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## SUMMER

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For most of us, summer has wound down and school is either in session or just around the corner. The time for preventing summer brain drain is over. But you can continue to reinforce math skills with your kids (and even yourself!) no matter what time of year it is. Here are some really neat games, puzzles and books that help:

Rush Hour

As the video below shows, this game looks like it’s for little kids — but it’s not! I became obsessed with Rush Hour a few years ago, and I periodically bring it out to give myself a challenge. Additional cards can be purchased in expansion packages. Kids (and parents) can play alone or challenge one another to see who can get out of the traffic jam quickest! (Ages 8 years old and up, \$19.99, ThinkFun)

Sudoku

If you’ve ever done one of these puzzles, you know that Sudoku doesn’t have much to do with everyday math. But they do reinforce pattern-identification skills, which is critical for basic math skills. These puzzles aren’t limited to numbers, either. For little kids (Kindergarten through first grade), try picture-based Sudoku. Or use a number Sudoku to help your child remember or learn his numbers.

Connect the Dots

For really little kids, this perennial favorite is a great way to reinforce counting numbers. But these puzzles aren’t just for tiny brains. Look for options that count by 2s or 10s or even consecutive prime numbers. Check out Monkeying Around for much more challenging designs.

Set Game

This is an oldie, but a goodie. The idea is to identify a “set” of three cards (from an array of 12 cards), based on four characteristics: color, shape, shading and number. It takes a while to get hang of this, but once players see the similarities and differences in the cards, the game can get really fast. Check out other games made by SET Enterprises. (Ages 8 years old and up, \$12.99, SET Enterprises)

Books by Greg Tang  (Bonus suggestion, which wasn’t a bonus until a kind commenter pointed out that I didn’t count accurately. Oy.)

Featuring an intuitive approach to learning and understanding math, Greg Tang‘s books aren’t contrived stories that have a math lesson. Each page is chock full of problem-solving skills that encourage kids to discover new connections in math. New York Times Bestseller, Grapes of Math centers around a series of math riddles that delve deep into kids understandings of grouping and creative addition processes. His website was just amped up with cool online games, too.

Do you have a favorite game or book that sneaks in some math? Share it in the comments section!

I wrote the following post for Simply Budgeted last August. Given our topic this month, I thought I’d share it as a great example of how parents can extend learning outside the classroom. Enjoy!

You probably find it pretty darned easy to encourage literacy.  In fact, there are countless magazine articles and books and workshops out there on this very subject.  And so all good parents read to their kids every night, play word games with them, give them magnetic letters for the fridge.

But what about math?  If you’re like most parents, the idea of working math into the day probably seems down right daunting.  Scary even.

It’s not as hard as you think, especially if you’re willing to give into your children’s demands for a regular allowance.  Money is an instant math lesson—and can motivate even the most reluctant student (adult or child).

Here’s how:

The Even Split: If you want to use allowance to encourage savings and charitable giving, you’re at least half way there.  One way to do this is to require kids to split their allowance into three equal accounts: spending, saving and giving.  If your five year old gets \$3 per week, \$1 goes in each pot.  But what about the kid who gets \$6 a week?  Or worse, \$10 a week?  Pose these questions, and let your child figure it out.

The lesson: Factoring and division

Percent, Per Week: For a more complex math problem, consider uneven distributions, say 20% spending, 20% giving and 60% saving.  Or encourage your child to put aside a certain percent of savings for a particular goal, like a new iPod.  Or enforce a different distribution around the holidays, when she buys gifts for her friends.  If she can’t do the math, she doesn’t get paid!

The lesson: Percents

Accounting for Savings: If you have a little investor on your hands—and some of us do—show him how to create a simple register for recording his savings and spending.  He’ll get a first-hand look at how his stash can grow (or shrink).

Project Savings: Your child will inevitably want something she can’t afford.  In that situation, help her figure out when she’ll have enough money in savings.  Can she wait that long?  If not, consider giving her a loan, with interest and a regular payment plan.  Show her how the interest is calculated and even help her figure out the total interest on the loan.

The lesson: Using formulas and problem solving

Math may be hard for you, but with a little bit of creativity allowance can help your kids practice their skills—and become a little more savvy with their own money.  Now all you have to do is remember your kids’ payday.

How have you used allowance as an impromptu (or regular) math lesson? Share your stories in the comments section.Save

I remember the first week of my fifth grade year. I had a math worksheet for homework, and I was completely stumped.

“I don’t remember how to do this stuff, Mom.”

“What do you mean?” she said. “It’s just long division!”

Yep, in three blissful months of summer vacation, I had completely forgotten to long divide. My mother, a teacher herself, was shocked. Brain drain can sneak up on even the pros.

Being ready for school is much more than having a new backpack, plenty of No. 2 pencils and a healthy breakfast. Studies show that during the lazy months of summer, all kids suffer from “brain drain” or the loss of learning. In fact, students lose (on average) 2.6 months of mathematical competency in June, July and August. Wow!

I promise: I will not tell any parents that they should be teaching math over the summer. I’m not big on academically based summer camps (unless kids desperately need remediation or love these kinds of activities). I hate the idea of kids being subjected to flash cards or worksheets when they could be playing at the pool or reading a great book.

But I do believe — whole heartedly — that parents can help slow the loss of mathematic comprehension with some really simple and even fun activities.

And that’s what August is about here at Math for Grownups. We’ll focus on parenting, primarily, but I’m guessing that even non-parents can gain some additional understanding from some of the activities I’ll suggest. (No one should feel left out!) I’ll also hit on a variety of grades and ages — from toddlers to college students. And I hope to bring you some Math at Work Monday interviews that will inspire even the most reluctant math student.

But first, I want to know: What are your questions? What kinds of activities are you looking for? What topics are you having trouble helping your kids with? You ask ’em, and I’ll answer ’em — or at least point you in the right direction (perhaps to my posts at MSN.com’s Mom’s Homeroom).

So let’s start easing back into the school mindset — so September is not a shock to anyone’s system!

Each third week of July when I was a kid, my family headed down to Virginia Beach — with around 15 of our closest relatives. Along with sharing a large beach house, each family split the tab, based on the size of each family. No one got stuck with too large a bill and no one got away with a nearly-free vacation. As a child, the process seemed pretty simple, but as an adult, I know there was a lot of thought behind it all.

The problem is that each family was a different size. Mine had six people, while my Aunt Dottie only had two. So it wasn’t fair to add up the costs and simply divide by the number of families. Plus, little kids usually slept on the couch or in a sleeping bag on the floor, and they didn’t eat as much. Why should their parents pay as much?

The key to this system was assigning a share to each person. Adults and teens were one share and kids 12 and under were a half-share. (I think infants were free; they don’t eat much shrimp at all.) Each share covered a place to sleep (or a fraction of the house rental) and food, which went into the kitty. On the first day, we went on a huge grocery store run to purchase all of the food for the week, using money from the kitty. Fresh corn, shrimp and other mid-week food purchases were also taken from the kitty. Any other expenses, like our one dinner out during the week, were covered out-of-pocket. Oh, and Grammy, the matriarch of the family, didn’t pay a dime.

But how did my parents and the other adults come to those shares? I don’t know for sure, but I can guess, based on what my addled brain remembers and what I would do.

There were four families, all of differing sizes. In fact, the family sizes changed from year to year, but let’s look at the last year I went to the beach:

My family: Two adults, two teens and two under 12s or 5 shares

Aunt Barb’s family: One adult, two teens and one under 12 or 3.5 shares

Aunt Dottie’s family: Two adults or 2 shares

Uncle Bud’s family: Two adults, three under 12s or 3.5 shares

That means there were 14 shares in all. Once we figured out the cost of a share, we could find what each family owed. Make sense?

Remember, the costs included the rental and food.  Simple, right? In fact, since the money for the rental was due at different times (some up front and the remaining when we arrived), it makes sense to have two different shares: one for the rental and one for food.  It was the 70s and 80s, but let’s look at today’s costs for this example.

Rental total: \$7,500

Food total: \$1,200

But we can’t just divide by 4 to find the amount owed by each family. Gotta find the cost of each share. Since there were 14 shares in all, just divide.

Rental: \$7,500 ÷ 14 shares = \$535.72 per share

Food: \$1,200 ÷ 14 shares = \$85.72

Note: I intentionally rounded up for very good reason. It’s better to have too much than too little. If I rounded as I normally would (down for any value less than 5 and up for any value greater than 5), the person paying the tab would be short. Not fair!

From there, we can figure out how much each family owes — based on the value of each share (rental and food) and the number of shares per family. All we have to do is multiply. Let’s just look at my family:

Rental: 5 shares • \$535.72 = \$2,678.60

Food: 5 shares • \$85.72 = \$428.60

That means my family spent a total of \$3,107.20 for our week at the beach (not counting travel and other costs). Not a bad deal for a big family!

How has your family split the costs of a big vacation? Did you use a different process? Share your ideas in the comments section.

Lordy, it’s hot. And the heat makes me cranky. When I saw that the temps were creeping up to the 90s and beyond this week, I vowed to stay in the airconditioning. Trust me; it’s best for everyone involved.

So don’t even tell me what the heat index is. I really don’t want to know. But I have always been fascinated with how it is calculated. What are the variables that affect the heat index? Let’s take a look.

The heat index is how it really feels when the humidity is figured in. (Those of you who live in a climate with dry heat have no clue about this. Count yourselves lucky.) When the humidity is high, the heat index goes up, producing a hot, sticky mess that makes my hair frizzy and sours my otherwise lovely temperament.

The thermometer may say 95 degrees Fahrenheit, but if there’s significant humidity, it might feel like it’s 105. But of course meteorologists don’t guess at this number. There’s an actual formula that’s used to find the heat index.

Before we get to that, let’s consider the variables involved. According to the National Oceanic and Atmospheric Administration (NOAA), there are 20 (yes, twenty) variables that are used to calculate the heat index. These range from vapor pressure to the dimensions of a human to ventilation rate to sweating rate (ew). Because most of these are very specific to each person, a mathematical model was used to determine an appropriate range for each. This allows meteorologists to use a (relatively) simple formula for finding the heat index:

HI = -42.379 + 2.04901523T + 10.14333127R – 0.22475541TR – 6.83783(10-3T2) – 5.481717(10-2R2) + 1.22874(10-3T2R) + 8.5282(10-2TR2) – 1.99(10-6T2R2)

Pretty, right? It’s actually not that hard to understand, if you break down the pieces. First, let’s define the variables.

HI = heat index

T = ambient dry bulb temperature (in Fahrenheit)

R = relative humidity (integer percentage)

So there are basically three variables, one being what we are looking for — the heat index. If you were to use this formula, you would need to know two things: the ambient dry bulb temperature (which is merely the ambient temperature as measured by a thermometer) and the relative humidity.

If you put to work the logical part of your brain that notices connections and patterns (yes, you do have one), the math becomes clear. When the temperature and relative humidity go up, so does the heat index. How do you know that? Look at the equation. It’s full of addition and multiplication. In fact, aside from the negative exponents (which actually yield smaller numbers), the equation is based solely on increasing values.

(That is, unless you have negative values for T and R. But in that case, you wouldn’t be figuring the heat index, right? A negative T means a negative air temperature, which is really cold in Fahrenheit. And I’m not sure that relative humidity can be negative at all.)

Now, almost nothing is absolute in weather prediction and measurement, right? And this equation is no exception. As NOAA points out, this equation is created by multiple regression analysis, which means it is not exact. (Basically, in this process, the mathematicians are fitting points to the closest line. Think of a bunch of points on a graph and how you can draw a predictable line or curve that is closest to all of those points.) There is in fact an error of ±1.3 degrees Fahrenheit. But what’s 1.3 degrees when you’re looking at a heat index of 102? Either way, it’s still darned hot.

How do you manage the heat? Do you head inside or hide in a cool, dark place? Share your ideas in the comments section.

I’m on vacation! (Can you tell?) So this week’s schedule is way off. But when I saw that Lee Doyle, owner of BTO Self Serve Yogurt in Colorado had sent along her Math at Work Monday responses, I decided to spend just a few moments during a delicious hotel breakfast of Cheerios and milk to post the interview. Then I’m back in the car, headed to Cincinnati to my cousin’s wedding.

There’s nothing better than a cool treat on a hot summer’s day, and since I was a little girl, the options have expanded exponentially. From popcicles to snowballs (a Maryland-only experience) to frozen yogurt — ice cream isn’t the only sweet, cold treat available. At the Doyle’s Highland Ranch location of BTO Self Serve Yogurt, you can create your own delicious treat. But first, the math:

Can you explain what you do for a living?

I am responsible for creating and making all the yogurt at the shop, buying ingredients for recipes and estimating useage of product and toppings weekly.

When do you use basic math in your job?

I use math all day, everyday. Since I create and follow recipes, I use addition, subtraction, liquid and dry measurements, fractions, estimation, equivalency charts multiplication, division, just about every kind of basic math you can think of. For example, if I am creating a new recipe, I use one cup of our basic yogurt and add a teaspoon or tablespoon of various flavors to come up with a new flavor I like. Then I have to write a recipe using a gallon of basic yogurt, because all our recipes are based on one fluid gallon.

Do you use any technology to help with this math?

When I shop for ingredients, I use a calculator constantly to determine price per ounce to be sure the ingredients are within our pricing guidelines.

How comfortable with math do you feel?

I always liked math and feel very comfortable using it. In high school, I took algebra, trigonometry and solids but did not take calculus.

Do you have questions for Lee and Jack? Ask them in the comments section. And of course stay cool with a sweet treat, like frozen yogurt.

I am not a particularly athletic or physically active person. If given a choice between a hike through the woods or a book and a hammock, the good read always wins out. I start and stop exercise routines at least once a year — usually more. But I do have a bicycle, and once a year, I sit atop that tiny seat and pedal my way through 14 miles of parks in Baltimore.

That was yesterday, and today I’m paying for it, big time. Not only do I have a funny-shaped sunburn on my back (from the one cool exercise shirt that I have), but my legs and feet and rear end are screaming: “What the hell??” Still, I know I’ll do this next year, too. Because it’s the one time a year that it’s worth hoisting three bikes on top of our car and driving 15 minutes away to explore the city parks.

Of course, I think about the math involved. Between birdwatching and listening to my almost 12-year-old complaining, what else is there to do? Here’s what I came up with.

1. I woke up yesterday morning with one thing on my mind: I do not want to spend all day on a bike. But would it be all day? Not likely. So I went to the interwebs to help me estimate the time I’d actually be cycling. Here’s what I found:

For the kind of biking I was about to do, an average speed is about 10 miles per hour. I didn’t even bother with a formula; this information was enough to help me estimate that I’d be pedaling for about 90 minutes or so. (I figured I’m slower than average, we’d have one 5-minute break, and we were biking 14 miles, not 10.)

How did I do with my estimate? Not bad. We pushed off at 9:00 a.m. and were munching hamburgers and hotdogs by 11:45 or so.

2. I once thought that the pedals and brakes and chain were the most important parts of the bike. But it turns out that the seat height has more to do with a comfortable ride than most anything else.

Last year, I spent the first half of the course on a seat that was way, way too low. My thighs were burning by the time we hit the rest spot. Luckily, there was a bike tech there who showed me how to adjust my seat and where. I thought I would fall off the precipitous height when he was done, but the rest of the ride was a breeze, comparatively speaking.

Here’s how it works: The leverage of your pedaling is controlled by the seat height. If your seat is too low, you’ll work way, way too hard to get up even the most modest hill. In other words, when your seat is adjusted properly, you’ll get the most efficient pedal stroke. (And your rectus femoris muscle will thank you.)

There are formulas and online calculators that can help you figure this out. But as a once-a-year biker, I rely on a simple idea. When sitting on my bike, I position my feet at 12:00 and 6:00. If my leg is completely extended in the 6:00 position, my seat is at the correct height.

There’s tons more math in cycling, I’m sure. But as a novice, these little calculations and estimates are enough for me. By next year, I’ll forget how sore I am today — and the trouble it is to get our bikes into the rack — and hit these trails again.

Are you a cycler? What math have you used to help keep your pedaling efficient or manage your rides? Share your ideas in the comments section.

Wait! Isn’t it Monday? Where is Math at Work Monday? It’ll be back, I promise. I had some scheduling problems with some sources, so you may see an interview later this week. Don’t worry!

I grew up a few miles from the Appalachian Trail in Southwest Virginia and my grandparents lived in the Shenandoah Valley, near Big Meadows a popular stop-off for trail hikers. While I’ve never had any inclination to take the entire trail from Georgia to Maine, I have done a few tiny sections — an hour or two hike each.

It’s way too late in the year to start a thru-hike (doing the entire trail), but a section hike would be perfect for a lazy summer day. These are generally less than 5 miles, though you could string together two or more for a weekend adventure. And if you’re nowhere near the Appalachian Trail, just choose another trail to explore.

But how much time should you allot for your hike? This is an important consideration, since it will determine the time you set out (there are no lights on the trail, so once the sun sets, it’s black as pitch) and what you’ll need to bring (food and water are essentials if you’re planning to be gone more than an hour or so).

Experienced hikers can probably gauge how long it will take to hike a given number of miles. But if you’re like me, you don’t have a clue. That’s where pace counting comes in. The length of your stride will tell you how many steps it will take you to go a certain distance. From that, you can get a good estimate of how long it will take you to complete the hike.

To measure the length of your stride, you’ll need two pens, a tape measure and a long hallway or sidewalk. Place one pen at the end of the hallway or sidewalk and stand with your feet together and hells against the pen. Now, walk 10 steps, taking normal strides. After the tenth step, bring your feet together again, and place the second pen behind your heels. Measure the distance between the pens, using the tape measure. Then divide by 10 to find your stride length. Ta-da!

Another method is to estimate your stride based on your height. There’s a simple formula for this, but you’ll first need to have your height converted to centimeters. If you’re a man, multiply your height (in cm) by 0.415; women will multiply by 0.413.

Once you have your stride length, you can use this to estimate the number of strides you’ll take when hiking a particular distance. Let’s say your stride is 28 inches long, and you’re hiking the Chestnut Knobsection in Virginia, which is 2.6 miles round trip. How many steps will you take in that hike?

Ultimately, you’re going to divide the total hike by the length of each stride. But that means you need to have these measurements in the same unit. In other words, you need to convert 2.6 miles to inches. There are 63,360 inches in a mile, so the entire hike is 2.6 • 63,360 or 164,736 inches. Now divide, to find the total number of strides:

164,736 ÷ 28 = 5,883

So on this hike, you’ll be taking a total of 5,883 strides. Still, you don’t know how long the hike will take you, right?

For that step, you need to know how long it takes you to walk a certain number of strides. Let’s go back to the where you found your stride length. If you timed how long it takes you to walk 10 paces, you can easily find the time, right? All you need to do then is use a stopwatch while you take 10 paces. Let’s say that value is 6 seconds. A little bit of math will get you closer to your answer.

First, divide the total paces by 10. Why? Because your time is based on 10 paces, not one.

5,883 ÷ 10 = 588.3

Now multiply this answer by 6 or the number of seconds it takes to walk 10 strides.

588.3 • 6 = 3,529.8

So, it will take you 3,529.8 seconds to hike this section of the trail. It’s probably easier to understand, if you convert this to minutes or hours.

3,529.8 ÷ 60 = 58.83 minutes or just under an hour

Of course this estimate assumes a lot of things: that the terrain is easy to maneuver and that you’re not going to stop to look at the view of Burkes Garden. In other words, you can bet that you’ll be on the trail for longer than an hour, especially if you’re there to metaphorically or literally smell the flowers.

Still, you can use these calculations to estimate the time it will take you to complete any number of hikes. Once you know your stride length and the time it takes for you to walk 10 paces, the math is pretty simple.

What kind of hiking do you love to do? How have you used math to help you plan a hike or other outdoor activity? Share your stories in the comments section.

I grew up in the 70s and 80s with teacher parents and in a small town that I could roam pretty much at will. Summer was both amazing and boring. School was out, and I could stay up late (at least until the sun set). These were the months when we traveled — sometimes on a big trip, but always for a week to Virginia Beach, where we would rent a big house with all of my cousins, and I would get brown as a berry. I remember riding my purple bike with the banana seat and long handlebar streamers. Or spending my days at the pool and nights at the local movie theatre. Instead of canned green beans or tomatoes, we’d have at least three sides of fresh vegetables every night at dinner, and I could pick the raspberries in my yard as I mowed the lawn.

Life was slow and easy in the summer. And that’s exactly what I strive for now. I’m not as tolerant of the heat as I once was, but I’d much rather be barefoot and sleeping with the overhead fan on high. I try to knock off of work a little early each day, and I visit the farmer’s market every single Saturday morning.

So even though it’s not officially summer yet, June is dedicated to the math of summer. I promise not to sap all of the fun out of the most relaxing month of the year, but I will point out the math that is around you — from the vegetable garden to the pool, and from bike riding to watching the temperatures rise. In Math at Work Mondays, you’ll meet summer camp coordinators, a summer sweets maker, a pool manager and more.

A note about kids and math over the summer: I know that some parents worry about their kids losing math skills while on vacation. While this month’s content can certainly be used to keep kids engaged with the math side of their brains, I’ll devote all of August to this important task. And you can always visit me at Mom’s Homeroom, sponsored by Kellog’s Frosted Mini-Wheats on MSN.com, for great advice. (More articles and Q&As are coming soon!)

I hope you’ll join me in exploring the math of summer. If you have questions you’d like to see answered or themes that you’d like me to explore, please drop me a line or comment below. I’m always looking for great ideas to explore.

Meanwhile, enjoy the warmer months. Let’s dive into summer!

Okay, so most parents really do understand how to encourage literacy.  We read signs, the backs of cereal boxes, the comic section and of course classics like Harry Potter and the Deathly Hallows. But injecting a little everyday math into long summer days can be a bit of a challenge.

Good Morning America to the rescue!

In a regular feature, the morning show brings in a “sneaky teacher” to show parents how to continue learning through July and August.  And my good friend and fellow freelance writer, Debbie Abrams Kaplan was featured last week.

It’s a cool video, but unfortunately, I can’t figure out how to embed it.  So just click on the picture below to view it.  It’s worth the extra step!  (Debbie’s kids — and she! — are adorable.)

Happy Friday, ya’ll!