Tag

DECEMBER

Browsing

It’s been a mere eight months since this blog launched.  And it’s been only six months since Math for Grownups (the book) hit the shelves.  What a crazy time it’s been!

In reviewing the posts that you dear readers loved most, I came up with this list.  And in case you missed anything, I thought I’d share these posts again.  Happy New Year!

Math Secret #2: You Were Born This Way

Nope, you weren’t born without a math gene.  In fact the opposite is true — you were born with a natural instinct for mathematical concepts.  Really!

Top 10 Highest Paying Degrees

“Holy crap!” That’s what I indelicately exclaimed when I saw the list of 10 highest-paying degrees, as determined by the PayScale College Salary Report.  I didn’t expect to see American Literature or Elementary Education, but I also didn’t expect this.

When Journalists Get the Math Wrong

One of the most eventful weeks of my year was when USA Weekend profiled my book — and got the math wrong.  The really interesting part, though, were the responses.  Apparently making math mistakes in public is unforgivable to some.  No wonder people are afraid to do math!

There’s More than One Way to Skin a Math Problem

The more I talk to people about math, the more I hear this refrain: “I don’t like math, because math problems have only one answer.” Peshaw!

Summer Session: What your rising first grader should know

Math for Grownups blog readers tend to fall into two camps: grownups who are not parents and really hate math (or think they’re not good at it), and parents who are worried that they’re going to pass along their math anxiety to their kids.

Are there any topics you’d like to see covered here at Math for Grownups next year?  Share them in the comments section or shoot me an email.

Math for Grownups readers love Math at Work Monday.  And here are the top 10 interviews of the year.

Mary Ellen the FBI Profiler

In her book, Dangerous Instincts: How Fear Can Betray Us, Mary Ellen O’Toole, PhD, puts these experiences to work everyday life.  And in this interview, she reveals how she uses math in her work.

Melissa the Speech Therapist

Lots of people think of speech therapists in the school setting, working with kids.  But my sister, Melissa, works with adults, who are critically ill or recovering from an injury or illness in rehab.

Katie the Costume Designer

As a costume designer and technician, Katie Curry worked for the Berry College Theatre Company and the Atlanta Shakespeare Festival. She recently started her own venture called Nancy Raygun Costuming that caters to folks who are into cosplay and conventions or just want a fun costume.

Jennifer the Retail Buyer

Merchandise at your favorite store doesn’t magically appear on the store shelves.  In fact, there’s a lot of planning that goes into the number and types of candy bars that fill checkout-line racks. And that’s where Jennifer Cassara comes in.

Graham the Fish Hatchery Technician

Graham Laing is my brother, and I don’t think he’d be offended by my telling you that some of us in the family were a little worried that he might not amount to anything.  But that’s another story for another day.  Today, he’s afish hatchery technician, which basically means he raises trout — “from eggs to eating size,” he says.

Tiffany the 6th Grade Teacher

I know what you’re thinking. “It’s so obvious how a 6th grade teacher would use math! She’s teaching fractions and division and percents!” But there’s always a lot more to teaching than the rest of us may think.

Brette the Cookbook Author

When my friend and fellow writer, Brette Sember let me know that she has a cookbook coming out, I jumped at the chance to feature her here.  It should be no surprise that math is a critical ingredient of all recipes.  The Parchment Paper Cookbook is no exception.

Shana the Jewelry Designer

Art and math are diametrically opposite, right?  Wrong. Shana Kroiz is a Baltimore-based, acclaimed jewelry designer and artist, whose work has been shown in the some of the country’s most esteemed galleries and museums, including The Smithsonian and the Museum of Arts and Design in New York City.

Kim the Copywriter

If you’ve ever visited the website of a prescription medication or picked up a brochure from your doctor’s office, you’ve seen the kind of work that Kim Hooper does.  And she’s proof that math and writing are not mutually exclusive endeavors.

Ron the Web Designer

Ron S. Doyle is both a web designer and a freelance writer.  In fact, he’s found a particular niche in developing web sites for other freelance writers.  He’s also got a wicked sense of humor and uses math in his work.

I’m planning for the New Year. Who would you like to see interviewed for Math at Work Monday?  Share in the comments, or shoot me an email.

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.

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!

Everybody loves a sale, right? The thrill of the hunt, the sense of accomplishment when landing a great deal.

But how many times have you reached the register and realized your purchase was more than you expected?  Or have you ever passed on a purchase because figuring out the discount was way too much trouble?

You don’t have to be afraid of the mental math that goes along with shopping.  (That goes for in-person and online sales.)  You also don’t have to be that giant geek standing in the sports goods aisle using your cellphone calculator to find 15% of $19.98.  Who has time for that anyway?

Believe it or not, figuring percents is one of the easiest mental math skills.  And it’s one of those things that you may do differently than your sister who may do differently than your boss.  In other words, you are not required to follow the rules that you learned in elementary school.  Now that you’re a grownup, you can find your own way.

Don’t follow?  Let’s look at an example.

Once again you’ve put off buying Mom’s gift.  It’s just about time to leave for her house, and you have literally minutes to find the perfect present for her — at the right price.  You’ve collected $40 from your brother and sister, and you can contribute $20.  Darn it, you’re going to scour the department store until you find something she’ll like that’s in the right price range.

And suddenly, there it is: a countertop seltzer maker, just right for Mom’s nightly sloe gin fizz. Bonus! It’s on sale — 40% off of $89.95.  But can you afford it?

There are a variety of different ways to look at this.  But first, let’s consider what you know.

The seltzer maker is regularly priced at $89.95.

It’s on sale for 40% off.

You can spend up to $60 ($40 from your sibs, plus the 20 bucks that you’re chipping in).

You don’t necessarily need to know exactly what the seltzer maker will cost.  You just need to know if you have enough money to cover the sale price.  And that means an estimate will do just fine.  In other words, finding 40% of $90 (instead of $89.95) is good enough.

Now you have some choices.  You can think of 40% in a variety of ways.

40% is close to 50%

It’s pretty easy to find 50% of $90 — just take half.

50% of $90 is $45

So, if the seltzer maker was 50% off, you could afford it, no problem.  But is 40% off enough of a discount?  You probably need to take a closer look.

40% is a multiple of 10%

It’s not difficult to find 10% of $90 either.  In fact, all you need to do is drop the zero.

10% of $90 is $9

What is 40% of $90?  Well, since 40% is a multiple of 10%:

There are 4 tens in 40 (4 · 10 = 40)

and

10% of $90 is $9

so

 4 · $9 = $36

It’s tempting to think that this is the sale price of the seltzer maker.  Not so fast!  This is what the discount would be.  To find the actual price, you need to do one more step.

$90 – $36 = $54

Looks like you can afford the machine. But there’s an even more direct way to estimate sale price.

40% off is the same as 60% of the original price

When you take 40% off, you’re left with 60%. That’s because

40% + 60% = 100%

Or if you prefer subtraction

100% – 40% = 60%

So you can estimate the sale price in one fell swoop.  Like 40%, 60% is a multiple of 10%.

There are 6 tens in 60 (6 · 10 = 60)

and

10% of $90 is $9

so

 6 · $9 = $54

The estimated sale price is $54, which is less than $60.  You snatch up the race-car red model and head for the checkout.

There are so many other ways to estimate sales prices using percents.  Do you look at these differently?  Share how you would estimate the sale price in the comments section.

Whether you’re buying gifts for under the tree or just taking advantage of holiday sales, December is one of those times when you might need some mental math skills.  And while it can seem overwhelming to find out how much that 15%-off cashmere sweater will actually cost you, there are some easy ways to make quick work of these calculations and move on to the next item on your to-do list.  (We’ll look at those on Friday.)

But first you need to answer one big question: Is an estimate good enough?

What’s the total cost?

Let’s say you’re picking up a few things for your Aunt Millie. She has given you a $20 bill and a list.  You absolutely cannot exceed $20, and Aunt Millie is adamant that you get as much as you can for that amount.  In this case, you may want to calculate everything down to the penny.

Or what if you’re purchasing holiday gifts for a family in need.  You’ve set your budget — and you’re not going over it!  Once you have everything in your cart, it could be reassuring to spend a moment or two finding the exact cost of your purchases.

(Here’s a cool hint, though.  If you’re shopping online, these calculations are done for you.  Just put what you want in your online shopping cart, and the totals will be appear — including shipping!)

Can you afford it?

But I would guess that most of us merely need to know if we can afford a purchase — or if what we’re interested in buying is too expensive.  And that’s where estimation comes in handy.

Chandra’s family is HUGE.  And after years of buying a Christmas gift for each of her nine siblings and their spouses and partners, she initiated the good old Secret Santa exchange.  What a relief!

The process is simple. Over pumpkin pie after Thanksgiving dinner, Chandra’s mother brings out her best Sunday hat, which contains slips of paper — one for each of the 18 kids and their partners.  Each person selects a name and buys a present for that person.  The catch? No one can spend more than $50.

This year, Chandra is over the moon.  She drew her sister-in-law’s name, and she knows exactly what to get her — a handmade purse from the local craft fair.

A week later, struggling through the crowd of candle-buying, carol-humming shoppers, Chandra finds exactly what she’s looking for: a cute little bag made of repurposed, 1940s dish towels.  What a find!

She snatches up the bag, and pays $40 for it.  But she’s got $10 left over.  Should she find something to put inside?

Chandra starts looking for a little something more: there’s a handmade key fob for $2.50 or a little zipper pouch for $10. She starts feeling like Goldilocks — the pouch is too much and the key fob is not enough.  She leaves knowing she can make up the difference while shopping elsewhere.

And she hits jackpot later that week.  While picking up a few things at her local, independent bookstore, she spies a sweet little journal at the checkout line that would just fit into the purse.  On sale for $6.50, she figures she has enough to pick up a rollerball pen to go with it.

Just right.  (And notice — very little math!)

Is estimation mandatory?

So let’s say you are really into knowing your costs down to the penny.  What if just having a general idea of what something costs is way too unnerving for you?

Pull out that calculator, sister or brother.  There’s nothing wrong with finding the exact answer, if that’s what you need or want to do.  Just do the rest of us shoppers a couple of favors — move to the side of the aisle while you do your computin’ and while you’re at it, don’t look down your nose at other’s estimations.

Are you an estimator or an exacting kind of person? If you estimate, how? If you like an exact answer, what tools do you use?  Share your stories in the comments section.