I’ve got a bachelor’s degree in advanced math, and a 12-year-old daughter who hates anything to do with the subject.

I’m an unschooling mama who loves to do math puzzles and logic problems for fun.

I’m not sure if that combination makes me an expert or just crazy, but because of it, I agreed to take part in the iHomeschool Network’s “5 days of…” series this week with a look at 5 days of real-world math.

Today, we’ll look at three types of math you need to play sports and do other fun stuff.

Work your angles: Geometry in bowling, billiards, building and more

Almost any sport with a ball works based on angles.

In baseball, it’s easier to hit a home run to either right or left field than it is to the center, because, with the shape of the field, the distance you need to hit the ball is shorter. In bowling, if you tip a pin more than 13 degrees to either side, it will fall; that’s called the “topple angle.” In billiards, of course the entire game is dependent on the angle at which you hit the cue, and the angle at which the ball you’re aiming for hits the edges of the table.

Meanwhile, almost anything fun to build requires solid shapes and angles.

Whether you’re working with Legos, blocks, K’nex, stacking cups, houses of cards or whatever, you’ll soon realize what foundations make for strong structures and which end up falling over.

You will probably never in your real life get out a protractor and measure angles. However, if you’re conscious of it, you’ll be able to spot a lot of math, especially geometry, in your favorite sports, and you can pretty intuitively develop the knowledge that right angles are sturdy, that hitting EXACTLY on the head pin in bowling is actually worse than hitting it just slightly to one side, that you can change the angle at which the baseball flies by hitting it with the early or late part of your swing.

Where to start: If you have a Wii video-game system, play Wii Sports. A lot. I’m not kidding; this is the way we’ve worked on angles in everything from golf to bowling to baseball.

You will be amazed at what you – and your children of all ages – will pick up from that.

Barring the Wii, watch sports. Watch them in person, watch them on TV, watch them online. If you can, PLAY sports. You don’t need to play them in an organized fashion for this. Go to a tennis court and hit the balls around, and talk about what you notice about the angle at which the ball flies depending on the angle of your racket.

Play an “angle bounce” game. Have one person stand against the garage door or another large wall, and have someone else stand several feet away; mark that person’s starting spot with an X, and from there, have that person throw a ball at the door. (NOT into the person standing there, though!)

The person standing near the door should try to put their hand near where they saw the ball hit the door, and the person who threw the ball should go try to put their foot where the ball bounces back. It’s a goofy game – you’ll both be running around like crazy – but if your thrower starts at the X each time, you’ll get a feel for all the different ways things bounce and angles and all.

For kids who actually play sports like baseball or soccer, videotape their practices and see if you can point out any “angles” they can work to change their game. Watch videos of professionals, too, and notice their angles!

Finally, build stuff. Build with blocks or Legos or plastic cups or playing cards, and experiment to see if you can find shapes that allow you to build taller or stronger.

There’s no right or wrong answer here, but for any age, this is a fun way to see geometry in action.

Go, speed racer: Physics in your favorite sports

Right up there with geometry in terms of “stuff you really use” is physics. Stuff moves. It moves the way it does for a reason. That’s physics at its simplest.

Much like with angles, most sports played with a ball incorporate a heavy dose of physics. Why is it harder to sink a close shot in basketball than a medium-distance one? When is the pitch FASTEST in baseball – when it leaves the pitcher’s hand, or when it connects with the bat? (That’s a trick question – it’s actually technically a complete stop, zero on the acceleration scale, for the split second when it hits the bat, before it starts moving in the other direction.)

Where to start: You can certainly get a great dose of physics by watching NASCAR – or any other kind of race. Watch the runners – or any other athletes – in the summer Olympics. Talk about what they’re doing, and guess why (then do some research to check your guesses.)

If you’re interested in baseball, one of my favorite sites, Exploratorium (remember them from the recipe conversions?) offers a great “science of baseball” page here. They’ve also got a great collection of “sports science” resources overall here.

Real-world physics is perhaps the easiest type of math to experiment with. Drop stuff. Race Matchbox cars. Race marbles down ramps of different sizes. You can make some incredibly complex experiments with multiple variables for older kids, or you can do real neat “drop different-sized balls and see which one hits first” experiments with younger kids.

Mostly, keep an eye on all the movement around you. This becomes important later in life when you drive a car. I truly believe that kids who have an awareness of motion and how it does – and doesn’t – work are intuitively better drivers than those who are less motion-aware.

Smarter than the “average” bear: Statistics are fun (honest)

What, statistics? That’s, like, numbers for really boring people, right?

You wound me. I really like statistics – but I also know how easily they’re manipulated.

Our whole family loves following the stats for our favorite team, the Phillies. (Less so this year than in previous ones, but I digress.) Talk about a wealth of math that you don’t even realize – win/loss ratios, earned-run averages, batting averages; you name it, baseball can calculate it.

But, while sports are cool, the most important reason to understand statistics as an adult is to be sure you’re not being lied to. Check out any presidential campaign – or any “research study” put out by a company with an interest in your purchases.

Every day, you read “numbers” in life that are designed to motivate you to act – either to encourage you TO do something, or to encourage you NOT to. If you’re not good with numbers, that’s fine. Realize, though, that if you can gain an awareness to “think twice” about any statistics you see, you’ll be better off than most people around the world!

Where to start: Even young children can keep track of wins and losses for a favorite team. If you don’t have rabid fandom in your house, pick the most local team you can – because, as a bonus, you can watch some of their games in person. Check your local newspaper to see what information they publish after each of that team’s games. Follow along; compare your team to other teams in the same league.

Not into sports? Look for the “stats” in your favorite hobby! One of Ashar’s favorite hobbies is birdwatching. She loves to keep track of which food attracts which birds, and how many of each type of bird she sees in a particular season.

We don’t do that officially, but you could easily write it down and draw some statistical conclusions.

Finally, check the news – and more importantly, check commercials – for “statistics” stories. See if you and your kids can brainstorm some tough questions about the research.

And check your packaging – we’re often told that something is “25% better” or “40% bigger” or “80% healthier,” but in comparison with what? 40% bigger than the smaller size of the same brand? Uh, OK, sure. That’s a statistic that’s designed to encourage you to purchase the larger size, right? Don’t fall for it – go back to your “grocery math” and check unit price!

The rest of the series

Sunday: When numbers matter: A look at math in the real world (introduction)
Monday: The math you need at the grocery store
Tuesday: The math you need in your kitchen
Wednesday: The math you need to manage your money
Today: The math you need to play sports and do other fun stuff (yes, really!)
Friday: Real-world math resources you’ll love

You can read all the posts here!

More five-day fun

This post is part of the iHomeschool Network’s summer “Five Days Of…” series. Click the collage below to see how some of my fellow bloggers are spending their “five days,” and to learn more about our series sponsor, the BEECH Retreat bloggers’ conference!

18 Jul

The math you need to manage your money

$real-world-money-math$

I’ve got a bachelor’s degree in advanced math, and a 12-year-old daughter who hates anything to do with the subject.

I’m an unschooling mama who loves to do math puzzles and logic problems for fun.

Today, we’ll look at three types of math you need to manage your money.

Inverse operations: That’s how you balance the checkbook

What, you don’t balance your checkbook? OK, first you have to go read about why I do in this post. Then come back here.

OK, you’re back? Here’s the thing. ASSUMING you keep track of your expenditures, it only takes basic addition and subtraction to see how much money you actually have. But to find out if you have missed transactions, you have to balance what you show against what the bank shows.

The REALLY simple version of this involves inverse operations. First, you’ll need to go through your bank statement or online record and make a note of which transactions you and the bank BOTH show. If they’ve got something you don’t (and it’s a valid charge), note that in your record. Then, you’re just left with the balance you have, the balance the bank has, plus a list of transactions that you show that haven’t cleared the bank yet.

To find out if you and the bank “match up,” you need to practice inverse operations. That just means you change the symbol. So if you show a balance of $500, but you have a check for $100 (a “negative”) that the bank doesn’t show yet, you need to ADD $100 to your balance, giving you $600 in “bank terms.” If that’s what they show – that’s perfect, because it means when your check clears the bank, you’ll have exactly the same amount.

Similarly, if you show a deposit that the bank hasn’t registered yet (a “positive”), you’ll need to SUBTRACT that amount to see if you balance.

It’s funny, but this is really hard for a lot of people to get – and, I think, a big reason why people don’t balance their checkbook as adults.

Where to start: First of all, I highly recommend having your children manage their own savings accounts, no matter their age. For the most part, this is simply a good place to put some birthday money, allowance (if you use it), loose change, etc., and have it start to earn interest, which your kids can track via statement.

As they get a bit older, withdrawing money for major purchases is a great lesson. My daughter has made two “major purchases” since opening her account four years ago – a bike and helmet, and a Nintendo 3DS video-game system.

She’s learned how to deduct her spending, and how to weigh the decision of how much to spend. Those are good starting points. As she gets older, we will help her manage her first checking account when she gets her first job. Some people fear this idea; I would rather her start this process WITH our guidance than without it when she’s 18!

If you personally don’t balance your checkbook, give it a shot – and let your kids see you doing so.

I’m a big fan of being open about money and how to manage it with children. How else are they going to learn? (Plus, you’ll be surprised at how much differently they act toward things when they see that your wallet is not an eternal fount of money!)

Dealing with credit and interest

This is another area in which your openness with your kids will be rewarded. No matter how you feel personally about credit cards – if you’re 100% OK with them or 100% against them – make sure your children know how interest and loaned money work.

I will never forget my nephew buying something pricey during college, then telling his parents, “Oh, I didn’t have to pay for that, I used a credit card.”

If you borrow money, it must be repaid eventually, and generally with interest. The longer you take to repay what you owe, usually the more interest you will pay on top of the original amount.

Do your children understand how the “business” of money works – and how they can either gain or lose money as part of it? Have you talked with them about what a bank does with your money – and how you can sometimes earn money by “loaning” yours to the bank temporarily?

Where to start: Again, be open. If you have an interest-bearing account of any kind, sit down with your kids and show them how you earned 10 cents or $1.18 or $450 this month simply by allowing that particular bank to use the money.

Interest isn’t too complicated when it’s earned simply, but the issue of credit is probably the most complicated part of this series, and the only part that I find hard to explain to really young children. That doesn’t mean you shouldn’t try!

One great thing to try with kids of any age is playing verbal “what if” games. “What if someone offered to give you $1,000 now, that you could pay back by giving them $10 a month for 100 months? Would you take it?”

Then add factors in. “What if you had to pay them for an extra year after that 100 months?” “What if you had to pay them for an extra year, but they gave you a really cool T-shirt?” “What if you had to pay them back $100 a month instead?”

For older kids, mix up what the money’s for. “What if you wanted the money for a car? What if you couldn’t get a job without the car?” If they don’t want the loan, have them brainstorm alternatives.

You don’t need to get into the “math” behind those decisions, but you need to start the thought process. There isn’t even a “right” or “wrong” answer in those scenarios, but you can add in ones that you think would sway your child one way or the other to see how he or she will respond!

Cost per use: When the thing that’s cheapest isn’t cheapest

I own a $300 purse, and it was one of the most economical purchases I’ve ever made.

No, I’m not a total spendthrift. I understand cost per use.

I use this purse every day. If I can use it for one year, my cost is less than $1 per day – about 82 cents. If I can use it for two years, that goes down to 41 cents per use. I fully expect it to go at least three years, which puts me about 20 cents per use, and beyond that I get down to about 10 cents!

I used to buy $30 to $50 purses, which would usually last me about three to four months before they’d get holes, or broken straps, or big stains. (I’m hard on purses.) Even at BEST, with four months of daily use, my cost per use on those is no lower than 25 cents, and usually closer to 42 cents. Then add in my time shopping for a new one, and suddenly I’m worse off than if I had gotten something “nice” in the first place.

Does it sound silly to break a purchase down like this? Probably. But it’s a great thought process, and one you can adapt to almost any purchase your family makes.

There are times when getting the least costly item AT THE TIME makes sense. When I need shower-curtain rings, I just want the set that’s going to cost me $1.50, not the $10 ones. No matter which set I get, I’ll use it for about the same length of time, so why not save some cash?

But there are other times when spending more is a savings in the long run. Another good example of this is in shoes. I can wear a $75 pair of shoes with great support for three months, and only visit my chiropractor once, for a $25 copay, a total cost of $100.

Or, I can have achy feet in a $25 pair of shoes and visit the chiropractor three times. Same total cost of $100, but a much more miserable Joan.

Where to start: Figure out the cost per use of something “expensive” in your house – maybe a video-game system or your computer. Have fun with it – let your kids estimate how many days a week it’s used, and how long you’ve had it, and how long you think you will continue to use it.

Then, figure out the same info for “cheap” stuff, like their sneakers. You may find that a laptop is “cheaper” than those Nikes!

Obviously, that’s comparing apples to oranges, but it’s a very real way to bring home what is actually a fairly difficult concept involving investment over time, depreciation and quality, and its uses are incredibly far-reaching. We make these considerations about almost every product we bring into our home. That’s math worth knowing.

The rest of the series

Sunday: When numbers matter: A look at math in the real world (introduction)
Monday: The math you need at the grocery store
Tuesday: The math you need in your kitchen
Today: The math you need to manage your money
Thursday: The math you need to play sports and do other fun stuff (yes, really!)
Friday: Real-world math resources you’ll love

You can read all the posts here!