Math for Grownups
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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.

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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.)

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.

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In Holidays

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!

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In Holidays

Using Math to Wrap Gifts

My shopping is done.  I’ve got no more baking to do.  And save one, all of the great holiday parties are wonderful memories.

But I still have this stack of gifts to wrap.

I figure there are two kinds of people in the world: those who painstakingly dress each gift with crisp paper and color-coordinated bows; and those who haphazardly slap on some paper and call it a day.  I’m not so precise about most things, but you can put me in the first camp as far as gift wrapping goes.

Still, I’m mighty lazy.  I don’t measure out paper or use double-sided tape.  Instead I use a little bit of geometry to get my gifts just right.  It’s not hard at all.

The trick to a perfectly wrapped gift is to have just enough — not too much and not too little — paper to cover the package.  And to do that, use a box, if the item is oddly shaped.

Now consider the width of the box.  Line the box up on one end of the paper, like this:

And then turn the box up on the left edge, over onto the other large side and up again on the last edge, like this:

You want to have some left over paper on the left.  This will overlap so that there’s no gap in the seam.

Now you can look at the length of the package.  This is where things get a little tricky.  You need a little more than half the height of the package.  (I just eyeball it, but you can be more precise, if you want.)  You’re ready to cut.

So your paper is cut.  (Did you notice that throughout that easy process, you thought about the width, length and height of the box?  That’s the geometry at work here, folks.)  It’s time to start wrapping.  Turn the box upside down onto the paper.  This way, the seam will be on the bottom of the box.

Wrap one of the long sides of the paper over the box and secure with tape.

Do the same with the other side, making sure that the paper is tightly wrapped around the box.

Now it’s time to address the sides of the gift.  Fold down the top paper, so that it’s flush against the box.  If you’ve eyeballed your measurement correctly, the paper won’t be too long or two short.  Then fold in each side of the paper, making little angles.  Crease each one with your fingernail.  Then fold the last flap up, so that it looks like an envelope.  Use tape to secure that flap.

The other side is much easier, because now you can put the box up on the side you just wrapped.

Once everything is folded and taped up, use your fingernail to make sharp creases along each of the edges of the box.  Add a bow — I like using wired bows made of fabric, because they’re easy to manage, and I can reuse them again next year.  Ta-da!  The perfect gift!

Do you have a gift-wrapping technique to share?  If so, tell us in the comments section.

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In Holidays

Last-Minute Mathy Gifts for Kids

Looking for a last-minute gift for your budding Eistein?  You’ve come to the right place.

I’m not about to suggest that kids love “educational toys.”  But one thing is for sure — kids learn best when they’re having fun.

I’ve gathered a few of my most favorite gift ideas for kids–whether they like math or not.  The best part is that these gifts for sale at your local Target, bookstore or toy store, for not much cash.

Games

SET is a sneaky — and honestly fun — way for kids to learn and practice logic and set theory.  The object of the game is notice similarities in the cards, each of which has a variety of shapes that differ in number, shape, color and shading.  I promise, this is a cool way to spend some time with your kids.  (Ages 6 and up)

Yahtzee?  Yep.  There’s quite a bit of math involved, in fact.  Developing a good strategy requires a solid understanding of probability.  And being able to quickly spot a full-house, three-of-a-kind or four-of-a-kind involves spacial understanding.  Then there’s adding up the scores to find totals.  See?  Math is all over this game. (Ages 8 and up)

Toys

Kids (and grownups) can create complex and simple mazes and runs in a variety of different marble run toys, some with transparent tubes and others with brightly colored pieces.  Where’s the math?  First off, kids are playing with their spacial abilities, noticing where the marble goes when the track positions are changed.  Then there’s the experience of trial and error — which goes hand in hand with math. (4 years and up)

For the tiny set, you can’t go wrong with shapes.  Toys like shape sorters help toddlers and preschoolers learn their shapes.  You can extend the learning by encouraging other ways of sorting — like colors.  (15 months to 5 years)

Books

David Schwartz writes really wonderful math and science books that don’t smack kids over the head with their educational focus.  How Much Is a Million is one of my favorites.  Illustrated by Steven Kellog, the book demonstrates how much a million is.  (Grownups will probably learn something from this one, too!) (Ages 3 and up)

There’s no sneakier way to tap into a kid’s curiosity about math than with The Phantom Tollbooth, by Norton Juster.  This classic children’s novel takes readers on a mythical journey of Milo and his “watchdog,” Tock.  The book touches on a variety of mathematic topics — from infinity to three-dimensional shapes.  Bonus: there’s an equal emphasis on language, including idioms and puns.  It’s bound to be a homerun for any young reader.  Oh, and 2011 is the 50th anniversary of this classic. (Ages 10 and up)

Do you have any great gift ideas for kids?  Share them in the comments section!

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In Holidays

Math at Work Monday: Kim the candle maker

Good grief the winter holidays include a lot of candles!  Earlier this month, Christians began lightingAdvent candles; Hanukkah begins tomorrow night at sunset; Thursday is the Winter Solstice; andKwanzaa starts on December 26.  

That’s a lot of wax!

Lately, I’ve been fascinated by how candles are made, and so I reached out to Kim Meade, owner ofAdirondack Chandler Candles.  In the interview below, she explains how math plays a role in candle making.  It’s a longer interview than usual, but Kim provided such great details, and I didn’t want to leave anything out!

Can you explain what you do for a living?

I make candles the same way they have been done for centuries, dipping candles in a variety of waxes, including paraffin, True Bayberry, and beeswax.  I have a hand made carrousel that allows me to dip 120 pairs of taper candles per dip.  I also make votives, tea lights, potpourri tarts and other items with wax in them.  This is a full time job for me.  I sell my candles to more than 100 retail shops, as well as several consignment shops and on Etsy. I also have a retail website as well as a very small retail shop in my studio.

When do you use basic math in your job?

I use math every day.  I have recipes that I use to make my candles in a variety of scents and colors.  I have to weigh the wax and adjust dyes and formulas depending on how much new wax I add to my batch.  For example, a fresh, new batch of wax requires 75 lbs of wax.  When I finish each dip, I always have a minimum of 30 lbs left over since the dippng vat has to remain full.  At the end of the day, I save the leftover for the base for the next dip of this particular scent or color.  The next time I am going to do this particular scent or color, I have to determine how much more wax I have to add to the melter.  This is basic addition and subtraction.

Then I have to calculate the percentage of dye and fragrance that I have to add.  For example, if I have added 45 new pounds of wax, I have to calculate the proportions — 45 lbs vs. 75 lbs.  If I add 24 ounces of fragrance for a 75 lb batch of a particular scent and 5 Tbs of dye, how much would I add for a batch with only 30 lbs of new wax?  (I always use a calculator for these calculations!)

I also have to consider the strength of the dye.  Green dye is much more “potent” than, for example, yellow dye.  I have color ratios that I use.  If combining dyes for custom colors, I have to look at these ratios to determine how they will affect the end result  For example, I may use only 1/2 the green dye vs. a red dye for a particular result.

With each dip, I determine how many of each size candle I have to make. I routinely make 6″, 9″ and 12″ candles.  I have to look at my sales projections and determine how many of each candle size I have to make.  I then measure the amount of wicking that I have to cut. As an example, for a 6″ candle, I need to cut a piece of wick that is 12″ long, since the wicking will hang over the holder to allow me to dip a pair of candles.  I also have to add 5″ extra to give room for the wick to hang over the holder.

I have to ensure that the candles are at larger than the 7/8″ standard taper base, but not so large they look malformed.  Wax will shrink when it cools, and temperature and humidity can affect it, so I have to be aware of each of these factors.  Temperature plays an important role, specifically if it is warmer than 76 degrees.  Over 80 degrees in studio temperature will negatively affect candle integrity.  Although my candles will be fine above 80 degrees, they will not cool correctly and will have imperfections in them as they cool.  Candles cannot be in a draft, as it will cause them to curve, so I have to consider weather (specifically in the summer).  I cannot run an air conditioner during production.

I have a melter that I use to melt the 75 lbs of wax required for each batch.  Each wax has a different melt point optimum pouring temperature, and flash point (point at which the wax will ignite).  If combining waxes, calculations are made to determine correct melt point and pouring temperature.   Fragrance also has a flash point.  Wicks have different coatings on them (i.e., standard melt point, high melt point, super high melt point).    I load this melter the night before, and have a timer that I use to start the wax melting at the appropriate time.  It takes approximately 5 hours for the wax to melt to the correct temperature. so my first math calculation is to determine when to have the timer set to come on, depending on when I plan to start the day.  Some days I try to get two dips done in one day (so I have to start very early).  The second melt takes less time since the melter is already hot, so I have to make an educated “guess” on how long it will take based on temperature and size of the batch.

When making votives or tealights, I have to add other additives to the wax, such as stearic acid, vybar and other additivies depending on what is being made.  These are based on proportions compared to the weight of the wax.   I usually melt less wax, using a melting pot and a hot plate to melt this wax.  Usually I will melt 5- 10 lbs, so I have to calculate how long it will take to melt, and how much dye,fragrance, etc to add along with the additivies .  I base the dye on the original 75 lb recipe.

Finally, I use math during the packaging and shipping.  I have to determine correct box size, weigh the candles and gather measurements from shipping boxes.

Do you use any technology to help with this math?

I always use a calculator or computer to do my math calculations.  Just a few percentage points off in the production of my candles can ruin an entire batch.  I made an entire batch one time with just 1/2 a teaspoon too much green dye and had to redo the dip and the candles I made, although beautiful, were the wrong color for the scent.

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

Just about everything I do requires math.  I have several sizes of wicking that  I use depending on the size and type of wax I am using.  Large pillar candles require a larger wicking than, for example a 4″ petite, 1/2″ bas candle.  Votive candles require larger wicks  than tea lights.  I also have all the proportions and ratios to consider.  Without math, my candles would not have the correct proportions and most likely would not be successful.

How comfortable with math do you feel?

I actually do not like doing math at all.  But, at my job it is second nature to me now.  Without it, my products would not be successful.  For example, I order 500 lbs of wax at a time, but each candle is only ounces in weight.  I add ounces of fragrance to the entire batch, but how much of that cost is in each single candle?  I purchase wicking by the yard, but the candle is measured in inches.  Dye are purchased by the pound, but measured into the recipe by teaspoon or tablespoon.  I have some complex spreadsheets that I have created in Excel that allow me to plug in the cost of my raw materials and it calculates the cost of my individual batch and candles.  But, even with this, the cost of my raw materials changes at different times, and some of the materials I use, such as dyes, will last for several years.

What kind of math did you take in high school?

In high school I took algebra, geometry, trigonometry and calculus.   I was very good at algebra, found geometry to be difficult, was pretty good at Trigonometry and found that I really enjoyed Calculus.

I have actually continued to learn ways to do math throughout my varied careers.  There are always things to learn to help you do your job better.  Learning to use Excel was a big boost for my business.  It helps me to compare prices, past years sales, calculate my formulas, project raw material requirements, etc.  It is amazing, when I think about it, how much math I use daily.  I am used to doing it, but considering it for this interview, I realized that I use math in almost every aspect of my candlemaking, from ordering raw materials through to the finished product and sales.

Do you have questions for Kim?  Ask them in the comments section!

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In Holidays

Cookie Exchange Math

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.

Each year, I bring cow cookies to my neighborhood cookie exchange.  What are cow cookies, you ask?  Just what they sound like: sugar cookies cut into the shape of a cow.  The spots are made of melted chocolate.  (They’re Holsteins, of course.)  And around each of their little necks, I create little (icing) wreaths with red (icing) berries.

(Why do I make cow cookies?  It’s a long story.  But I’ve been these to holiday parties for more than 20 years now.  Kids love ’em.)

The problem is that my cow-shaped cookie cutter is larger than most other, eh-hem, more traditional Christmas cookie cutters.  So, while my recipe says it yields 36 to 48 cookies, I know I won’t get that many.

So each year, I triple the recipe.  That way I have enough for the cookie exchange (5 dozen), plus some to take to my mom’s house and give away to friends.

I can’t share the recipe here, because it’s copyrighted by Better Homes and Gardens (otherwise known as the Red Plaid Cookbook).  But we can look at the ingredient amounts.  My recipe requires the following measurements of various ingredients:  1/3 cup, 2 cups, 1 tsp and 3/4 cups.

Since I’m tripling the recipe, I’ll need to multiply each of these amounts by 3. Then I can measure out the ingredients using the altered amounts.

The first three calculations are simple, but what about that last one?

The really easy way to get around this fraction is to fill a  one-fourth cup 9 times.  And honestly, if that’s how your brain works, go for it.

But if you want to, you could turn the fraction into a mixed number.  Here’s how:

Ta-da!  In only a few steps, I’ve done the simple math needed to alter this recipe.  Now, I just need to keep my fingers out of the bowl — so that I can actually bring enough cookies to the exchange.  (Honestly, I’d rather eat the dough than the baked and decorated cookies!)

What are your holiday recipe math tricks?  Can you think of other, more creative, ways to alter a recipe.  Share your thoughts in the comments section.

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Holiday Organization: Get your elves in a row

I have a love-hate relationship with the winter holidays.  I love the hustle and bustle of shopping for the perfect gift, making cookies and candies, decorating the house and going to special events.

But every single December, I find myself completely overwhelmed with all that I’ve attempted to achieve.  Some years are worse than others.  There was that time that I was frantically trying to finish up a scrapbook for my sister — at 11:00 p.m. on Christmas Eve.  And then there was the year I sobbed because I didn’t have enough time to string cranberries and popcorn for the tree.

Love-hate.

Like most 40-something folks who celebrate Christmas, I’ve spent the last few years trying very hard to get and stay organized during December.  I’ve prioritized what’s important to me and my family, and I’ve tried to let go of the things that we just don’t have time for.  (We no longer send Christmas cards.  We wait until February, sending Valentines cards.)

This month, I’ll spend a great deal of time here at Math for Grownups looking at the math that is used during the holidays — from making cookies to planning a holiday buying budget.  You’ll meet a candle maker, a personal shopper and (hopefully) a pastry or candy chef.  I’ll introduce you to some fun activities, as well as show you how math can help make some of these bigger tasks much easier.

(This is a good time for a little disclaimer.  In December, I celebrate Christmas, the Solstice and, if I’m not too worn out, New Years Eve.  But not all of my dear readers do.  During this month, I’ll make all attempts to be inclusive, however, I’ll often refer to my personal preparations, which are not all-inclusive.  I hope everyone will understand.)

But first, organization.

Organizing your tasks for the month may not seem like math.  And in some ways it isn’t.  But it does draw on your problem-solving skills — the very same abilities you put to work when solving a word problem in school.  Do you need to make a table? Draw a picture? Make a list?

For me, holiday planning revolves around the calendar.  Already I have certain deadlines to meet and events that are set in stone.  For example, my family is purchasing gifts for another family who is currently living in a shelter.  Those gifts must be delivered no later than December 9.  That means, I have to shop well before then.  And we travel to my mother’s house on Christmas Day, so all wrapping and making and buying and cooking must be done by then.

What is easiest for me is to create a weekly calendar.  I could dole out tasks for each day, but inevitably I end up with far too many changes in my schedule.  It’s easier to think about things one week at a time.

So here goes:

Week of November 28: Finish shopping for adopted family, string cranberries and popcorn, get Christmas tree, decorate tree and house, make sugar cookies, start shopping for my family, help daughter make her Christmas gifts.

Week of December 5: Ice sugar cookies, make little cakes, make peppermint patties, continue shopping, rehearse singing for Solstice and Christmas services, attend neighborhood party, attend cookie exchange, help daughter make her Christmas gifts.

Week of December 12: TAKE WEEK OFF OF WORK! Make peanut butter balls, rehearse for Solstice and Christmas services, help daughter make her Christmas gifts, continue shopping, send cookies to parents-in-law, finish crocheting scarf.

Week of December 19: Finish shopping, finish daughter’s homemade Christmas gifts, make Kiss cookies, package tins of cookies for friends, make Solstice cookies, wrap gifts, get car ready for the trip to Virginia, pack, make potluck dish for Christmas Eve.

Week of December 26: RELAX!

Now I can look at that list and see if anything is out of order — I’m not wrapping gifts before I buy them.  I’m not attending the cookie exchange before I make the cookies.

I can also ask myself if there is anything missing. Or does any one week look overly burdened?  Ideally, I’d like to get most of my preparations done before December 19, leaving that week to tie up loose ends.

How do you organize your time when you have way too much to do — and too many other things that you want to do?  How do your problem-solving skills help?  Respond in the comments section.

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