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Basic Math Review Math for Grownups Math for Parents Math for Teachers

Multiplying and Dividing — Integer Style

Continuing on in our review of basic math, I welcome you to Day 2. The answers to Day 1 questions are at the bottom of the post — along with new questions. But first, let’s learn how to multiply and divide integers.

Let’s say you have a bank account with a service fee of $15 per month. If that amount was deducted every single month, how can you represent the yearly amount for these fees? Well, you would multiply -$15 (the fee is negative because it’s taken out of the account) by 12 (the number of months in the year). But how the heck do you multiply negative and positive numbers? Let’s find out.

Remember integers — those negative and positive numbers that aren’t fractions, decimals, square roots, etc.? I like to think of them as positive and negative whole numbers (though most real mathematicians would argue against that classification). On Wednesday, you learned how to add and subtract these little buggers. (Check out the post here, if you missed it.)  Today, we multiply and divide.

Her’s the really good news: it is way, way easier to multiply and divide integers than to add and subtract them. First, though, it’s a good idea to understand how the rules work. When you first started multiplying numbers, you did things like this:

2 x 3 = 2 + 2 + 2 = 6

In other words “2 x 3” is the same thing as adding up three 2s. Get it? And because you started working with positive numbers when smacking a girl upside the head meant you “like-liked” her, you know without a shadow of a doubt that the answer is positive.

Let’s see what happens when you multiply a negative number by a positive number:

-2 x 3 = -2 + -2 + -2 = -6

Now to understand this, you need to either pull up your mental number line and count or remember the addition rules from Wednesday’s post. When you add two numbers with the same sign, add the numerals and then take the sign. So -3 + -3 is -6.

But what about multiplying two negative numbers? Admittedly, this is a little trickier to explain. It helps to look for a pattern using a number line. Let’s try it with -2 x -3.

-2 x 2 = -4
-2 x 1 = -2
-2 x 0 = 0
-2 x -1 = ?
-2 x -2 = ?

Based on the pattern shown on the number line, what is -2 x -1? What is -2 x -2? If you said 2 and 4, you are right on the money.

And now we can summarize the above with some rules. Believe me, this is one math concept that is much, much easier to remember with the rules. Still, if knowing why helps anyone get it, I’m all for pulling back the curtain.

When multiplying integers:
If the signs are the same, the answer is positive;
If the signs are different, the answer is negative.

Bonus: The same rules work for division. That’s because division is the inverse (or opposite) of multiplication.

When dividing integers:
If the signs are the same, the answer is positive;
If the signs are different, the answer is negative.

The only tricky part is this: Sometimes it seems that if you are multiplying or dividing two negative numbers, the answer should be negative. It’s a trap! (Not really, but you could think of it that way, if it helps.) The key in multiplying and dividing integers is noticing whether the signs are the same or different.

In fact, if you are doing a whole set of these kinds of problems, you can simply run through the problems and assign the signs to the answers — before even multiplying or dividing. (I tell students to do this all the time, because I think it helps them to remember the rules.)

4 x -3 → signs are different → answer is negative
-4 x -3 → signs are the same → answer is positive
-4 x 3 → signs are different → answer is negative
4 x 3 → signs are the same → answer is positive

Then all you’d need to do is the multiplication itself:

4 x -3 = -12
-4 x -3 = 12
-4 x 3 = -12
4 x 3 = 12

And like I said, division works the same way:

-24 ÷ -2 = +? = 12
24 ÷ -2 = -? = -12
24 ÷ 2 = +? = 12
-24 ÷ 2 = -? = -12

Got it? Try these examples on your own.

1. 5 x -6 = ?

2. -18 ÷ 9 = ?

3. -20 ÷ -4 = ?

4. 8 x 4 = ?

5. -2 x 7 = ?

Questions? Ask them in the comments section. Up Monday are fractions. If you can’t remember how to add, subtract, multiply or divide fractions or mixed numbers, tune in. 

Answers to Wednesday’s “homework.” (It’s not really homework, I promise.) -10, -4, 2, -15, -2. How did you do?

Categories
Basic Math Review Math for Grownups Math for Parents Math for Teachers

Pluses and Minuses: Adding and subtracting integers

Welcome to Day 1 of our tour of basic math. If your New Year’s Resolution is to brush up on your math skills. You’re in the right place. 

Winter is really the perfect time to talk about integers.

But first, what are integers? It’s quite simple, really. They’re positive and negative whole numbers. These are integers: -547, 9, 783, and -1. These are not integers: 0.034, -0.034, √3, and -1/2.

You are very familiar with positive integers. For the first three years of your formal education, you probably worked exclusively with these little buggers — or as you called them, “numbers.” You learned to count them, tell time with them, add/subtract/multiply/divide them, and even write them out as words.

(Soon after, you learned about fractions and then decimals, which are not integers, but are still positive, so it was all good.)

If you’re like me, the part that completely blew your mind was when you first learned that numbers could be negative. Now that I think back, this was kind of a silly surprise in my world. I grew up in an area of the United States that gets pretty cold in the winter. This means two things: we measured temperatures with Fahrenheit and the temps got below zero. And those two things pointed to negative numbers. Duh.

Regardless, with a lot of work and determination, I finally understood integers, which included adding and subtracting negative and positive whole numbers. But before I show you how this is done, let’s take a look at the number line, which can help you visualize how this works.

The number line isn’t a real thing. It’s just a way to visualize how numbers work. And the key is the zero in the middle of the line. Notice what happens on the right — the numbers get larger, one by one, right? And what happens on the left? Yep, they get smaller.

Did you get that smaller part? If not, don’t worry. You’re just a little rusty. See, when two numbers are negative, the smaller one actually has the larger numeral. In other words -37 is smaller than -1, while 1 is smaller than 37.

(This is a good time to note something else that you may have forgotten. If a number has no sign, it is positive. The positive sign, +, is understood.)

If you can picture a number line, you can add and subtract integers, no problem. Here’s how:

-1 + 3 = ?

Start at -1 and count three places to the right. We’re counting to the right because we’re adding. What is the number on the number line? If you said 2, you’re right on target.

4 – 5 = ?

This time start at 4 and count five places to the left. That’s because we’re subtracting. What do you get? If you said -1, give yourself a gold star.

So this number line thingy is pretty cool, but it’s not all that useful if you need to find an answer pretty quickly. And what happens if the second number is negative? (Well, you change direction, actually, but that’s pretty clunky and somewhat confusing. So how about if we find another process?)

Once you understand the why of adding and subtracting integers, you can learn an algorithm that works every single time. It goes like this:

This is much easier to understand with an example:

-10 + 4 = ?

We’re adding two numbers with different signs. That means we need to ignore the signs, find the difference and take the sign of the larger numeral. But what does “find the difference” mean? It’s pretty simple, actually. Just subtract the smaller number (without the sign) from the larger number (without the sign). 10 – 4 is 6, and if we take the sign of the larger numeral, the answer is -6.

Another way to think of “difference” is the distance between the two numbers on the number line. So if you got back to the number line, it’s a matter of counting spaces between the two numbers. Then take the sign of the larger numeral. Make sense?

-10 + 4 = -6

Okay, let’s try a subtraction example.

-3 – 9 = ?

First step is to change the subtraction to addition and change the sign of the second number.

-3 + -9 = ?

Now all you need to do is follow the addition rule for numbers with the same signs. That means to ignore the signs, add, and keep the sign.

-3 + -9 = -12

So, no need to pull out a number line for these. Just practice with these rules, and you’ll have them down in no time at all. Here are a few additional examples to help you.

5 – 8 = 5 + -8 = -3

-7 – 4 = -7 + -4 = -11

3 + -3 = 0

-12 + 8 = -4

Now, try these out on your own. I’ll post the correct answers on Friday. And if you have questions, ask them in the comments section.

1. 15 – 25 = ?

2. -7 – -3 = ?

3. 10 + – 8 = ?

4. -3 – 12 = ?

5. -6 + 4 = ?

Categories
Basic Math Review

Happy New Year! Time to brush up on your math skills

For nearly two years now, I’ve been harping on the same old message: Whether you like it or not, math is necessary. In other words, suck it up, cupcake. You’re going to have to do the math.

And yet, I still hear the same thing over and over again: I’m no good at math; I hate math; I just let my husband/wife/child/parent do math for me; I’ve never had to use the math I was forced to take in high school; etc., etc., etc.

That’s why January will be devoted to brushing up on your math skills. Week by week, we’ll look at a few areas of math that tend to trip people up.

Week One: Integers
How do you add, subtract, multiply and divide negative and positive numbers? And what’s the point of those stupid things, anyway?

Week Two: Fractions
I’ll remind you how to find a common denominator, perform various operations, and visualize fractions so that you can manipulate them easily.

Week Three: Percents
Do you remember how to convert fractions to percents or find a percent off or even the percent change? If not, relearn it.

Week Four: Statistics
If the recent election had you tied up in knots, perhaps a little statistics refresher is in order. Finally figure out the difference between a mean, median and mode. And learn what makes a good sample size or how to spot sample bias. It’ll be just enough info to help you analyze the news.

Week Five: Word Problems
Everyone’s favorite! Not. Here’s where I’ll show you how to dissect a problem in real life — so you can feel confident and eager to find a solution. We’ll also consider when estimation is a good idea (lots more than you might think) and when you should reach for a calculator or an online tool.

But wait! There’s more! I also have a few promises for you.

1. No grades. This is what we call low-stakes learning. As grownups, you aren’t required to study for tests or memorize formulas. At the end of each post, I’ll throw in some problems that you can choose to solve or not. But you won’t be graded or evaluated in any way. This is just for fun. Promise.

2. No trains or cantaloupes or pizzas. Stupid word problems make me crazy. Everything I offer will be grounded in reality, not constructed for a particular answer or to make a point.

3. No required algorithms. I’ll show you why these things work, so that you can find your own way to a solution. Don’t get me wrong — I’ll include a step-by-step process in most cases. But you might get alternative methods, too. And I’ll always encourage you to look for your own way.

4. No assumptions about what you do and don’t know. If we need a fancy vocabulary word, I’ll define it. If we need to follow a process, I’ll show it to you. I won’t talk down to you, but I won’t expect you to know everything.

So is it a deal? Will you join me in this New Year’s Resolution? If so, grab a No. 2 pencil (or crayon, fountain pen or stylus) and let’s get to work. Meet me back here on Wednesday, and we’ll talk integers.

What questions do you have about the topics I’m going to cover? Ask them in the comments section, and I’ll try to include them this month. If they don’t quite fit — or there’s not enough time — I’ll answer them here.

Categories
Holidays Math at Work Monday Math for Grownups

Math at Work Monday: Santa Claus

There’s a lot of magic involved in Santa Claus’s annual journey around the world. Delivering presents to that many households can’t be done without it. But there’s also quite a bit of math. And I’m thrilled that Santa agreed to do this interview with us, revealing a few secrets of how math helps him in his work.

Can you explain what you do for a living?

Well, throughout the year, my main job is to oversee a large toy production facility at the North Pole. This includes supervising thousands of elves, who are responsible for toy manufacturing, as well as management of the reindeer stables, grounds work, sleigh maintenance and other smaller details.

But my main responsibility is only on one night of the year. On Christmas Eve, I pilot a large, flying sleigh, driven by eight reindeer and Rudolf, throughout the world to deliver presents to all good boys and girls. It’s a big night, and I usually take off the entire month of January to recover!

When do you use basic math in your job?

There’s a surprising amount of math involved in my work. These days, the naughty-and-nice list is in a database. A sophisticated set of formulas help me map out my once-a-year trip, which determines how the sleigh is packed. If Los Angeles gifts are on the top of the pack when I land in New York City — well, that’s a big problem.

I also need to manage my time, since I have so little of it that night. The different time zones help me stay a little ahead of the clock in most cases, but I sometimes have to do some on-the-spot figuring when weather becomes a problem.

But the real math is in the sleigh. Much like an airplane pilot, I must maintain a steady speed and take into account things like wind and visibility. The elves have helped equip the sleigh with state-of-the-art equipment, like gauges for altitude and speed. However, there have been some times when I’ve need to apply distance/speed/time ratios on the fly.

Do you use any technology to help with this math?

Absolutely. As I mentioned, we depend heavily on databases on the North Pole. These are housed in a large server, allowing us to manage our manufacturing quickly and easily. If a formula needs to be changed — for example, we need to greater ratio of purple bicycles to red bicycles — that alteration can be made in the database and applied throughout the facility. It streamlines the process considerably.

And I couldn’t fly to as many houses as I do today without my computerized dashboard in the sleigh. Each year, it’s calibrated to the specific weather conditions that are expected and even the current weight of the reindeer. Being able to customize these variables means making the most of those 20 hours that I’m in the sky.

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

I’m sure many people have said this: I couldn’t do my job without math. From the elves’ payroll to the naughty and nice list, every point of this whole operation hinges on how well we’ve done the math.

How comfortable with math do you feel?

I’d much rather talk to a child about what he or she wants for Christmas than sit down and solve a bunch of algebraic equations. But I’ve learned that in order to accomplish all that I do, I need to do some computing, too. I feel pretty comfortable with math, but it’s not my favorite thing in the world.

What kind of math did you take in high school?

School was a lot different way back then. You have to remember, I’ve been around for a long, long time! Heck, calculus wasn’t even invented yet, and forget about the calculator! But I did fine with the little bit of math I did take in school.

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

When you’ve been in a job like mine for this long, you definitely have to pick up some new skills. The biggest changes have been technological. And once computers came on the scene, all of my operations had to be redesigned. I’ve even brought on some elves who are experienced with math modeling, so that we can stay ahead of any climate changes that will certainly affect our work. They’re developing up several models now with regards to the North Pole itself.

Thanks so much to Santa for taking time out of his incredibly busy schedule to answer a few questions. Happy holidays to everyone! In honor of the season, I’m going to take the rest of the week off. I’ll see you back on Monday, December 30, when we’ll kick off a really cool month designed to help you meet a special New Year’s resolution: brushing up on your basic math skills.

Categories
Holidays Math for Grownups Math for Parents

Christmas by the Numbers

There’s a lot more to this time of year than the 12 days of Christmas, 3 wise men or 5 golden rings. Between digging out our credit cards and stringing hundreds of twinkly lights on the gutters, most of us have more numbers than sugar plums dancing in our heads.

And so, I bring you Christmas by the Numbers, a round up of interesting statistics about this huge holiday.

93: Percent of Americans (in 2008) who say they celebrate Christmas

81: Percent of Americans (in 2008) who identify with Christian faith

$427 million: Predicted sales of Christmas cards in 2012

4.1: Percent that holiday sales are expected to rise in 2012 over the previous year

12: Percent that online holiday sales are expected to rise

625,000: Predicted number of seasonal workers expected to be hired this holiday season.

25-30 million: Number of real Christmas trees sold in the U.S. each year

7: Average growing time (in years) of a six- to seven-foot tall Christmas tree

4,000: Number of Christmas tree recycling programs across the country

749.51: Dollars expected to be spent on gifts, decor and cards by the average holiday shopper this year

60: Percent of holiday shoppers expected to “self-gift”

1: Rank of gift cards in list of popular Christmas present requests

10: Percent chance of a white Christmas in my city (Baltimore, MD)

Any statistics that you’d like to see? Share your ideas in the comments section. Happy holidays!

Categories
Holidays Math for Grownups Math for Parents

Last-Minute Gifts for Geeks and Not-So-Geeks

I don’t know about you, but I’m still pulling together some gifts — with less than a week before Christmas. Each year, I try to get done before December, but no dice. I must love the stress.

So, if you’re still looking for a little giftie or two for the geek — or geek-lover or geek-wannabe? — in your life, here are some ideas.

Mathletic Department Hoodie

I am not an athlete. Not by any stretch of the imagination.  But even I would wear this hoodie. It’s the perfect mix of geek and cool. Well, at least I think so.

From Cafe Press.

Math Love Onesie

It might take you a moment to see the beauty of this design. I’ll wait.

Get it? Even if you can’t follow the solution to from start to finish, the last line is perfection. (Must speak internet.) And while you’re baby is sporting this fashionable accessory, you can review solving inequalities.

Made by Skyhawk Press, Monterey, Cal. Available on Etsy.

Number Cookie Cutters

Because how else can you make a π pie? I have a set like these, and while they’re terrific for really geeky cookies, they’re also great for making cute kid-party sweets — Like a bunch of 3s for a three-year old’s party. They’re also handy when you need number “stencils.”

Available at Barnes and Noble (order online and pick up at the store).

Tiffany & Co. Infinity Bracelet

Splurge for the platinum with diamonds or stuff her stocking with a more moderately priced bobble in sterling silver. Either way, you’re telling her that you mean forever in a delightfully geeky way.

Available at Tiffany & Co.

Obsessive Chef Cutting Board

We all have one in our families or among our friends: the home chef who cooks with the precision of a surgeon. And finally, here’s a cutting board they can truly appreciate. With guidelines for julienne, chop and mincing — and even including curves and bias marks — veggies have never been so perfectly prepared.

Made by Fred & Friends.

Consul the Educated Monkey Calculator

This has to be my very favorite find of the holiday season. A reproduction of a 1916 toy created by William Robertson, this little piece of tin can find the product of two numbers in the shake of a tail. Give it to a particularly precocious child and ask him or her to figure out why it works. (Hint: It’s all about the triangles.)

Available at local gift shops and online.

Need more ideas? Check out last year’s list, which offers ideas specifically for kids.

And if you’re in the market for something funny and useful, check out my book, Math for Grownups, designed to ease the fears and pain of even the most resistent math-phobe. Promise. (Available online, at local independent bookstores and Barnes & Noble.)

Do you have gift ideas to share? Please post about them in the comment section. (I still have a few things to pick up myself!)

Categories
Math at Work Monday

Math at Work Monday: Sole the fashion designer

I’ve been dying to have a fashion designer in this spot for a very long time. So when designer Sole Salvo‘s message arrived in my inbox on Friday morning, I was thrilled! As an avid sewer — who doesn’t like using patterns — I am fascinated with the process of fashion design. I know there is a lot of math involved. Some of it has to be a gut instinct — how will this angle work on a human body? And some of it is very calculated — what do I need to add in order to get a 5/8″ seam allowance?

Sole has been working as a designer for nine years, currently working for a large clothing company in New York. Here’s how she uses math in her job.

Can you explain what you do for a living? 

I design women’s clothing. I sketch new styles then give the specs (measurements of the garment, like length, waist measurement, neck drop etc) to the tech designer or pattern maker to make a sample. I pick out fabrics, colors and trims, like buttons and thread, to complete the look of each garment. Once my seasonal collection is complete, I review it with my merchant team who decided what to buy for the store.

When do you use basic math in your job?

Math is important for design. We have to measure our sample garments to know where we need to add or subtract fabric to make the garment fit well. Additionally a strong understanding of geometry is important for understanding how the flat pattern shape will make up into a 3D garment as well as what part of the flat pattern to change to fix the fit.

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

I usually don’t use technology for this myself because the calculations I have to do are usually simple, like adding 1/4″ here and 1/8″ there, but my cross functional partners on the tech team do use a computer program to digitally manipulate the flat garment pattern. I use Illustrator to draw my flat sketches — these are the detailed sketches that the factory pairs with the measurement specs to make up the sample. These drawings have to be very accurate and clear so the factory can see each detail of stitching and seaming, as well as the overall proportion and look of the garment.

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

Without math it would be impossible to keep sizes consistent, and it would be impossible to draft a garment pattern. In addition it would be impossible to create trim pages — the list of trims required to make a garment. We use numbers on those as well to tell the factory how many buttons to use on each shirt. The factory must multiply the number of buttons by the number of shirts they are making to order enough buttons. It becomes very important when ordering because if you make a little mistake on a style that has 100,000 pieces on order, all of a sudden you could wind up with 100,000 too many buttons!

How comfortable with math do you feel?

I feel very comfortable with math in what I do. I deal with whole numbers and simple fractions for the most part.  I also have a strong sense of geometry. I can visualize what a pattern piece would look like if it is draped on the body, and this helps me design and also helps me make comments in my fittings.

What kind of math did you take in high school?

I took algebra, geometry and calculus.  Algebra was manageable, geometry I could do with my eyes closed. I can essentially reander 3D models in my head, so anything that involves shapes and how to manipulate them comes naturally to me. Calculus was more of a challenge. When it came to doing more complicated problems, I struggled. I did ok in the end, but I had to really study in calculus.

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

Knowing how to add fractions comes in handy every day.  Also area is important. If you are working on a garment, sometimes the size might be right, but the fabric is just distributed in the wrong place. To fix it, you might have to keep your total area the same, but just shift it around to make it lay flat or to drape just the right way.

Thanks so much, Sole! If you have questions for her, ask them in the comments section. 

Categories
Holidays Math for Grownups Math for Parents

Tis the Season to Give Generously: Do the math first

Yesterday afternoon, I dropped off the gifts I had purchased for a mother and son who are spending the holidays in a women’s shelter. He’s not even three years old, and he’s already had a much rougher life than I. But at least this year, he’ll have a Little People fire truck and new set of ABC and counting board books.

I don’t share this story to toot my horn. Plenty of people do as much or more than that each year. And I’m guessing their motivation is the same is mine — it feels good to give.

At the same time my math brain loves some guidelines. I grew up Lutheran, and I was expected to tithe 10% of my allowance. It was a great practice to get into, but now that I’m not a tithing church-goer, I miss having a formula. How much giving is “enough”? How can I know if I’m pushing myself enough?

Last year, I came across Peter Singer, who developed a really wonderful set of formulas based on a variety of different incomes. I wrote about it last fall, and I thought I point you to it today — in case you didn’t see it or need a reminder.

The Math of Generosity

No matter what holiday you celebrate in December, the month has traditionally marked a time for charitable giving.  The weather is growing colder in some areas, making it much tougher on the homeless.  The end of the year is creeping up, and with it the deadline for tax exemptions for charitable giving.  And holiday cheer often means counting our blessings and remembering those who are less fortunate.

Yes, December is the time for giving.  But how much is enough? And what is too much?  As we attempt to balance our own needs (especially in these difficult economic times), many of us struggle with our own sense of guilt and generosity. Read the rest of this post.

Do you have a formula for developing your yearly contributions? Share it — or your thoughts about using math to make charitable giving decisions — in a comment.

Categories
Math for Grownups Math for Teachers

12-12-12: A once-in-a-lifetime date

Today, the Museum of Mathematics (MoMath) in New York City has its opening ceremony. But that’s not what makes this date really special. Organizers of this tribute to numeracy chose 12-12-12 very carefully. Want to guess why?

Geeks and superstitious folks around the world love dates like today’s. It’s exactly six years, six months and six days from the last time we saw such a repetitive day: June 6, 2006 (06-06-06). And there won’t be another one until 3001. I don’t know about you, but I won’t be around for that one.

I imagine there were a few people up at 1:21:02 this morning, admiring an elegant numerical palindrome — when the time and date reads the same left-to-right as right-to-left.

2012-12-12, 1:21:02 = 20:12:1, 21-21-2102

What can I say? Some people like patterns. Brides and grooms are tying the knots in record numbers today. According to a report by David’s Bridal, about 7,500 couples will wed in the U.S. today. That’s a 1,446 percent increase over December 12, 2011.

An anniversary date like that is easy to remember, right?

But for us mathematically minded folks, it’s the number 12 that really stands out. That’s because it’s so flexible. Its factors are 2, 3, 4 and 6, which means it can be evenly divided by all of these numbers. This has a great number of applications — from a clock face to an egg carton. If you have to file your taxes quarterly — as I do — you know that this means every 3 months. That’s simply because:

4 quarters • 3 months = 12 months

As a result of this numerical flexibility, 12 is a pretty big deal in geometry as well. A cube as 12 sides, and there are 12 pentominoes, or shapes that can be created with five squares that share sides.

Each of these wooden tiles is a pentomino. Photo courtesy of Jeffrey Bary.

Pythagoras got so excited by the number 12, he taught that it has divine meaning.

Perhaps this significance is why the number 12 is such a big deal in some religions and spiritual practices:

  • 12 Tribes of Israel
  • 12 disciples of Jesus
  • 12 feasts of Eastern Orthodoxy
  • 12 stations of life in Buddhism
  • 12 Jyotirlingas, Hindu Shaivism temples
  • 12 direct descendants of Muhammad in Shia Islam

And in everyday, secular life, this special number also abounds:

  • 12 members of a jury (U.S.)
  • 12 inches in a foot
  • 12 steps in Alcoholics Anonymous (and its sister programs)
  • 12 zodiac signs
  • 12 basic hues on the color wheel
  • 12 pairs of ribs in the human body

So whether you love the idea of a repetitive date, a numerical palindrome, or the inherent beauty of the number 12 — or perhaps you’re just really glad it’s hump-day — welcome to 12-12-12. Besides, any day is worth celebrating, right?

Did you notice the special nature of today’s date? Have you planned a special event — like a wedding! — for today? Share your thoughts on today’s date in the comments section.

Categories
Math at Work Monday Math for Grownups

Math at Work Monday: Cecilia the grant writer

While we’re on the subject of museums, I thought I’d introduce you to Cecilia Meisner, who is the Director of Grants and Government Relations at the Baltimore Museum of Art (BMA). In short, she’s a fundraiser, specializing in writing grants (rather than asking folks like you and me for donations). These grants may come from foundations or government agencies or corporate funding divisions. 

And with a newly renovated contemporary art wing, the BMA can use all of the funds it can get. Naturally, Cecilia uses quite a bit of math in her job. Here’s how.

Can you explain what you do for a living?  I oversee fundraising from foundation, corporate, and government sources to support The Baltimore Museum of Art.  A lot of my work is writing (grant proposals, reports, letters of inquiry or acknowledgement), but I also do a lot of work with creating grant budgets, tracking grant-funded expenses, and reporting back to the funders.

When do you use basic math in your job?  It can be as simple as applying a percentage to a salary to show the value of staff benefits in a grant proposals, and as complicated as tracking hours worked on a project for dozens of employees over the course of two years.

Do you use any technology to help with this math?  I NEVER do math in my head: I always use an old-fashioned adding machine with a paper tape for quick calculations, and I loooove spreadsheet programs for creating budgets and tracking expenses.  The first one I ever used was Lotus 1-2-3 but now I use Excel.  I have been working in this job long enough that I used to use huge binders full of ledger paper to track expenses with pen on paper – hence the need to run a paper tape on everything: they didn’t add up automatically, unlike computerized spreadsheets!

How do you think math helps you do your job better?  Funders don’t want to give money unless they feel secure that it is enough to get the job done, and that the recipient will manage the money carefully.  And since we are audited every year by an outside auditing firm, it is a lot easier to make sure everything is done right the first time, rather than having to go back and make a lot of end-of-year journal entries in the organization’s books.

How comfortable with math do you feel?  I am very comfortable with the math I use in my work: basic functions plus percentages (which a surprising number of people do wrong, I find as I review draft grant budgets).  That being said, I am utterly incapable of helping my 10th grader with his Algebra II/Pre-Calc, Trig, Probability & Statistics, or Physics homework.

What kind of math did you take in high school?  I didn’t take any math after 9th grade “pre-Geometry.”  I was very intimidated by math, and I took enough science courses (Chemistry, Physics, Geology) to fulfill my high school’s joint math/science requirement. Because I got a high enough grade on the ACT test math portion, I was able to exempt out of Freshman Mathematics in college. I didn’t need any additional math as a requirement for my major. I escaped math in high school and college, but it caught up with me in the work world, and it turns out that it isn’t so bad after all! I wish I had Math for Grownups when I was in high school and college – I might not have been so intimidated!

Did you have to learn new skills in order to do the math you use in your job? I was totally set with the basic addition-mulitplication-subtraction-division-percentages skills, but I did need to learn how to use spreadsheet and double-entry accounting, and how to use the specific spreadsheet software programs.

Do you have questions about grant writing and administration? If so, ask in the comments section, and I’ll let Cecilia know!

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Holidays Math for Grownups Math for Parents

Hanukkah by the Numbers

Tomorrow, at sundown, marks the beginning of the Festival of Lights or Hanukkah (or Chanukah, Chanukkah or Chanuka). By most standards, this is not a significant holiday for those who practice Judaism, but it is fun for the kids — oh and the latkes! (Until this morning, I did not know that it’s traditional to eat fried food during this holiday, to commemorate the miraculous oil that lasted eight days and eight nights. Learn something new every day.)

[laurabooks]

In honor of Hanukkah, I bring you some numbers that are important to this holiday. Enjoy!

6.6 million: Estimated Jewish population in the U.S. in 2011

2.1: Percent of the entire U.S. population in that year

8: Days and nights of Hanukkah, and a number of days that a one-day supply of oil miraculously burned during the time of the rededication of the temple by the Maccabees.

25: The day of the Jewish month of Kislev, on which Hanukkah is celebrated each year

9: Including the shammus — or service — candle, number of candles in a menorah

3: Number of blessings recited during the first night of Hanukkah

2: Number of blessings recited during all other nights of Hanukkah

30: Minimum number of minutes the Hanukkah candles should burn each night

44: Total candles lit (including the shammus) overall eight days.

4: Number of Hebrew letters inscribed on a dreidel

92: Approximate number of years that American chocolatiers have been making chocolate gelt.

4: Number of potatoes required for Debbie Koenig’s most delicious latke recipe. (My favorite one I’ve ever tried!)

19: Number of celebrities mentioned in Adam Sandler’s Hanukkah Song.

2: Number of those who are not Jewish

What other numbers are important to Hanukkah? Share them in the comments section.

Categories
Holidays Home Math for Grownups Math for Parents

Time for Holiday Cookies — and Fractions

I haven’t started my holiday baking yet, but that time is just around the corner. Today, I bring you a post from last year, Cookie Exchange Math, in which I look at the fractions involved in tripling my cow cookie — yes, I said cow cookie — recipe. If you need to feed the masses, check out an easy way to manage those pesky and sometimes strange fractions that come from increasing a recipe.

Ah, the cookie exchange!  What better way to multiply the variety of your holiday goodies.  (You can always give the date bars to your great aunt Marge.)

The problem with this annual event is the math required to make five or six dozen cookies from a recipe that yields three dozen.  That’s what I call “cookie exchange math.”

Never fear! You can handle this task without tossing your rolling pin through the kitchen window. Take a few deep breaths and think things through.

To double or triple a recipe is pretty simple — just multiply each ingredient measurement by the amount you want to increase the recipe by.  But it’s also pretty darned easy to get confused, especially if there are fractions involved.  (And there are always fractions involved.)

The trick is to look at each ingredient one at a time.  Don’t be a hero!  Use a pencil and paper if you need to.  (Better yet, if you alter a recipe often enough, jot down the changes in the margin of your cookbook.)  It’s also a good idea to collect all of your ingredients before you get started.  That’ll save you from having to borrow an egg from your neighbor after your oven is preheated.

Read the rest here — and you’ll avoid fractions-related, messy kitchen mistakes.

While you’re at it, check out this interview I did with fantastic candy-maker, Nicole Varrenti, owner of Nicole’s Treats. (I love her chocolate mustaches, personally.) It shouldn’t be any surprise that she uses math daily.

Finally, if you have some holiday-related math questions, would you mind sharing them with me? What trips you up — mathematically — at this time of year? Comment below!