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Personal Finance

Squirreling Away for Winter: Saving with math

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

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

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

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

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

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Holidays Math for Grownups Math for Parents

Scary Statistics: Halloween by the numbers

For many folks along the East Coast, Halloween will (at the very least) be postponed, thanks to the very real terror of Super Storm Sandy. I know all of us keep these folks in their thoughts.

And the rest of us? For the most part, tonight marks a very strange annual tradition here in the U.S.: going door to door in costume, asking for free candy. To mark the occasion, I’ve collected some scary statistics about the night of tricks and treats. Read at your own risk! Bwa-ha-ha-ha! (Um… that’s my attempt at an evil laugh.)

170 million: The number of people who plan to celebrate Halloween in the U.S. (National Retail Federation)

$79.82: The average spent on costumes, decorations and candy this year. (National Retail Federation)

$113 million: The total value of pumpkin crops in the three top pumpkin-producing states (Agricultural Marketing Resource Center)

1,818: Number of pounds weighed by the largest pumpkin on record. (Guinness World Records)

15.2: The percent of costume ideas that come from Facebook. (National Retail Federation)

15.1: The percent of people that will dress their pet in a costume. (National Retail Federation)

0: The percent of pets that enjoy this tradition. (Just a guess)

6: Number of times I went trick-or-treating as a “hobo,” because I was too lazy to do much else. (Personal data)

268: The population of Skull Creek, Nebraska — named for “A LOT” of buffalo skulls and bones found in a nearby creek. (U.S. Census)

1690: The number of pieces of candy that will fill an average-sized pillow case. (www.myscienceproject.org)

41: The percent of adults who admit eating candy from their own candy bowl between trick-or-treaters. (National Candy Association)

90: The percent of parents who admit stealing from their kids’ trick-or-treat stash. (National Candy Association)

99.9: The percent of parents who actually steal candy from their kids’ trick-or-treat stash. (Just a guess)

30: The percent of kids who sort their candy before digging in. (National Candy Association)

0: Number of kids who would rather get a toothbrush than candy, while trick or treating. (Just a guess)

Happy Halloween, everyone! Just one last word of warning: Watch out for the zombies. (Here’s how math can help you plan during a zombie apocalypse.)

What are your Halloween plans?

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Math at Work Monday

Math at Work Monday: Rick the pediatric plastic surgeon

Yes, you read that right — pediatric plastic surgeon. But don’t make the dumb assumption that I did when I first met Dr. Rick Redett. He’s not doing nose jobs on preteens. He’s expertly repairing cleft lips and palates, doing skin grafts and addressing nerve injuries at Johns Hopkins Children’s Center. And this is pediatrics, so he’s working with teeny-tiny parts — little hands and noses and even nerves in these little bodies. One measurement that’s even a little bit off can mean a very big problem. 

It’s no wonder that Dr. Redett uses lots of math in his work — from conversions to measurements to basic geometry. On top of that, he helped found Bring Hope Through Healing, a non-profit that helps fund surgical trips to South and Central America, so that children (and even a few adults) with cleft palates and lips can get restorative surgery. But in terms of his everyday job? Here’s how he uses math. 

Can you explain what you do for a living? I am a pediatric plastic surgeon, caring for children with cleft lip and palate, nerve injuries, congenital and traumatic hand problems and burns.

When do you use basic math in your job?  Most of the medicines we give children are weight based, which means we give a specific amount of medicine calculated using the weight of the baby. Giving too little or too much medicine may be harmful. I also use math during surgery. When a baby is born with a cleft lip, one of the nostrils is much bigger than the other. To determine how much smaller I need to make the bigger nostril, I use device which measure the diameter of each nostril. Multiplying the difference in diameter of the nostrils by 3 (approximately π) will equal the amount of tissue which needs to be removed from the bigger nostril to make it the size of the smaller nostril.

Notice how the nostril on the left is larger than the one of the right. Rick uses the formula for the circumference of a circle to help him even out the nostrils along with repairing the cleft lip.

Do you use any technology to help with this math? I use an app on my iPhone when calculating medication doses in children

How do you think math helps you do your job better?  I couldn’t do my job without math.

How comfortable with math do you feel?  I enjoyed math in school and am comfortable using it at work. Most of the math I use at work is relatively simple but necessary to practice medicine safely.

What kind of math did you take in high school? Math was one of my favorite classes in high school. I especially liked trigonometry

Did you have to learn new skills in order to do the math you use in your job? I didn’t have to learn anything new, but I have had to review things that I didn’t know I’d need. When I was learning how to make the nostrils symmetric during cleft lip surgery, I had to look up the formula for the circumference of a circle (C = dπ, where C is circumference, d is diameter and π can be rounded 3.14).

Did you think that the formula for the circumference would ever be useful? I was surprised. Oh, and parents, next time your little one is at the doctor or (god forbid) needs surgery, be glad that the doctor took math! If you have questions for Dr. Redett, post them here. I’ll let him know about them and get answers for you. 

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Math Education Math for Grownups Math for Parents Math for Teachers

Pre-Algebra on Facebook: How Mark Zuckerberg helped a frustrated parent

Wednesday on Facebook, I had the most amazing experience. Suffering from an all-day migraine, I had spent the afternoon bored out of my mind, obsessively checking Facebook while the television droned in the background. At one point, this status update from my friend Alyson appeared in my feed:

ALGEBRAAAAAAAAAAAAAAAAAAA!!! (Shaking fist angrily in air at math gods)

I was Batman and here was the bat signal. How could I help?

The first response was from someone I didn’t know and very typical: “Outside of college, you don’t really need it, right?” I rolled my eyes inwardly and thought about why Alyson might need to solve an algebra problem. Then I remembered her incredibly bright son, who is completely enamored with computers. I mean in love with the machines. I’d bet my last dollar that the boy will find himself programming or engineering or something in STEM as an adult. In other words, he would need algebra.

I posted a few questions to see how I could help, and eventually Alyson posted the original equation to solve:

algebra fractions equation
fraction algebra
fraction algebra

Whew! It is a doozy, right? Alyson had one very specific question: how to handle the last term of the equation: . I told her the simple answer — that it was the same thing as . Still a teacher at heart, I wanted to see what she could do with that information. Was it enough to help her solve the problem?

Meanwhile lots of other people were chiming in, and Alyson was expressing lots of feelings:

And just so everyone knows, I suck at fractions. Always have, always will. When I took SAT and ACT and whatever else, I literally turned all fractions into decimals because I can never remember how to add, subtract, divide, multiply, etc. fractions.

I’m close to crying…I still don’t understand what you’re saying. He worked the whole thing out at got what my online algebra check thing says is a wrong answer, and I’m trying to work it out so I can figure out how to get the RIGHT answer and I really do think I’m going to cry…

Frustration cry. Because I didn’t think I’d ever use math. And I was wrong. For the record. Sorry, Mrs. Blankenship.

This is a super smart lady. She edits college-level courses of all kinds, and she’s had a successful freelance writing career for many years. And I can completely identify with her frustration. I’d been struggling with Venn diagrams and conditional statements all day. No wonder I had a migrane.

But then something really amazing happened. Really amazing. A mutual facebook friend and writer, Jody (owner of Charlotte on the Cheap) tagged us both in her status update:

Do I have it right? Do I?

She had attached this photo:

At 6:15 on a Wednesday evening, she had not only worked out a challenging pre-algebra problem but also taken the time to scan it and post on Facebook. She was so excited. And, yes, she had gotten the correct answer.

She had also done it differently than I did. But that’s not even the best part. Alyson saw Jody’s process and looked carefully — very carefully. She posted this:

I worked through it on my own twice using your strategy, which ended up making a lot of sense to me once I talked it out a few times. So now I can explain it to [my son] and actually have a clue what I’m talking about. THANK YOU.

Within an hour, another of Alyson’s friends had posted one more way to do the problem. It was a smorgasbord of solutions!

But here’s the very best part: with all of these threads, there were very few people chiming in to say that they were too dumb to help or “who cares?” In fact, I saw many more people posting things like this:

This I can do. Proof reading for grammar errors…….not so much!

I will be glad to do some algebra when the time comes.

 I love math, call me, text me pictures!!!! I will PM you my number.

Why WHY WHY are you having an algebra party without ME?! I love me some equations!

It wasn’t a complete love-fest, but it was worlds different than I’m used to seeing. The tenor of the discussion was supportive and positive, rather than defeated. Sure, there’s was lots of frustration. And I’m betting that there were lots of people reading the threads and thinking, “Good god, I’m going to be in BIG trouble when my kid takes algebra.” But what played out in the end was a good experience — not just getting the right answer but learning different ways to approach the problem.

I originally became a math teacher because I was convinced of two things: math is important and anyone can do math. For years, I’ve felt pretty alone in those two estimations — especially after leaving the classroom. Yet, here was a community of people who were working from the same premise, encouraging Alyson and excitedly trying out the problem themselves.

I can’t think of a better way to end Back-to-School month at Math for Grownups. If you parents can express this enthusiasm — along with your frustration, if you have any — you’ll be doing your kids a big favor. It’s the pushing through and looking for ways to understand things differently that makes a difference. Imagine how much more empowered and confident our kids will feel if they get the message that math is important and that they can do it.

What positive messages about math have you seen lately? Have you found ways to be more encouraging about math with your own kids? Share your thoughts in the comments section.

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Math Education Math for Parents Math for Teachers

Forget the Ping Pong — Let’s Do Some Math

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

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

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

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

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

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

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

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

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

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

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

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

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Math at Work Monday

Math at Work Monday: Robert the veterinarian

With a blind, deaf, 18-year old toy poodle who has dementia (canine cognitive disorder), I’ve gotten to know our friendly neighborhood veterinarian very, very well. Dr. Robert Z. Berry, DVM at The Village Vet has helped us manage some strange symptoms and supported us in the last year since Roxie was diagnosed with dementia. Just like people doctors, vets must have excellent bedside manner, and Dr. Berry has it in spades.

I also noticed that he does quite a bit of math in his work. Roxie has been on a variety of medication, as we’ve looked for the right combination to keep her happy and healthy. And she’s only 6 pounds. That means converting measurements like crazy. At a recent visit, I finally got the idea to ask Dr. Berry to answer my Math at Work Monday questions. If your kid aspires to be a vet, read on!

Can you explain what you do for a living? 

I examine sick and healthy animals, provide preventative care such as vaccinations or parasite (intestinal and blood born worms) screening and offer early disease detection, blood tests or imaging (xrays and ultrasound). In the case of sick animals, we can hospitalize and provide medical care or medical surgical care to help return them to normal health. Additionally we provide routine surgical and dental services such as spaying , neutering, tumor removal, dental cleaning and extractions.

When do you use basic math in your job?

Everyday, from basic math skills to algebra. Here’s an example : An animal weighs 22 pounds and needs medication which is dosed at a rate of 20 mg/kg and given three times a day. The animal’s weight is measured in pounds, so the first step is to convert to kilograms. Then I need to multiply the weight in kilograms by 20 mg/kg. Now we have a milligram dose of 200 mg. But things can get even more complex. Suppose the drug is supplied in 400 mg/ml strength? I use division or an algebraic formula to arrive at a milliliter (or cc, cubic centimeter) dose of 0.5 ml.

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

I really prefer not to use a calculator because I think it can make my brain become lazy. It is remarkable how much agility you lose (even basic math skills) when you don’t use basic math skills on a daily basis. I calculate in my head but verify with the calculator.

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

It’s absolutely necessary with any sort of drug therapy.

How comfortable with math do you feel?

I feel very comfortable with math and have all of my life. Vets must be mentally sharp and learn to rely on their most important assets — their brains! I took calculus in high school, and I felt very confident in the class. School prepared me very adequately for the nuts-and-bolts part of my job. I was fortunate to have good teachers and also to have been raised in the time period before calculators were allowed in school. A good primary education prepares one for the rest of his or her life.

So there you have it, a vet who is both compassionate and math-savvy — a great combination! Were you surprised by the math that Dr. Berry uses in his practice? Share your response in the comments section.

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Math Education Math for Parents Math for Teachers

More Sneaky Math for Kids: Guest post from Erin Flynn Jay

When you’re balancing work and home and all sorts of other responsibilities, it can be downright overwhelming to consider doing everyday math with them, so they can perform well in school. That’s why I invited author Erin Flynn Jay to guest post on this very topic. Her recently published book,  Mastering the Mommy Track, tackles many of the questions all of us working parents have, and today she addresses math.

How do your kids do with their math homework? Is it a struggle to get them to concentrate, or do they have a good handle on calculations?

I grew up watching my mother tutor grammar school kids in math at our home. She was also a substitute math teacher at our local schools when I was in grammar school and high school. Because I am not a math whiz, I asked for her viewpoint on this blog post (she read this and offered a critique).

Kids need examples, which will allow them to understand numbers better.

— Beginning when they are toddlers, help them count their snack food like Cheerios or Goldfish from one to ten. It’s wise to get them counting at the earliest age possible.

— When you take your kids grocery shopping, explain to them what your purchases cost. If they are learning how to add numbers in school, ask them for a total. You could ask them, “Okay we have this corn which is $2, chicken for $8 and lemonade for $2. How much money do I need? What is 2 plus 8 plus 2?”

— Give your kids a weekly or monthly allowance depending on your budget. Take them to the pizza place or movie theater and ask them to pay for their purchase themselves. This way, they can understand the value of a dollar or 50 cents more easily. They can get change back and will get a better grasp of what their favorite items actually cost.

— Finally, teach them how to measure their TV shows in 30 minute intervals. For example, you could say, “Alright, you can watch your show for 15 minutes before bedtime.” When the time is up, let them know 15 minutes has passed and it’s time to pack it in.

One final suggestion is to check with your local librarian or bookstore–get recommendations for age appropriate math books. Read them one math book per night.

When your kids sit down to do their math homework, they will perform better if you have introduced basic math concepts at the preschool age. Repetition will reap results.

Erin Flynn Jay is a writer and publicity expert, with articles appearing in a diverse list of publications, including careerbuilder.com, MSN Careers and Wealth Managers. Order her book Mastering the Mommy Track at Amazon.com or barnesandnoble.com. 

Here at Math for Grownups, you’ve gotten a lot of ideas on how to sneak math into your kids’ everyday lives — from reading time to when you’re on the road. What suggestions have you tried? How have they worked out? I’d love to hear about your successes (and yes, failures)! 

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Math Education Math for Grownups Math for Parents Math for Teachers Math Secrets

The Problems with PEMDAS (and a solution)

If you’re on Facebook, you’ve probably seen one of a variety of graphics like the one above.

The idea is to solve the problem and then post your answer. From what I’ve observed, about half of the respondents get the answer correct, while the other half comes to the wrong answer. The root of this problem? The order of operations.

Unlike reading English, arithmetic is not performed from left to right. There is a particular order in which the addition, subtraction, multiplication, and division (not to mention parentheses and exponents) must be done. And for most of us old-timers, that order is represented by the acronym PEMDAS (or its variations).

P – parentheses
E – exponents
M – multiplication
D – division
A – addition
S – subtraction

I learned the mnemonic “Please Excuse My Dear Aunt Sally” to help me remember the order of operations.

The idea is simple: to solve an arithmetic problem (or simplify an algebraic expression), you address any operations inside parentheses (or brackets) first. Then exponents, then multiplication and/or division and finally addition and/or subtraction.


But there really are a lot of problems with this process. First off, because multiplication and division are inverses (they undo one another), it’s perfectly legal to divide before you multiply. The same thing goes for addition and subtraction. That means that PEMDAS, PEDMSA, and PEMDSA are also acceptable acronyms. (Not so black and white anymore, eh?)

Second, there are times when parentheses are implied. Take a look:

If you’re taking PEMDAS literally, you might be tempted to divide 6 by 3 and then 2 by 1 before adding.

Problem is, there are parentheses implied, simply because the problem includes the addition in the numerator (top) and denominator (bottom) of the fraction. The correct way to solve this problem is this:

So in the end, PEMDAS may cause more confusion. Of course, as long-time Math for Grownups readers should know, there is more than one way to skin a math problem. Okay, okay. That doesn’t mean there is more than one order of operations. BUT really smart math educators have come up with a new way of teaching the order of operations. It’s called the Boss Triangle or the hierarchy-of-operations triangle. (Boss triangle is so much more catchy!)

The idea is simple: exponents (powers) are the boss of multiplication, division, addition, and subtraction. Multiplication and division are the bosses of addition and subtraction. The boss always goes first. But since multiplication and division are grouped (as are addition and subtraction), those operations have equal power. So either of the pair can go first.

So what about parentheses (or brackets)? Take a close look at what is represented in the triangle. If you noticed that it’s only operations, give yourself a gold star. Parentheses are not operations, but they are containers for operations. Take a look at the following:

Do you really have to do what’s in the parentheses first? Or will you get the same answer if you find 3 x 2 first? The parentheses aren’t really about the order. They’re about grouping. You don’t want to find 4 + 3, in this case, because 4 is part of the grouping (7 – 1 x 4).  (Don’t believe me? Try doing the operations in this problem in a different order. Because of where the parentheses are placed, you’re bound to get the correct answer more than once.)

And there you have it — the Boss Triangle and a new way to think of the order of operations. There are many different reasons this new process may be easier for some children. Here are just a few:

1. Visually inclined students have a tool that suits their learning style.

2. Students begin to associate what I call the “couple operations” and what real math teachers call “inverse operations”: multiplication and division and addition and subtraction. This helps considerably when students begin adding and subtracting integers (positive and negative numbers) later on.

3. Pointing out that couple operations (x and ÷, + and -) have equal power allows students much more flexibility in computing complex calculations and simplifying algebraic expressions.

Even better, knowing about the Boss Triangle can help parents better understand their own child’s math assignments — especially if they’re not depending on PEMDAS.

So what do you think? Does the Boss Triangle make sense to you? Or do you prefer PEMDAS? What to learn to solve these and other problems, buy the book that will help grown-ups like you with these and other math problems here.

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Math for Parents Math for Teachers

3 Ways to Turn Reading Time Into Math Time (Psst… You may be doing these already!)

Yesterday, Karma Wilson stopped by to describe how she uses math in her work as a children’s book author. She’s the author of such wonderful best sellers as Bear Snores On and Bear Says Thanks. And she got me thinking about the days when I used to read her (and other’s) books to my daughter (who is almost a teenager now!).

I guess because I like math and learned to incorporate numbers and math concepts into my everyday life pretty quickly, I naturally looked for the math hidden within each book I read to my daughter. But after having lots of conversations with other parents, I’m realizing that many don’t see the connection between literacy and numeracy. (Remember, numeracy is to math as literacy is to reading.) So I thought I’d share my ideas today in this special post.

It’s not actually very difficult to bring math into almost any picture book. But perhaps parents think they should shoot for the stars — asking kids to add, subtract, multiply or divide. Unless that’s part of the plot, I’m guessing such ideas come off a bit forced. Or they may just suck all of the fun out of sitting down and reading with your child. So try these suggestions on for size.

Count

In Bear Snores On (illustrated by Jane Chapman), a hibernating bear is visited by a variety of forest animals who host a mid-winter party in his cave. The easy thing to do here is to count the animals. How many are there by the middle of the book? How many are there by the end of the book? When you count, point at each animal and say the number out loud. As your child grows, ask him to point and count.

This process is a really easy way to reinforce something called one-to-one correspondence (or as we math geeks write, 1:1 correspondence). It’s so stupidly easy, that it’s hard to imagine kids aren’t just born knowing this. But the idea is that each animal in the book corresponds to a specific number. If you count the animals in the order that they appear in the book, the mouse will always be 1 and the raven will always be 7.

Addition

In Karma’s A Frog in the Bog (illustrated by Joan Rankin), the protagonist (yes, a frog in a bog) makes a very large meal of a variety of different critters in a variety of different numbers.  There is one tick, two fleas, etc. This is the perfect time to prompt some addition. After the frog eats the tick and both fleas, how many critters are there in all? Count them in the picture, again by pointing to each one and saying the numbers out loud.

Tiny ones won’t necessarily learn to add simply by reading this book, but asking these kinds of questions can help lay the groundwork for an idea called counting up. In this process, when kids are adding two numbers, they start with one and count up using the second number. So 2 + 3 becomes 2, 3, 4, 5 — visually counting from 2 to 5 using fingers or something else concrete.

Proportions

Whopper Cake (illustrated by Will Hillenbrand) features a grandpa who is making a mighty big cake for Grandma’s birthday. From the title, we adults can predict that this cake is going to be huge, but your little one may not have those literary skills down pat. Guide him to that place by pointing out the sizes of things. The recipe calls for two cups of sugar, but Grandpa puts in 23 pounds of the sweet stuff. “Is that more or less sugar?” you can ask. Same with the eggs, which are increased from four to 84. Again, this may seem really basic, but young children (preschool and kindergarteners) are just learning about size comparisons. Until we teach them about bigger and smaller, they don’t have a clue.

Bonus: Have your child play with measurements and follow an algorithm (or a set of steps) by making a Whopper Cake from the recipe at the end of the book.

So, there you have it — a few ways to turn reading time into math time. These ideas don’t look so hard, do they? They should seem pretty darned simple. And they pay off, big time. Not only will your child be learning some basics about the foundation of numeracy and mathematics — he’ll likely pick up the message that math is everywhere and even a little bit of fun. Not even Bear should sleep through that!

What are ways you’ve incorporated math into your kids’ nightly reading? Share your ideas in the comments section.

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Math at Work Monday Math for Writers

Math at Work Monday: Karma the children’s book author

Do you know Bear of Bear Snores On and Bear Feels Sick? Or Pip of Where is Home Little Pip? If so, you also know my very talented friend, Karma Wilson. Karma has been a published author for 12 years (not including the three years it took for her to get published the first time). She is the author of 30 books, and begrudgingly, she admits to using math from time to time. 

Can you explain what you do for a living?

I write — specifically for the 4- to 8-year-old set. It is my goal to write engaging books and poetry for children that is also appealing enough to adults that they don’t hide it under the hamper lest it be requested again. To accomplish this I utilize rhyme, alliteration and two-tier humor that is directed to children on one level, adults on another.

When do you use basic math in your job?

I wrote a rhyming counting book (Frog in the Bog), does that “count”? It only went to five, which gives you a good idea of my math skills. Seriously though, in my line of work there is a lot of math that my literary agent mostly deals with. I have to pay him 15% of my income. My royalties are usually 6.5%. My publisher holds out profits from sales in case of large returns on my books, and that’s usually 25% of my royalties. All this adds up to a good reason for me to have an agent!

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

If I have to do math I generally do use calculators, mainly because I’m a very wordsy, artistic type and math has never been a strong suit for me. In case of serious math questions I panic and turn my friends who know math, like the amazing Laura Laing!

Karma Wilson

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

Well, for me the biggest way is with word counts. If I have a story that goes over 1000 words I better darned well subtract a bunch of those words. Wordy picture books don’t typically sell very well. Also, my words need to fit into a formula, which translates to a 32-page book with end pages that have no words. It’s important that the words to my stories fall naturally and rhythmically into that formula, which sometimes requires a break down of words per page. Luckily, I am sort of “savant” in that area, and rarely do book dummies, but I know a lot of picture book writers who are lost without that breakdown.

How comfortable with math do you feel?

I don’t feel comfortable with math at all. The math that accompanies my work is relatively simple, so it doesn’t give me panic attacks. But for my taxes and running my corporation (Karma Wilson Books Incorporated) I get a little math-addled.  That’s when I turn to people who are more comfortable with math than I am, like accountants and agents.

What kind of math did you take in high school?

The highest I got to was pre-algebra. I was pretty horrible at it. That letter x never needed to fear I would discover his or her secret identity. Ha!

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

Since I have an agent who does the hard math for me I was able to skate on my pre-algebra level skill set. However, if you’re in this industry trying to figure out the contractual stuff without an agent, you should at least have some basic accounting math skills. Otherwise, you’ll be lost in royalty rundowns and not know if your contract was fulfilled or not. It really is that important.

While my specific line of work isn’t all that math intensive, the times that I’ve wanted to understand my royalty statements were severely hampered by my fear of math. I strongly encourage every adult to refresh their math skills so they feel more confident discussing numbers with professionals in their industry.

Karma is on tour right now, promoting her newest book Bear Says Thanks. Her next stop is Denver CO at the Mountains and Plains Bookseller’s Association Author Tea on 9/21/12 at 3:45 p.m. 

Categories
Math Education Math for Parents Math for Teachers

Math Homework: 5 important ways to help your kid

By 8:30 on Tuesday night, I was ready to go home and curl up with a good book. But there I was, crammed into a windowless computer lab with 25 other exhausted parents, listening to the new math teacher describe how math instruction would work this year.

He described how the Common Core standards will change math education and showed off the fancy online curriculum that our school is lucky to have. Then he asked for questions — and the parents pounced. Poor guy.

See, this fellow is exactly what students need. He’s tough; he’s smart; and he thoroughly understands a critical element of mathematics education: Kids have got to take risks that might not lead to a solution. Just like Sir Isaac Newton and Albert Einstein and Ada Byron Lovelace (yes, she’s Lord Byron’s daughter and the founder of scientific computing) went down long and winding roads to their discoveries, our kids must do the same.

But the parents were having none of that. The homework that Mr. T is sending home each night is really challenging. Really challenging. My daughter was complaining and crying and slamming doors because of it. And I know we weren’t alone in our little nightly soap opera.

As the parents got more frustrated and asked more and more questions about grading and building confidence and avoiding stress, I realized that they were missing the whole point. As parents, it’s not our job to shelter our kids from struggle and frustration. I was having a really hard time resisting the urge to step up to the front of the room and do some damage control.

So I figured I should take this opportunity to share my ideas here. Fact is, Common Core may mean that your child is more frustrated. But there are ways to cope.

1. Get proactive

What do the Common Core objectives say? Well, they’re no big secret. Check out this grade-by-grade list. I want you to notice something really, really important: the list of concepts your child is expected to grasp by the end of the year is pretty darned short. At the same time, these ideas are pretty robust. The objectives cover less material and fewer facts, but they do so more deeply.

Armed with some information about Common Core, you will be better able to set the parameters around what your child is learning at home. If solving for x is not on that list, don’t expect your child to do it. But if ratios are, it could be helpful for you to brush up on those concepts. (See Wednesday’s post for help on this.) But not so you can walk your child through a process. (Keep reading for more info on that.)

2. Meet the teacher

And at this meeting, don’t get hung up on grades and tests. Ask her what her teaching philosophy is. Ask what she wants you to do to help support your child’s learning. It is very possible that you’re making assumptions about your role. Depending on your child’s age, you might need to offer a great deal of help. Or you might need to back off. Your child’s teacher can tell you for sure.

If your child has math anxiety, this is a great time to share that with the teacher. Sometimes even the best teachers inadvertently send messages to their kids that unnecessarily ups the anxiety. (Some struggle is good; too much can shut down the pathways of critical thinking.) Offering the teacher a little background in your kids’ previous math experiences can be really useful.

3. Trust

This is probably the hardest step, but unless you have really good reason not to, you must trust your child’s teacher. Seriously. In my observation, many parents think they understand everything about teaching, simply because they were once students.* That approach undermines teachers’ authority and ignores their education and expertise. It’s actually pretty insulting in some ways. Just because you can flush a toilet doesn’t mean you are a plumber. The same goes for teaching.

Teachers are not just experts in their field of study (math, Spanish, English, science); they’re experts in pedagogy, which is the practice of teaching. And pedagogy is much more mysterious than trigonometry or set theory.  It’s where the science and art of teaching collide. The way in which topics are introduced and explored in the classroom is a careful dance. Sadly, some of this can be undone at home, during the homework wars.

Unless you believe your child’s teacher is downright incompetent, you’ve got to trust that she knows what she’s doing. Chances are, there’s very good reason she sent home those challenging problems.

*This goes for homeschooling parents, too. Anyone who has been successful with homeschooling will tell you that there’s a lot to learn about pedagogy — from the developmentally appropriate times to introduce certain concepts to proven ways to encourage exploration and discovery.

4. Stop spoonfeeding

Especially when kids enter middle school, we parents need to back off — big time. Yes, we want them to succeed. But what may be even more important is this lesson: failure is a part of learning.

I don’t mean that you should be okay with a failing grade or ignore his bellowing, “I DON’T UNDERSTAND!!’ But at some point (very soon!), you must stop checking his assignments or walking him through each and every problem. You also need to endure his frustration. When children make mistakes, they can learn from them. When they struggle, they learn they can overcome adversity.When you swoop in to rescue your child from struggle and frustration, you are actually depriving him of these important lessons. (If you want your kid to live in your basement, rent-free, after graduation, ignore the above.)

Check with your child’s teacher about the grading process for homework. Will he be expected to get the answers right? Or is the teacher merely expecting an honest effort? If effort is the main theme (and I hope it is!), quit trying to explain to your child how to do the work. Instead, offer support and encouragement. If you believe your child can succeed, he’ll believe it too.

5. Get curious

One of the best ways to get involved with your child’s education is to ask questions. Kids are rarely given an opportunity to verbalize what they understand about math. Curiosity is a is a huge gift you can give your kids. But in case you’re stuck, try keeping these questions in your back pocket for stressful times:

— What do you know about the problem? (Encourages your child to think critically about the information included in the problem.)

— What are you being asked to do? (Prompts the child to identify the question in the problem.)

— If your math teacher were here, what would she say? (Demonstrates an alliance between yourself and the teacher, and gives you information about her expectations.)

— What ideas do you have for solving the problem? (Helps students identify problem-solving techniques, like making a list, guess-and-check, drawing a picture, etc.)

Read through the above questions again. What do you notice about them? Yep, not a one of them has anything to do with getting the answer. Not a single one. And that’s because it’s not your job to find the answer. Your job is to help your child move towards an answer, not solve the problem for him.And with questions like these, you’re helping your child see math as a process, not merely a solution.

This is hard work. Even with my background in math education, I’m struggling with homework histrionics. It is no fun to come home from a long day at work, only to be pulled into an emotional tangle over math. But I will guarantee this: If you’re working with a good teacher and you practice the steps above, your child will learn to feel very confident in his math skills. And he’ll be a much better grownup for it.

What do you think about this advice? Which of these steps are you already practicing? Which do you think are challenging to implement? Are there any that you think are downright wrong? Share your feedback in the comments below. And if you have further questions, ask them!

Categories
Math for Grownups Math for Teachers

Zombie Math!

It’s a special Thursday edition of Math for Grownups, and today we have a guest post from Bon Crowder of Math Four, a great blog that was featured in the Wall Street Journal last month. Here’s her creative take on math and zombies.

Math isn’t only in real life, it’s in our fantasy and fear worlds too!

I’m a huge fan of The Walking Dead – the popular zombie show on AMC that returns October 14.

While watching season two, I started pondering if our heroes even had a chance against the hoards of zombies.

I realized that regardless of how science explains the start of a zombie epidemic, the way it continues and the way to stop it is explained with math.

Zombies make other zombies.

If you’re bitten or otherwise infected by a zombie, you’ll turn into a zombie yourself. Since zombies never sleep, and are constantly on the lookout for human victims, they have the ability to create many more zombies very quickly.

Killing zombies is a chore.

According to The Walking Dead the only way to kill a zombie is by ceasing brain function. In other words: removing or impaling the brain.

That sounds simple enough. But just watch one episode and you’ll see how challenging it can be!

Do we have a chance against a zombie epidemic?

There are around 30 humans in The Walking Dead. Let’s assume that represents reality: there are only 30 humans on the entire planet, and the rest of them have been turned to zombies (or will be soon).

We can do a little math to figure out how long it would take for our 30 heroes to rid the world of this epidemic.

There are a little over 7 billion people in the world. That’s 7,000,000,000. (A whole bunch of zeros, I know.)

Each hero will be responsible for killing about 230 million zombies. That’s 7,000,000,000 zombies ÷ 30 heroes.

(Notice I’m rounding like crazy – a fun thing to do when estimating anything. Including zombie deaths.)

Suppose now that each of our heroes could be expected to live 60 more years.

60 years • 365 days = about 22,000 days of life left.

We can calculate how many zombies each hero must kill per day:

230,000,000 zombies ÷ 22,000 days = over 10,000 zombies each day!

Um… we only have 24 hours in a day. That’s 1,440 minutes or 86,400 seconds. So each hero has to kill one zombie every 8 seconds.

Yipes!

Check out Bon’s blog at MathFour.com.