Category: Math for Parents

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Math at Work Monday: Nate the Restoration Hero

Properties that are damaged by fire, water, storms, smoke, or mold require the services of a professional.  This is a job for Nate Dawson, Restoration Hero and President of Sterling Restoration.  Read on to see how he uses math to restore damaged properties back to mint condition.

Can you explain what you do for a living?

Sterling Restoration specializes in emergency repair to real property whether damaged by fire, water, storm, smoke or mold. Sterling Restoration is trusted for high quality and comprehensive cleanup, mitigation, and restoration services for both residential and commercial projects. We are a locally owned company based in Springfield, Ohio serving the Miami Valley and Central Ohio areas. We take pride in knowing that our team of professionals and extensive network of resources have the expertise to return any property to its pre-loss condition as quickly as possible.

When do you use basic math in your job?

Basic math is used in all aspects of our business including our accounting, estimating and production departments. Our accounting department uses it to calculate payroll, receivables, and payables. Our estimators use math more than anyone in our business. During the estimating process for reconstruction, we use square footage formulas (L x W) for calculating materials used, for example:  subfloor framing, roof framing , insulation, drywall, painting, etc.. We use square yard formulas (L x W/9) for calculating vinyl floors and carpet. Basic algebra formulas are used for calculating rafter lengths based on the rise and run of roof slopes.

One of our most interesting uses of basic math, and one I will focus on going forward is with water mitigation (returning a structure to dry standard). Basically, drying a wet building! Once we determine the affected area we then use a cubic footage formula (L x W x H) along with the extent of saturation to know how much dehumidification is needed. Dehumidifiers are rated based upon how many pints of water they are capable of removing from the air within a specific amount of time (AHAM Rating). Therefore, depending on the type of dehumidification used and it’s rating, we are able to determine the number of dehumidifiers we need to dry a structure within the standards of our industry (S-500 ANSI approved standard). We also use the atmospheric readings to determine whether we are creating the desired conditions required to remove water from affected materials and to determine the effectiveness of our equipment. To do this we use the temperature and relative humidity to determine specific humidity (the weight of moisture p/lbs of air) and dew point (the temperature at which water vapor will begin to condense). The formula we use to determine the number of dehumidifiers needed is as follows:

Step 1 – Determine Cubic feet (CF).

Step 2 – CF/Class Factor(a low grain refrigerant dehu has a class factor of 40 in a class two loss) = # of AHAM pints needed.

Step 3  – AHAM points needed/Dehumidifier rating = number of dehumidifiers needed.

I know! It’s starting to sound a little complicated but it is all basic math.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

Absolutely! Even though we are in the building trade we are not in the dark ages. We use the most advanced estimating system designed specifically for the insurance restoration (property repair) business. After in-putting the dimensions into a sketch type format, this system automatically calculates all the square footages, cubic footages, and linear footages. The next step is to add a specific line item. For example, when you add drywall to your estimate  it uses a current square foot price to calculate how much to charge for hanging, taping and finishing the drywall in your project. It will also calculate how many sheets of drywall, how many fasteners are needed , how much drywall tape, and how much joint compound is needed. Finally, it will calculate the material sales tax and any state sales tax on the service.

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

I do not feel it’s a matter of doing my job better. I simply could not perform my job without math! As I stated earlier, we use math in every aspect of our business. I do not feel there are too many moments throughout the day that I am not using some form of math.

What kind of math did you take in high school?

During my high school years I completed algebra and some trigonometry. If I remember correctly, that was all that was offered (yes, I graduated high school 32 years ago). Once leaving high school I furthered my math education in mechanical engineering. In my opinion, the levels of math being taught in high school today are far superior to what was then taught.

Did you like it/feel like you were good at it?

I feel like there are individuals that have an aptitude for math and those who do not. Math will obviously come easy for those who have this aptitude. I would also say that if you are good at something, the chances of enjoying it are far greater than if you are not good. Having said that, I do not believe I had this aptitude. Therefore, I had to work a little harder than others, and, at best, I was average at math. Guess where I’m going with this…no I did not like it.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pick up using the skills you learned in school?

I had to learn how to use the math skills I had already acquired to accomplish the task at hand. For example, if you have the lengths of two sides and the angle of a triangle, you can calculate the length of the third side. It is crazy how much I use this algebraic formula; however, it took some time and experience to learn how many applications this formula has. Having said that, ninety percent of my daily tasks require math learned in high school.

Are you interested in learning more about restoration? Let me know and I will pass your information along to Nate.

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Math at Work Monday Math for Grownups Math for Parents Math for Teachers Math for Writers

Math at Work Monday: Tammy the Purchasing Coordinator

When we purchase a product we do not even think of the processes that have to take place in order for the product to reach our hands.  So much is involved on the back end of things. Tammy Landrum is the purchasing coordinator BSF, Inc., and she understands the entire process including the math.

Can you explain what you do for a living? 

I work in the purchasing department, and I have been in this profession for seven and a half years.  Our company makes pump motor adaptors.  I process all of the purchase orders, and I purchase products from outside sources that are needed to complete the orders we receive.  I schedule shipments and create documents needed by our machinists in order to make the parts and the documents needed by our shipping department to ship the parts.

When do you use basic math in your job?

I use math each day when I send an order acknowledgement to the customer verifying the cost on each order. Sometimes I have to cost the part before I process the order.  Costing involves calculating the cost to manufacture the part during each phase of production and the marking that price up by a certain percentage to produce our profit margin.

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

Yes, I use a computer everyday to input the orders and also to cost the orders. We have a configuration that calculates the price of each part. We quote the part to a customer and they place the order.

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

I would not be able to calculate the total amount due for each order without using math. Also, I could not calculate the price of each part without math.

How comfortable with math do you feel? 

I’m somewhat comfortable with math. I don’t have to do many calculations in my head.  I have a computer for that so I don’t think I would be very comfortable doing my job without my computer.

What kind of math did you take in high school?

I took algebra and basic math.  I liked math a lot. I always did well in my math classes.

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

I had to learn to use the software programs needed to do my job. I think my basic math skills made it easier for  me to learn what I needed to in order to do my job well.

Anything else you want to mention?

Math is important in our everyday lives. We use it more than we realize.

Of course, if you want to learn more about the role of math in the job position of purchasing coordinator, just reach out to me, and I will connect with her.

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Math for Grownups Math for Parents Math for Teachers Math for Writers

Confession: I See Numbers Differently. (And it’s not what you think.)

I’ve shared about this little quirk I have on Facebook and to my friends and family, but this is the first time I’ve ever written it down. And I’ll admit it. I’m a little nervous. Either I’m going to come off looking like a total weirdo or like the adorable, kooky geek that I feel like. I’m hoping it’s the latter, but if it’s the first, please be kind.

Here goes.

I personify numbers.

You read that right. In my mind, the digits 1 through 9 not only have genders and personalities and ages — they have relationships. Yep, there’s a whole nursery book of stories going on in my head when numbers cross my mind. And, strangely enough, great kiddie lit didn’t put this idea in my head.

This phenomenon is called ordinal-linguistic personification. (It has a name!) And a definition: it is the automatic process of assigning personalities to sequential linguistic units–including letters, numbers, months, days and more. This is a subset of the larger condition called synesthesia, in which the senses, words, colors and other incongruous experiences all meld together. Someone with synesthesia might “taste” colors or see bright hues in letters.

Me? I have always known numbers to have personalities. Like for as long as I can remember.

Let me introduce you to the family:

0 is god-like. It has no gender but is recognized as the spiritual guide of all of the other numbers.

1 is male and very passive. He’s middle aged, perhaps the patriarch of the number family.

2 is female and extremely bossy. Married to 1, she is the matriarch of the number family.

3 is male and a loner. He’s somewhat angry, but he generally keeps to himself.

4 is female. She’s sweet and easy to get along with, but she will stand up for herself. Her brother is 3.

5 is female and bossy. She particularly likes to tell 4 what to do, but in a sisterly way.

6 is male and passive. He’s married to 4, who is head over heels in love with him.

7 is male and neutral. Like 3, he’s a bit of a loner, but he’s not angry.

8 is male and friendly. He’s particularly fond of 4 but in a brotherly sort of way.

9 is male and sneaky. He doesn’t get along with anyone but 3.

Multi-digit numbers, like 10 or 99, also have personalities, largely based on the personalities of the single digits. So 99 is super-duper sneaky, while 64 is a really trustworthy, happy number.

It took me years and years to admit that I see numbers this way. When I was in my 20s, my uncle fessed up that he does the same thing. That’s an interesting fact, because synesthesia runs in familiesand is passed down maternally. More women than men have this characteristic, and more lefties than righties. (I’m a righty, by the way, but my uncle is a lefty.)

I also do something like this with calendars. Months and weeks don’t have personalities, but the annual calendar has always followed a very distinct shape in my mind. It’s a wavy kind of oval–almost like the path on the Candy Land game board–made up of large blocks (months) divided into rows (weeks). At any given time of the year, I can immediately call to mind where we are on my visual calendar. This helps me estimate times and remember dates.

Clearly I’m a very visual thinker, eh?

So what does this have to do with math? I have no idea. This quirk doesn’t help me memorize strings of numbers — from telephone numbers to bank PINs — easily at all. And I’m guessing that it hasn’t been particularly helpful in learning some math facts, like multiplication tables. (Is that why I can’t remember that 6 • 7 = 42? Both 6 and 7 are male, but 4 and 2 are female. I don’t know why that doesn’t compute, but there you have it.)

But it has been a boon to my daydreaming. When I’m writing algebraic equations for a curriculum development assignment, the results might end up as little stories, simply based on the numbers I choose. Certainly this is where the math and writing has come together.

So how about you? In your mind, do numbers have personalities? If so, would you be willing to share about it? What do you think of how numbers look to me? Or do you see abstract ideas, like letters or dates, in some similar fashion? I’d really love to hear from you in the comment section. (Please assure me I’m not alone!)

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Math for Grownups Math for Parents Math for Teachers Math for Writers

My Most Embarrassing Professional Moments Have Involved Math

The first email came in at about 2:00 p.m.

600 million divided by 660,000 equals a little over 909.

The next a few moments later.

5.4 billion people is nearly the population of the whole World (estimated at 7 billion in 2012 by USCB)

“Well, shit,” I said aloud. It had happened again.

As part of my virtual book tour for Math for Writers, Linda Formichelli (the original Renegade Writer) had offered me a great chance to reach out to her readers, through her “Monday Motivation” email. I penned a piece called “4 Math Mistakes Writers Make—and How You Can Avoid Them.”

Unfortunately, there were 6 mistakes. Two of them were unintentionally made by little ol’ me. In the whirlwind of my virtual book tour, I had not edited carefully enough. I know what to do; I just didn’t take the time to do it.

Honestly, this is my worst nightmare. If anyone else in the world had made these mistakes, I’d easily reassure them: “Math isn’t life or death! We all make mistakes, and the world still spins. [Tweet this]The thing is to learn from our mistakes and move on.”

Easier said than done, apparently.

I don’t know where I got my math performance anxiety. Perhaps it stems from my strong sense of perfectionism in some areas of my life. I’ve had that trait since childhood, and I see it in my daughter. It’s why I prefer sewing to woodworking — with fabric and thread, I can pull apart mistakes and start again. Wood is not so forgiving.

Regardless, I must want to push through it. Why else would I choose two careers (teaching and writing about math) that put my math mistakes in the spotlight?

Want to share this image? Go right ahead! Just right click, save and share.

When I was a teacher, I had less of a problem with this issue. I told my students very plainly that I would make math errors. They were invited to correct me (nicely), and we would move on. (I had the same rule for spelling, which I really don’t care one whit about.) In the classroom, I saw my public mistakes as a teachable moment. Perfection is not required. Math is difficult, and we all screw up from time to time.

In regards to my most recent public math mistakes, I’m not worried that someone thinks that 600,000,000 ÷ 660,000 = 9 or that a reader went away from my article believing that there are 5.4 billion people in the U.S. I’m worried that these readers lost trust in my ability to teach them something about math. It’s what I tell other writers all the time: If you get the math wrong, your readers can lose faith in you.

But in the end I have to go back to my more gentle self. These mistakes happen — even to big wig mathematicians. (I’m not one of those, by the way.) If you made that mistake, I’d tell you not to worry about it. And in my line of work, I’d better get that message loud and clear. Because this is not the last public math mistake I’ll ever make. Not by a long shot.

When I worried out loud about this yesterday, a dear friend and colleague told me, “Whatever. People love to point out others’ mistakes.” And she is right. It’s not that anyone has been mean about it — none of Linda’s readers were at all. It’s about connecting. I don’t need to feel ashamed or worried. I’m pretty sure Einstein would laugh and tell me to forget about it, too.

Besides, I’m sure I’m not the only writer who is worried about making public math mistakes. Right?

Do you have fears about making math mistakes — in public or elsewhere? Help me feel better, by sharing your story. Please?

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Math for Grownups Math for Parents Math for Writers Other Grownups

Hey, Does This Place Look Different?

If you’re used to a completely different Math for Grownups website, hold up. You’re not in the wrong place. For the last two months (or more?), I’ve been working on a redesign of the site. I wanted something fun, punchy and energizing — kind of how I feel about math. And with my newest book, Math for Writers, hitting Amazon last month, this was a great opportunity.

And it’s not just a new book to celebrate! You’ll notice some really cool additions, plus a few old friends. Here’s a quick run down.

Sections for Writers, Parents, Teachers, and All Grownups

If you fall in one of these categories — and unless you’re a kid, you do! — you can zip right over to see the content I’ve developed just for you. Writers will find great ways to develop their craft and manage their writing. Parents will find tips for growing math-confident kids — without losing their minds. Teachers will find resources they can share with parents and students, including the answer to the age-old question: “When will I ever use this stuff?” At the same time, everyone can learn how math can help us make smarter financial decisions, save time and think about math in a completely different way.

OMG, Quizzes!

I can’t tell you how excited I am to introduce original, interactive quizzes. But before you freak out: There is no timer. There are no grades. No one has to know how you did. And that’s exactly how I wanted it. My goals are pretty simple: Show you what kids are learning at various grade levels, and give you a chance to see what you remember (or don’t). I’ll be adding quizzes over time — hopefully one a week or so. And I’ll add some non-math quizzes too, like “Are You REALLY Math Anxious?”

Coming Soon: Online Learning

If reading a blog or a book is not enough for you, I’m gearing up to offer some very targeted online learning. First up will be courses designed just for writers. Over time, I’ll add courses for parents and others. Through Facebook groups, webinars and “homework,” you’ll have a chance to take a deeper dive into the math that you need — but can’t quite grasp. These aren’t college courses, and you won’t be graded on your assignments. The idea is to give you a little special attention, so you can ask specific questions, gain some confidence and learn a few things. Stay tuned!

Math at Work Monday Is Back!

I know that this is a very popular feature on Math for Grownups, and I’ve got a whole series of greatMath at Work Monday interviews lined up. You’ll meet recycling truck drivers and cancer radiology specialists. And if you have a suggestion of someone I should interview, send me a note. I’m always looking for fresh ideas!

Take a look around. Read my new Math for Grownups Manifesto. And let me know what you think. I’m really looking forward to injecting even more energy into math.

Oh, and if you haven’t received my free gift for you, don’t miss out. Just sign up in the bright yellow box to the right, and you’ll get a free copy of Multiply Your Math Moxie: A Painless Guide to Overcoming Math Anxiety. Get comfortable with math, once and for all.

Enjoy!

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Holidays Math for Grownups Math for Parents Math for Teachers Math for Writers

Happy Valentines Day!

valentines day

I couldn’t resist sharing this happy little math gif. Mathematically speaking, it makes no sense, but it’s still sweet.

Happy Valentines Day!

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Ask a Math Teacher

What Does “Hundreds” Mean?

Welcome to the first edition of Ask a Math Teacher, which will feature real, live math questions from real, live people. How often will I do this? As often as I can. What kinds of questions can you expect? Whatever people ask. If you have a question, please post it to the Math for Grownups Facebookpage (after clicking “like” of course!) or email me at lelaing-at-gmail-com.

Today’s question comes from my friend and cookbook author, Debbie Koenig. You really should check out her blog and book, Parents Need to Eat Too. Debbie posted this question on Facebook, which led to a two-day long post-a-thon. We finally got to the root of the question — and answer — and I thought you would like to hear about it.

My son’s math homework has me scratching my head–he’s supposed to “Draw a picture of 600 hundreds” in a space that’s maybe an inch and a half high. How does one draw 600 of anything in that small a space? And why is he drawing 600 of something? I have no idea how to help him. 

One thing that isn’t clear in this question is that her son is in second grade. This is a really important piece of information, because the answer is going to seem completely counter-intuitive to us grownups.

Some background: When children learn their numbers and then learn to count and then learn to write 3s, 7s and 4s (sometimes backwards), they are picking up teeny-tiny bits of number sense. When all of this information is put together, we call that numeracy. You can think of numeracy like literacy. It’s not just being able to count or add; it’s being able to understand how numbers work together in a much larger sense. As you can imagine, this is a big, hairy deal. It takes years and years to get to where we adults are. And most of us grownups take for granted the numeracy that we do have.

I say this because what this “hundreds” thing is getting at is place value, or the position of a digit in a number. Teachers can just tell students that the 4 in 9433 is in the tens place, or — and this is a muchbetter idea — students can learn a great deal more about numbers by really exploring this concept.

You see, place value is not some random construct. There are reasons that the first place to the right of a decimal is the ones place and the fourth place to the right of the decimal is the thousands place. Exploring this can help kids get better at multiplying or dividing and lay the foundation for decimals and even percentages.

So with that said, the first thing to do is ignore what you think hundreds means. Unless you’ve had some experience in math education, you’re probably not going to take the right guess. In second-grade math class, hundreds does not mean one hundred. It means the hundreds place.

The easiest way to get into this is by looking at a hundreds chart.

If you have one of these hundred charts, you have 100, right? How can you represent 600 then? I’ll give you a second to think about it…

Yep, with six of these buggers! Here’s a visual representation without the numbers:

So what Debbie’s son was being asked to do was draw something like the above. It’s important because it has to do with place value. Only most second graders don’t have a clue about that stuff yet. And what they have learned so far sounds like a big mistake to the rest of us — because the language being used is not what we expect. He’ll learn the word “place value” in due time and forget about these hundreds tiles and charts and suchlike.

Asking students to draw “600 hundreds” is helping students visualize place value and other important concepts. Teachers call these manipulatives, especially because they’re often real objects that students can pick up and move around. But on a homework worksheet, they’re a little harder to translate, especially for a parent who went to elementary school more than a few years ago.

So that’s the story of “hundreds,” at least as far as a second grader is concerned. I’d love to hear your thoughts! Do you know of other ways to get to the basics of place value? Do you, personally, think of place value differently? Share in the comments section.

P.S. I’m going to be speaking to parents of elementary-aged kids at my daughter’s school later this month. If you have questions that you think I should address, feel free to shoot me a quick note or post on the Math For Grownups Facebook Page. And if your school — in the D.C.-Baltimore area — would like to have me come down for a Math Chat, let me know. I’d love to meet you!

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

Five Cool Math Tricks You Didn’t Know

When it comes to basic calculations, kids can benefit from knowing math facts cold. When the arithmetic is simple, we can focus on more complex concepts.

That’s one reason your children are encouraged to memorize their multiplication tables. But over the years, educators have discovered that straight memorization is not always the best. In fact, when kids spend a great deal of time really unpacking what these math concepts mean, they’re far more likely to expand their understanding of many other concepts.

So are math “tricks” a good thing or a bad thing?

“Kids should have a way of figuring out the math fact that uses reasoning,” says Dr. Felice Shore, assistant professor and co-assistant chairperson of Towson University’s math department in Maryland. As an expert in mathematics education, Shore knows that when children’s natural curiosity is stimulated, they can make important mathematical connections that will deepen their understanding.

“But once kids can reason their way to the answer and understand various ways to do so, these ‘tricks’ can help them get answers quickly,” she continues.

The key is to introduce these tricks at the right age.

“I don’t think the third or even fourth-graders should learn tricks,” Shore says. “The important mathematics at those grades is still about building an understanding of relationships between numbers—the very reasons behind math facts. Once you show them the trick, it’ll most likely just shut down their thinking.”

But math tricks can be useful. If your fifth grader is still struggling with her multiplication tables, these can be a godsend. Even better is when they reveal something about the math that makes them work.

If you’re going to show your child a quick way to multiply, make sure that you help her understand why the trick works. Here are five cool examples—and the math behind them.

[laurabooks]

Multiplying by 4

This trick is so simple and logical, that it could hardly be called a trick. But it could come in handy for your budding Sir Isaac Newton. To multiply any number by 4, simply multiply it by 2 and then double the answer.

35 x 4
35 x 2 = 70
70 x 2 = 140
35 x 4 = 140

Why does it work?

This trick is based on a very simple fact:

2 x 2 = 4

That means that:

35 x 4 = 35 x (2 x 2)

And

35 x 2 x 2
70 x 2
140

The underlying lesson of this “trick” is that you can solve a multiplication problem by multiplying by its factors.

Multiplying by 9

Hold up both hands, with your fingers spread. To multiply 4 x 9, bend your fourth finger from the left. Count the number of fingers to the left of your bent finger—you should get 3. Then count the number of fingers (and thumbs) to the right of your bent finger—you should get 6. The answer is 36. This works when multiplying any number 1-10 by 9.

Why does it work?

Simple algebra can show that what you’re doing with your fingers boils down to this: When you multiply by 9, you’re really multiplying by 10 and then subtracting that number. But you don’t need to do the algebra. Some kids figure out that reasoning without the mysterious finger trick.

You can help your child extend her understanding of the number 9 by pointing out an important piece of this trick: in the 9s multiplication tables, the digits add up to 9!

4 x 9 = 36   —>   3 + 6 = 9

9 x 9 = 81   —>  8 + 1 = 9

Then you can prompt your child to notice other patterns. For example, 4 -1 = 3 and 3 + 6 = 9 and 4 x 9 = 36. The patterns in the 9s multiplication tables are endless and can lead to many other discoveries about numbers.

Multiplying by 11

Sure, multiplying a one-digit number by 11 is a cinch.

4 x 11 = 44
7 x 11 = 77

But did you know there’s a trick to multiplying any number by 11?  Here’s how using an example: 52 x 11.

The first digit of the answer will be 5 and the last digit of the answer will be 2. To get the digit between, just add 5 and 2.

5 (5+2) 2
572

You may have noticed that when you add the two digits together, you get a one-digit number. If you get a two-digit number, things are a little trickier.

87 x 11
8 (8+7) 7
8 (15) 7
(8+1) 57
957

Why does it work?

If you think of doing long-hand multiplication by stacking the two numbers, you’ll see right away:

But the more precise reasoning has to do with place value. What you’re really doing is multiplying 87 by 1, then multiply 87 by 10, and finally adding the two products together:

87 x 1 = 87
87 x 10 = 870
870 + 87 = 957

The trick itself is just a shortcut to the answer.

Multiplying by 12

Just like the previous track, you can multiply any number by 12 very quickly and easily. Let’s try it with 7 x 12.

First multiply 7 by 10. Then multiply 7 by 2. Finally, add them together.

7 x 12
7 x 10 = 70
7 x 2 = 14
70 + 14 = 84

Easy peasy. When this gets really impressive is with larger numbers.

25 x 12
25 x 10 = 250
25 x 2 = 50
250 x 50 = 300

Why does it work?

This trick works for the same reason that the 11s trick works. But there’s another way to describe it. Think of 12 as the sum of 10 and 2.

25 x 12
25 x (10 + 2)
(25 x 10) + (25 x 2)
250 + 50
300

Is a number divisible by 3? (Or in math terms: Is a number a multiple of 3?)

When a number is evenly divisible by another number it is said to be a multiple of that number. In other words: since 27 is evenly divisible by 3, 27 is a multiple of 3.

Turns out, there’s a nice little trick for this as well. Add up the values of the digits. Is that sum a multiple of 3? If so, the number itself is also evenly divisible by 3. Check it out:

Is 543 divisible by 3?
5 + 4 + 3 = 12
12 is divisible by 3
So 543 is divisible by 3

Why does this work?

Place value is key here, but there’s an easy way to show your child what’s happening before you even introduce the trick. Do this with something tangible, like M&Ms or pieces of cereal.

  1. Start with 45 candies.
  2. Have your child divide the candies into two piles based on the place value—one pile of 40 candies and one pile of 5 candies.
  3. Now ask your child to divide the 40 candies into groups of 10 candies. (She should notice that there are four groups of 10 candies.)
  4. Now ask her this question, “How can you change each of these groups often, so that the number is divisible by 3?” She should suggest that you take away one candy from each pile. (If not, coax her to that answer.)
  5. Have her take one candy from each group of ten and move them into another group.
  6. Point out that she has six piles of candies: four piles of 9 candies, one pile of 4 candies and one pile of 5 candies.
  7. Ask her what happens if she combines the pile of 4 candies and the pile of 5 candies. She should notice that she’ll get 9, which is divisible by 3.
  8. By now, she will probably notice that the 4 and 5 come from number 45. See if she can come up with the trick, after doing this with a few examples using the candies.

So what do you think? Are math tricks a good idea or not? Do you have any other tricks to share? And can you explain why they work? If you need help with your math, I have written these great books to help you learn the easy way.

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Math Education Math for Parents Math for Teachers

Lowering Homework Stress: 5 Easy Steps for Parents

Last week, I shared some unpopular opinions about homework. Mostly, here and on Facebook, people disagreed with me that three hours of meaningful homework was not too much. And looking back at that statement — which wasn’t exactly what I said — I see their point. Do I want my kid to be focused on academics for a full 10 hours a day? (Assuming that for those seven hours of school, she’s being taught.) When it’s put in those black-and-white terms, no, I don’t think that’s reasonable. Nor do I think the debate is all that black and white.

Regardless, parents all over the interwebs are pissed off about the amount of homework our kids are assigned. Their complaints range from the truly anguished (“I tried for two hours to help my son with his math homework, but with his learning differences, I just can’t get him to understand!”) to the kind of petty (“Having to sign a reading log is busy work — for me!”). It got me wondering, what do we do to lower this stress, for parents and students?

So I came up with some ideas. Try them out at home, and let me know how it works for you. And if you have your own ideas, please share them!

1. Reset the Priorities

What is the point of homework? Is it meant to help kids practice what they’ve learned? Extend lessons from class? Finish up something that didn’t get done in school? Complete a long-term project from start to finish? Torture you and your kid?

If you know what you want your kid to get out of homework, you can better set the parameters. See, this is your kid, not the school’s. What you want your kid to get out of his or her education matters. A lot. Once you know your homework philosophy, find out what the school and teachers think. (They might feel differently from one another.)

Then you’ve got to decide what hill to die on. If getting the right answer is a big deal for your kid’s math teacher but a conceptual understanding is what you value, someone’s going to have to compromise. For example, I’ve told my kid that I don’t believe timed math drills are useful tools. (And that’s backed up by research, y’all.) We agreed that if her grade was negatively affected by them, I would go in and talk to the teacher. Stress was instantly lowered. If signing a reading log is arduous for you, give your child that responsibility. Or decide that you’re not going to figure everything down to the minute and shoot for an estimate instead.

When the stress gets high, go back to those priorities. Talk to teachers about assignments that don’t meet your homework priorities. And if necessary, allow your kid to blow off things that are not meaningful. (Yes, I just said that.)

2. Set a Flexible Homework Routine

Whatever this schedule is, it needs to work with your family. Kids who go to aftercare may finish up their assignments before they get home. (At my daughter’s school, that’s a requirement for most assignments and students.) Other kids may come straight home, have a snack and shoot some hoops before hitting the books. Still others may not start homework until after dinner or even get up super early in the morning to finish an assignment.

Most kids really do count on structure, and it’s important that they know what to expect. At the same time, the schedule should be flexible enough to make room for everyday life — like a good cry after a fight with a friend or a quick trip to the ice cream shop for an after-school treat. When they know they can “break the rules” from time to time, they’re less likely to test their parents all of the time.

It’s also important to pay attention to how the schedule is working out — especially from year to year. My daughter used start her homework as soon as she walked in the door. But when she got a little older, it was apparent that she needed 30 minutes or so to unwind, to do something that had nothing to do with school. Of course, as kids enter middle and high school, this schedule should be their own.

3. STOP Reteaching

I can’t emphasize this enough. Stop it. Right. Now.

You are not the teacher. When you reteach, not only do you risk making your kid furious and even more frustrated with the work, you risk confusing your kid. Big time.

There is a reason that long division is going the way of the dodo bird. There is a reason that teachers introduce algebra in earlier grades. There is a reason that kids learn how to find the least common multiple before they learn to add fractions. And you might not know what those reasons are.

I would never attempt to perform brain surgery on my kid. I wouldn’t try to fix the hybrid system on my car. That’s because I’m not trained to do these things. And while many parents do an amazing job homeschooling their kids, mostly, they’re achieving this with the whole picture — and a lot of professionally developed resources.

This is probably the hardest step. It also holds the most promise for lowering stress. I promise.

4. Ask Questions, Don’t Give Answers

Want to know how to accomplish the last step? It’s pretty simple, actually. When your kid says, “I don’t know how to do this!” respond with a question.

“What does the assignment say?”
“Can you explain to me what the teacher asked for?”
“What is confusing you?”
“How can I help you figure it out?”

This puts the responsibility back onto your kid — where it belongs — without taking on any of her stress. Keep asking questions, even if she can’t answer them. Don’t solve the problems for her, but look for her to find her own solutions.

5. Let Your Kid Fail

Kids learn from making mistakes. We don’t do them any favors by preventing them from failure.

I’d rather my kid fail a homework assignment than a test and a test than a grade. And I’d rather my kid fail at something when she’s 10 years old than when she’s 40 years old. Failure at a young age won’t keep her from experiencing later failures. But she will learn from those little failures.

For that reason, you should quit checking your kids’ homework for accuracy. Heck, when they get to be in middle school, you should probably stop checking to see if their homework is done. Give them the right structure for success — space and time to complete homework assignments, little reminders, etc. — but let them chart their own way. (My friend and colleague, Denise Schipani calls this African-Violet Parenting. I call it parenting by benign neglect.)

So there you have it, five steps for lowering the homework stress in your house. I can’t promise that you’ll never have another fight with your kid, but I can say that following these steps will help you keep your cool.

Do you have other suggestions? Share them in the comments section. 

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Math Education Math for Parents Math for Teachers

The Homework Wars: What matters? What doesn’t?

Last week, I heard from many friends and colleagues about Karl Taro Greenwood’s Atlantic.com piece, “My Daughter’s Homework Is Killing Me.”

“Amen!”

“I could have written this!”

“When are teachers going to learn that they’re piling on way too much???”

It was clear to me that the emotion of this piece resonated. But really what I think is this: Mr. Greenwood is probably a very nice man, but he comes off like a whiney, know-it-all parent. And he’s worried about the wrong damned things.

If you read Greenwood’s story, you know he’s worried that his daughter is getting too much homework. At the tender age of 13 years, she wasn’t able to fall asleep until after midnight, because of her homework load. He admitted that bias up front, and decided to see for himself. He took on his daughter’s assignments for a full week.

But really, what he should be paying attention to is the kind of homework his kids are doing.

At the same time, I can compeltely identify with his frustration about his kid’s bedtime. My kid often goes to sleep after midnight. She spends way too much time on homework, but I can say without hesitation that the fault lies with her, because her routine looks something like this: text friends, try to find her worksheet, text, check out when the new episodes of New Girl are coming on Netflix, text, do three math problems, text, find a new Pandora station on her phone, read her library book, finish her math, start science… well, you get the picture. By 10:00 p.m., she’s an anxious mess sometimes.

Her homework load is not too much. It’s generally between one and three hours each night, depending on how much she’s procrastinated on her weekly projects/assignments. (That is, if she actually gets to work, instead of goofing off.)

Greenwood’s daughter averages about three hours. Yes, that’s a lot. But if she’s staying up so late, it’s because she’s not getting started until 8:00 p.m.. (He never says why.) That’s a full five hours after my kid gets out of school, and even with her three-times-a-week soccer practice, it’s way, way later than she usually gets started.

But the thing that bothers me the most is what Greenwood writes here:

The Spanish, however, presents a completely different challenge. Here, Esmee shows me that we have to memorize the conjugations of the future tense of regular and irregular verbs, and she slides me a sheet with tener, tendré,tendrás, tendrá, tendremos, etc., multiplied by dozens of verbs. My daughter has done a commendable job memorizing the conjugations. But when I ask her what the verb tener means (“to have,” if I recall), she repeats, “Memorization, not rationalization.”

She doesn’t know what the words mean.

Shocking. Certainly, each subject requires a little bit of “fake it ’til you make it,” but not to know what the verb means is pretty amazing. And the fact that his daughter has so completely internalized the message “memorization, not rationalization” is truly tragic. That message goes against any educational philosophy I was taught at university.

At the same time, the author is incredibly proud of his (and his daughter’s) ability to pick up on the patterns presented by combining like terms in algebraic expressions. He whizzes right through those problems (none of the math homework is excessive, in my opinion), but has he merely memorized or is he really understanding what the process means? I could be wrong, but my guess is that he might have trouble explaining why the process works.

In other words, critical thinking is important in Spanish, science and literature, but really thinking through the whys of math? Nah, it’s way better to finish those problems as quickly as possible.

Easy homework = good homework?

The homework wars will never end. And that’s because when we all get home from work and school, no one wants the fight that ensues. We want to play board games or curl up on the couch and watch stupid television or read books that weren’t assigned to us.

But if teachers assigned homework that really mattered, would parents still be upset? If teachers asked kids to answer the hard questions, like “How did you get your answer?” or “Ask a family relative about his or her experience with immigration,” would we revolt, because that’s hard too? When schools are serious about rigor, do parents retaliate?

Homework shouldn’t be busy work. But I still believe that there’s real value to asking students to practice what they’ve learned or make some connections on their own. When we parents approach this in a positive way, we have an opportunity to teach our children than learning doesn’t stop at 2:50 p.m. or when we graduate from college.

What would happen if we sent our kids a positive message about their homework? (While working against excessive or stupid assignments, of course.)

This afternoon, my kid walked home from soccer practice, grabbed a snack and ran up to her room shouting, “I’m going to work on my science essay!” I don’t think this thing is due  until the beginning of next month. I didn’t have anything to do with her being excited to get to work. I also didn’t get in her way. She likes this assignment — probably because it’s challenging — and she’s happy to do it.

I’d say that one step in that direction is a little less whining, and a little more listening to kids and teachers.

P.S. Greenwood had lots of reasons to be ticked off about his kid’s school, starting with the lousy parent-teacher conferences. I don’t mean to suggest that he was off-base with everything.

P.P.S. Atlantic also had a great piece from a teacher, who is reassessing her practice of giving homework. I thought her reasons and concerns were compelling. Parents should read that piece as well: Should I Stop Assigning Homework? by Jessica Lahey.

What do you think about the homework your kid is getting? Homeschooling parents, what’s your take on the homework wars?

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For the Love of Math

Last Friday, my family adopted a sweet, little poodle puppy, named Zipper. The foster mother, Sally, had brought him from a Mexico shelter to her own home in Silver Springs, Md. During the home visit on Friday, we talked about our careers, and I mentioned that I write about math. That’s when she told me about her neighbor, the mathematician and novelist.

“You two should meet!” she said. Apparently, we have some of the same ideas about math.

Well, I did “meet” Manil Suri today, via the pages of the New York Times op-ed section. His excellent piece, “How to Fall in Love with Math” points out some ideas I’ve been extolling for years — along with a couple that I might have said were hogwash a couple of weeks ago.

As a mathematician, I can attest that my field is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall.

Yes, yes, and again I say, yes! Mathematics is not exclusively about numbers. Hell, arithmetic is only a teeny-tiny fraction of what mathematics really is. Mathematics is the language of science. It’s a set of systems that allow us to categorize things, so that we can better understand the world around us.

Math is a philosophy, which I guess is what makes us math geeks really different from the folks who are merely satisfied with knowing how to reconcile their accounting systems or calculate the mileage they’re getting in their car. We mathy folks are truly interested in the ideas behind math — not just the numbers.

Last week, I attended a marketing intensive, a workshop during which I outlined my current career and explored how I want to take things to the next level. I’m ready to think bigger, and I need a plan to get me there.

The other entrepreneurs there thought there was real value in my creating a coaching service for entrepreneurs. My services would center around the numbers that these folks need to make their businesses survive and thrive. Marketing numbers, sales numbers, accounting numbers. They resisted the word “math” and advised me to really underscore the numbers.

From a purely marketing standpoint, I completely get it. I don’t have so much of a math wedgie that I can’t understand that the word “numbers” may be less threatening than “math.” So why not just go for it?

But the entire process left me thinking about what it is that draws me to mathematics. And ultimately what will drive me in a career, what moves me to get up in the morning and say, “Let’s go!” If you’ve been around here long, you know that it ain’t the numbers, sisters and brothers.

At the same time, I can’t say that I love math. But maybe that’s semantics, too. For the last two years, I’ve said that I’m attracted to how people process mathematics. But isn’t that just philosophy? So, isn’t that just math? This is what Suri had to say:

Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate. One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being able to use it to solve scientific or engineering problems.

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”

At first, I disagreed with Suri’s thesis that math is worth loving — for math’s sake alone. But his analogy here is right on target. I couldn’t paint my way out of a paper bag, but each and every time I see “Starry, Starry Night” at MOMA, I catch my breath.

We come back to a failure to educate, as Suri so wonderfully elucidates in his piece. When we allow people who hate — or don’t appreciate — math to teach the subject, well, does anyone think that’s a good plan?

At any rate, I hope you’ll take a look at Suri’s piece. Meantime, I’m going to reach out to him to share my appreciation of math. Maybe there is a way — beyond teaching — for me to make a living as a math evangelist.

What do you think? Do you notice a difference between mathematics and numbers? Have you changed your mind about math in recent years or month? Please share!

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Dear Math Teacher

I’ve been talking with grownups about math for more than three years now. Parents, 20-somethings, writers, DIYers, seniors… they all have something in common: a piss-poor relationship with math.

This bad attitude is probably your fault.

The stories I hear — over and over and over again — all point to a major breakdown in the educational system. Sure, we can blame standardized testing or the state standards themselves. Middle school teachers can blame elementary school teachers. High school teachers can blame middle school teachers. College professors can blame high school teachers. And by all means, let’s not leave out the parents.

But you, dear math teacher, have control over only one thing: yourself. So what are you going to do about it? Here are some ideas.

Be Nice

If I hear one more math teacher opining about how dumb his students are, I think I might scream. Why do people teach, if they don’t like their students enough to be nice to them? Your students aren’t dumb. They’re uneducated. And guess whose job it is to educate them? If they come to your class unprepared, tough noogies. You get the kids you get. You were hired to overcome those obstacles. That’s the job, and if you can’t deal with it, perhaps this isn’t the right profession for you.

Don’ take your frustrations out on your students. Quit talking down to them. Quit berating them in public. Quit rolling your eyes or slamming doors. Be a grownup. They’re kids, and they respond to kindness and respect. Give it to them, and you’ll likely see motivation.

Inspire

You don’t have to be Martin Luther King, Jr. or Oprah. But lose the this-is-good-for-you-so-do-what-I-say attitude. It doesn’t work.

Look, you teach math for some important, personal reason. What is it that motivates you? Dig deep, find that thing, and share it with your students. Go for that spark every single day. It’ll make you feel better and get your students motivated.

It’ll also make your job MUCH easier. An inspired kid will work, will stop playing around when you ask her to, will make deeper connections. An inspired kid will meet you halfway. This gives you more energy to devote to that kid who is still messing around in the back of the room or who is ready for the next unit before the rest of the class. Inspiration means autonomous learning.

Teach Students, Not Math

Wait, did you actually think you were going to teach math? Sorry, but that’s not the job. Math teachers don’t get to immerse themselves in math all day long. Nope, your job is to teach kids. Whiny, pain-in-the-butt kids who are more interested in last night’s episode of Pretty Little Liars than their upcoming geometry test. BECAUSE THEY’RE KIDS!

Whether you like it or not, most of your students don’t give a flying flip what x is. Most adults don’t care either. You want your students to learn math? Recognize each and every student as a person, not a container to be filled with math facts. Let them experience the subject for themselves. Let them teach you.

The most effective teachers have students who will follow them to the ends of the earth. And that’s no accident. Students of all ages can spot a bullshitter in two seconds flat. They yearn for genuine relationships with adults. You give them that when you recognize that math isn’t the be-all-end-all of their day. You give them that when you see them as a whole person, not just a math student.

Be Real, But Not Too Real

Having a bad day? Own it. Frustrated with how things are going? Take responsibility. All classrooms — even the most traditional — are two-way streets. When you are real with your students, they’ll be real with you.

But expect to get some pretty raw stuff in return. Kids can’t act like adults, because — guess what? — they aren’t gown up yet. You’re modeling for them every, single day what it’s like to be a grownup. When you react to their realness with childish behavior, well, that’s a pretty strong message.

And for goodness sakes, draw some lines. Sure, you hate standardized testing. (What teacher doesn’t?) But really, do you need to share that ad nauseam with your students? Heck, you might have tremendous disdain for how administrators are running the place, but keep your trap shut on that subject. These kids aren’t your friends. And again — they’re not grownups.

Notice something? There’s not a single number, mathematical concept or teaching strategy in the above advice. I really believe this from the bottom of my heart: It’s not about the math. It’s about how you relate to your students. Every.single.time. You have way, way more power than you can even fathom. Your students carry the messages you send to them — throughout their lives. Try it. Ask five friends about their math education. I guarantee that four of them will have detailed, sad stories about why they hate math.

You have a chance to turn this around for thousands of students. And honestly, if you’re not up to the task, get out of the freaking way. Let someone else do it. Because you can do a hell of a lot more damage to one student than a kid could ever do to you.

Sincerely,

Laura Laing (informal therapist to math-haters of all ages)