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

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.

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.

Our first Math Treasure Hunt winner is Marcia Kempf Slosser! Congratulations Marcia, you’ve won a copy of Math for Grownups (or if you already have a copy, I’ll send you a gift card). Want to enter? All you need to do is find an example of the daily clue, which is announced on the Math for Grownups Facebook page each day.

April 9, 2012
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.

April 6, 2012
$Five Things Math Teachers Wish Parents Knew$

Five Things Math Teachers Wish Parents Knew

Parents: when it’s time for math homework, do you suddenly have something else to do? When it’s parent-teacher conference time, do you first tell the teacher that you’re no good at math yourself?

First off, you’re not alone. It’s the number one thing I hear from parents: “I don’t know how to help my kid with math!” So I asked one of my favorite math teachers, Tiffany Choice. As an elementary and middle school teacher, Ms. Choice is a math education expert. And because of that, we instantly connected. Oh, she was also my daughter’s fourth grade teacher.

I asked Ms. Choice to share her best advice for parents. Want to help your kid succeed at math? Here’s how.

Just because you struggled in math class doesn’t mean your kid will.

Don’t pass on your dislike or acceptance of not being “good at math.” Always highlight the importance of math. If you cannot provide math homework support, find someone who can. Even if your kid has to call an uncle across country to try help clarify a problem, it goes a long way.

Math is best understood when applied to the real world.

Show your kids how you use dollars and coins at the store. Encourage understanding when they use birthday money to buy things. Discourage them from throwing the wad of money on the counter without understanding what they are doing. Explain to your child what you are doing when balancing that checkbook, measuring a wall or following a recipe. You are your child’s first teacher.

How you were taught to do something in math may or may not be the best way.

Education is swiftly changing to keep up with technology and each generation. Be open to many new ways of learning math concepts. Ask your child’s teacher to show you how a concept is being presented. I’ve had parents stop in during math instruction or for an after school conference.

Math isn’t learned right after the first lesson.

Parents should emphasize and allot time for practice — just like we encourage practicing the piano, ballet, reading, soccer, or French.

Realize the importance of and reinforce math vocabulary.

Math isn’t just numbers, it’s words too. Talk about what 20% off really means when they’re asking for that new toy. Use the words “total,” “difference,” and even “mixed number.” Believe it or not, truly knowing what those math words mean helps in the long run. I hate to mention standardized tests, but it’s something that’s here to stay (at least for now). More and more, math tests are transforming into reading tests. Most of the questions are word problems. Certain understanding of math vocabulary can and will help your child avoid the sneaky test-makers tricks.

I’ll add one more thing: Encourage your child to explain their reasoning behind the math they’re doing — whether you’re helping with homework or asking him to divy up candy pieces at a play date. One of the biggest things that kids are being asked to do is write about math. (In my daughter’s school, these are called BCRs or Brief Constructed Response and ECR or Extended Constructed Response.) The kids who already verbalize their understanding of math will have an easier time with these tasks.

Do you have advice for parents? Whether you’re a teacher, parent or innocent bystander share your ideas in the comments section. Have a question? Share that, too!

April 4, 2012