problem solving


I’ve hit the age when many of my friends and colleagues are managing the realities of having aging parents. Luckily, I’m not there yet — my mom is still very active, both physically and mentally. But many of us in our 40s or 50s are probably at least thinking about how we might manage our parent(s) affairs if/when they are unable to handle things on their own.

My friend and fellow writer, Beth, faced this problem last year, when she, her husband and her mother moved to another state. Beth’s mother needed a little more supervision, and so Beth and her husband arranged for her to live with them. That brought up some emotional and practical questions, which Beth shared in an online writing’s group that we both belong to. She gave me permission to share them here:

Mom lived independently until we combined households. She wants to pay us a monthly fee that covers “room and board.” The question is: How to figure a fair and reasonable amount.

It’s been a long time since [my husband] and I had a roommate. In those days, we simply divided the big stuff by three (rent, utilities, cable), and each person was responsible for his/her own food. That doesn’t seem fair in the current situation for a variety of reasons (not the least of which we’re talking about my MOM, not some friend).

I feel I’m making this unnecessarily complicated. Can anyone help me sort this out? I bring it up because Mom talks about it constantly. She seems to feel the amount she’s paying is too low, and I keep putting the brakes on changing the dollar figure until we have better data about our expenses.

Naturally, I think math can help us find some simple solutions to emotional problems. So I offered this:

I have a really easy and non-biased way to look at this. Calculate your total household costs — mortgage, utilities, food, etc. Then divide this by three. Each of these is a share.

Next, you can decide how many shares each person should have. For example, your mom may have only a half-share, based on what you think she can afford or how much she eats, etc. Take half of a share, and that’s her monthly rent.

Naturally, I like taking a mathematical approach, because it can help reduce the emotions. And if any of the variables go up or down — utilities, for example — you can adjust the rent really easily.

And that seemed to do the trick for Beth. In fact, she took things even farther, considering fair market value, as suggested by another group member:

Here’s how we solved the problem in the end:

1. I drew up Mom’s current monthly budget.

2. I drew up a list of household expenses that apply to her (including the mortgage payment). I didn’t include things like pet expenses or [my husband’s] fuel for commuting, obviously, because those are our sole expenses.

3. I used Laura’s methodology to divvy up the total household expenses into three full shares. Then I calculated partial shares: 3/4, 2/3, and 1/2.

4. I used [another member’s] data about the fair market value of a studio apartment in [my county] for comparison purposes.

5. Then I sat down with Mom and first explained her current budget. Next, I went over the household expenses.

6. I told her about the fair market value of a studio apartment and explained how that related to our attempt to determine what was a fair amount for her to pay us each month.

7. I showed her the share information.

8. I showed her how each share amount would affect her net income. Even at a “full share,” she still retains about 45% of her net income for “mad money,” and that’s without touching any investments. (I didn’t point that out to her, in terms of trying to steer her. I think what I wrote kind of reads that way. I just used a calculator to show her what each share amount would leave her, in terms of disposable income.)

9. I had written all these figures down on paper, so I stepped away to giver her time to peruse the numbers for awhile and consider what SHE wanted to do.

10. After a few minutes, she called me back and said she’d decided to pay a full share. She’s the type of person who likes to “pay her own way,” and she’ll still have plenty of mad money left over. She also was very happy she wouldn’t need to dip into any investments.

It’s important to note that this cut-and-dry approach didn’t erase all of the feelings in Beth’s situation. She was very nervous talking to her mother, and her mother felt responsible for paying a full share. See? Feelings.

Another interesting aspect is how flexible this process can be. With some simple parameters — the value of a full share vs. a half-share, for example — Beth’s family can alter the process depending on where everyone is financially. And if her mother needs more resources or Medicare helps to pay for things, the entire formula can be changed.

Just a bit of math helped Beth gain some perspective and offer her mother tremendous autonomy. The process also set them up to avoid conflict later on. Nice work, math!

Photo Credit: VinothChandar via Compfight cc

I’m currently reading The Organized Mind, by Daniel Levitin, and I can’t wait to share a review with you when I finish. He offers some really terrific math to help when medical decisions are tough. Four-square decision tables anyone?

What do you think of the process Beth worked out? (I also offer this approach as a way to divvy up the cost of a beach house among several family members.) Have you used math to help you come to a difficult or emotional decision? Do you think this approach would work for a young adult who hasn’t flown the nest? Share your stories in the comment 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).

The lesson: Addition and subtraction

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

Leah Davis is tough as nails. She’s been a firefighter in North Carolina for 17 years. These days, she is a Captain EMT — intermediate. I had never really thought about the math required to fight fires, but reading through Leah’s responses, it all makes perfect sense. If your little guy or gal is interested in firefighting as a career, this interview is a must read!

Can you explain what you do for a living?

I am a Captain on a fire engine. This means that I respond to and mitigate emergencies ranging from motor vehicle accidents, fires (all sorts), medical emergencies and rescues. In addition to providing emergency response I complete preplans of existing businesses; the preplans are walk-through inspections which provide information of a buildings layout and any hazards that might be associated with the business. As a member of the fire service I am responsible for participating and providing training in all aspects of the job.

When do you use basic math in your job?

Within the fire service there are many opportunities to use math. The first one that comes to mind is calculating pump pressure to determine the PSI (pounds per square inch) on the end of a nozzle.  Basic math skills, like addition, subtraction, multiplication and division, are necessary. A basic understanding of hydraulics and good understanding of formula usage is vital.

In order to calculate the amount of nozzle pressure is necessary, the engineer must find the friction loss of hose distance, along with appliances and elevation. Only then can the the pump be set up properly. Engine pressure is the sum of the nozzle pressure plus the friction loss plus any elevation or devices. Based on the engine pressure formula EP = NP + FL, if we need a nozzle pressure of 100 psi to flow 100 GPM then the engine pressure needs to be greater then 100 psi.

When determining how much water will be required for any given structure that is 100 percent involved in fire, the fire engineer must calculate the area and divide by 3. This gives the gallons per minute required to extinguishing the fire.

Math is also used when providing medical care. Division is used in calculating the correct dosage of medications to administer. Many medications are calculated milligrams per kilograms or mg/kg.

Do you use any technology to help with this math?

I use a calculator when finding the fire flow or GPM needed on the preplans.

Technology is not usually used on the fire ground when calculating the engine pressure. The engineer needs to be well trained and able to calculate the engine pressure in their heads.

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

Having math competency provides me with additional problem solving skills. The fire service is about problem solving.

How comfortable with math do you feel?

Although I am not a math whiz by any means, I do feel relatively comfortable with math most of the time. The math that is used within the fire service–like area of a structure, GPM needed, nozzle pressure, medication dosage–helps insure the safety of firefighters and others.

What kind of math did you take in high school?

I did not take much math in high school because I did not like it and did not feel successful. However, in college I was required to take remedial math courses and then was able to move on to taking more advanced classes, including calculus. I graduated from college with a good understanding of math and problem solving. I also found that I enjoyed the problem-solving aspect of math.  Too bad I didn’t pay more attention when I was in high school.

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

I was comfortable with my math skills when I entered the fire service.

Do you, or your child, have questions for Leah about firefighting? If so, ask in the comments section. As for summer-slide activities, why not take your child to a fire station for a tour? While you’re there, ask about the math required on the job.

Last week, we had some fun with the order of operations at the Math for Grownups facebook page.* Turns out remembering the order that you should multiply, add, etc. in a math problem is a tough thing for adults to remember. Imagine how kids feel! But this is a really simply thing that you can apply to your everyday life — all the while, reminding your kid how it goes.

First off, here’s the problem that we considered on facebook last week:2 • 3 + 2 • 5 – 2 = ?The answer choices were 38 and 14.I would say that the responses split pretty evenly. Lots of folks chose the incorrect answer first and then realized their mistakes.

So what’s the correct answer? 14. Why? Because of the order of operations. A lot of us learned the order of operations — or the set of rules that establishes the order we add, subtract, multiply, divide, etc. — with a simple mnemonic:Please Excuse My Dear Aunt SallyORParentheses, Exponents, Multiplication, Division, Addition, SubtractionORPEMDAS

(Before going further, I must acknowledge that there are some problems with this approach. First off, it doesn’t really matter if you add before your subtract or multiply before you divide. Those operations can be done in either order with no problem. Second, many teachers are approaching this differently, a topic that I’ll explore in September.)

If you do the operations in the wrong order — add before you multiply, for example — you’ll get the wrong answer. And that’s how people got 38, instead of 14. They simply did the math from left to right, without regard to the operations.CORRECT2 • 3 + 2 • 5 – 2 = ?6 + 2 • 5 – 2 = ?6 + 10 – 2 = ?16 – 2 = 14INCORRECT2 • 3 + 2 • 5 – 2 = ?6 + 2 • 5 – 2 = ?8 • 5 – 2 = ?40 – 2 = 38

All of this is well and good, but what does it have to do with the real world? How often are you faced with finding an answer to a problem like the one above? And that’s exactly what one reader asked me. So I promised to explain things using a real-world problem.

Thing is, you do these kinds of problems all day long, without even thinking of the order of operations. And that’s because you’re not writing out equations to solve problems. You’re simply using good old common sense.

Let’s say you’re going back-to-school shopping with your child. He’s chosen a pair of pants that are $15 and five uniform shirts that cost $12 each. But the pants are $5 off. What’s the total (without tax)?

You probably won’t write an equation out for this, right? (I wouldn’t.) Instead, you’d probably just do the math in your head or scribble some of the calculations on a scrap piece of paper or use your calculator. So here goes:

First the shirts: there are five of them at $12 each. That’s a total of $60, because 5 • 12 is 60.

Now for the pants: all you need to do here is subtract: 15 – 5 = 10. The pants total $10.

Finally, add the cost of the pants and the cost of the shirts: $10 + $60 = $70.

The above should have been super easy for most of us. And — surprise! surprise! — it used the order of operations. Here’s how:15 – 5 + 5 • 12 = ?The order of operations says you must multiply before you can add:

15 – 5 + 60 = ?

Then you can add and subtract:

10 + 60 = 70

There are other ways to set up this equation. In fact, I would use parentheses, simply because I want to keep the pants’ and shirts’ calculations separate in my mind:

(15 – 5) + (5 • 10) = ?

The result is the same, because the process follows the order of operations — do what’s inside the parentheses first and then add.

UPDATE: A reader asked if I’d also show how this problem can be done wrong. So here goes! When you do the operations in the wrong order, you won’t get $70.15 – 5 + 5 • 12 = ?10 + 5 • 12 = ?

15 • 12 = 180

That’s more than twice as much as the actual total!

Try this with your kid. You can make it more complex by figuring out the tax. And there are lots of different settings in which this works — from shopping to figuring the tip in a restaurant and then splitting the tab to dividing up plants in the garden.  Just about any complex math problem that involves different operations requires PEMDAS. And that’s something all kids need to know about.

When have you used PEMDAS in your everyday life? Did this example spark some ideas? Think about the math that you did yesterday — or today — and share your examples in the comments section.

*Have you liked the Math for Grownups facebook page yet? What’s stopping you? We’re having great conversations about the math in our everyday lives. And I ask questions of my dear readers. Come answer them!

In redesigning my blog, I’ve read a lot of the posts I’ve written over the last year. In fact, take a look at this math: On average, I’ve written 13 blog posts each month or 164 posts (counting this one) since last May. And so I decided to repost this one, in honor of Math Awareness Month, which addresses the language of math.

When I was in college, majoring in math education, I learned that math is the language of science.  In fact, we called it the Queen of the Sciences.  (You’d better believe that gave me a sense of superiority over the chemistry and physics majors!)  And yeah, I think that the math I was doing then–calculus, differential equations, statistics and even abstract algebra–is mostly useful for describing some kind of science.

In some ways, everyday math is also the language of science.  Home cooks use ratios to ensure that their roux thickens a gumbo just right.  With proportions, gardeners can fertilize their vegetable beds without burning the leaves from their pepper plants.  And a cyclist might employ a bit of math to find her rate or the distance she’s biked.

But I think too often we adults get caught up in the nitty gritty of basic math and lose the big picture.  This is when many of us start to worry about doing things exactly right–and when math feels more like a foreign language, rather than a useful tool.

Earlier this week, I read a blog post from Rick Ackerly, who writes The Genius in Children, a blog about the “delights, mysteries and challenges of educating our children.”  In Why Mathematics is a Foreign Language in America and What to Do about It, he writes:

Why do Americans do so badly in mathematics? Because mathematics is a foreign language in America. The vast majority of children grow up in a number-poor environment. We’ve forgotten that the language of mathematics is founded in curiosity.  We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar.  Being curious together can be a really special part of the relationship in families.

These Stevendotted ladybugs are not wrestling. Photo credit: Andr Karwath

And I couldn’t agree more.  For all of you parents and teachers out there: how many questions do your kids ask in one day?  10? 20? 100? 1,000?  As Ackerly points out, especially younger children are insatiably curious.  They want to know why the sky is blue and what makes our feet stink and how come that ladybug is on top of the other ladybug.

A full 90% of the time, we can’t answer their questions. Or maybe we just don’t want to yet.  (“That ladybug is giving the other one a ride.”)  With Google‘s help, we can find lots of answers.  But how often are we asked a math-related question–by a kid or a grownup–and freeze?

For whatever reason, many people are afraid to be curious about math.  Or they’ve had that curiosity beaten out of them.  I think that’s because don’t want to be wrong.  As fellow writer, Jennifer Lawler said to me the other day:

It’s funny because when I make a mistake in writing—a typo, etc.—I let myself off the hook (“Happens to everyone! Next time I’ll remember to pay more attention.”) But if I misadd a row of numbers I’m all “OMG, I’m such an idiot, and everyone knows I’m such an idiot, I can’t believe they gave me a college degree, and why do I even try without my calculator?”

The same goes for answering our kids’–or our own–calls of curiosity.

So what if we decided not to shut down those questions?  What if it was okay to make some mistakes?  What if we told our kids or ourselves, “I don’t know–let’s find out!”  This could be a really scary prospect for some of us, but I invite you to try.

What’s keeping you from being curious about everyday math? What do you you think you can do to change that?  Or do you think it doesn’t matter one way or the other?  Share your ideas in in a comment.

Our first Math Treasure Hunt winner is Marcia Kempf Slosser! Congratulations Marcia, you’ve won a copy of Math for Grownups (or if you already have a copy, I’ll send you a gift card). Want to enter? All you need to do is find an example of the daily clue, which is announced on the Math for Grownups Facebook page each day. 

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

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

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

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

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

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

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

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

The seltzer maker is regularly priced at $89.95.

It’s on sale for 40% off.

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

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

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

40% is close to 50%

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

50% of $90 is $45

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

40% is a multiple of 10%

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

10% of $90 is $9

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

There are 4 tens in 40 (4 · 10 = 40)


10% of $90 is $9


 4 · $9 = $36

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

$90 – $36 = $54

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

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

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

40% + 60% = 100%

Or if you prefer subtraction

100% – 40% = 60%

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

There are 6 tens in 60 (6 · 10 = 60)


10% of $90 is $9


 6 · $9 = $54

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

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

I have a love-hate relationship with the winter holidays.  I love the hustle and bustle of shopping for the perfect gift, making cookies and candies, decorating the house and going to special events.

But every single December, I find myself completely overwhelmed with all that I’ve attempted to achieve.  Some years are worse than others.  There was that time that I was frantically trying to finish up a scrapbook for my sister — at 11:00 p.m. on Christmas Eve.  And then there was the year I sobbed because I didn’t have enough time to string cranberries and popcorn for the tree.


Like most 40-something folks who celebrate Christmas, I’ve spent the last few years trying very hard to get and stay organized during December.  I’ve prioritized what’s important to me and my family, and I’ve tried to let go of the things that we just don’t have time for.  (We no longer send Christmas cards.  We wait until February, sending Valentines cards.)

This month, I’ll spend a great deal of time here at Math for Grownups looking at the math that is used during the holidays — from making cookies to planning a holiday buying budget.  You’ll meet a candle maker, a personal shopper and (hopefully) a pastry or candy chef.  I’ll introduce you to some fun activities, as well as show you how math can help make some of these bigger tasks much easier.

(This is a good time for a little disclaimer.  In December, I celebrate Christmas, the Solstice and, if I’m not too worn out, New Years Eve.  But not all of my dear readers do.  During this month, I’ll make all attempts to be inclusive, however, I’ll often refer to my personal preparations, which are not all-inclusive.  I hope everyone will understand.)

But first, organization.

Organizing your tasks for the month may not seem like math.  And in some ways it isn’t.  But it does draw on your problem-solving skills — the very same abilities you put to work when solving a word problem in school.  Do you need to make a table? Draw a picture? Make a list?

For me, holiday planning revolves around the calendar.  Already I have certain deadlines to meet and events that are set in stone.  For example, my family is purchasing gifts for another family who is currently living in a shelter.  Those gifts must be delivered no later than December 9.  That means, I have to shop well before then.  And we travel to my mother’s house on Christmas Day, so all wrapping and making and buying and cooking must be done by then.

What is easiest for me is to create a weekly calendar.  I could dole out tasks for each day, but inevitably I end up with far too many changes in my schedule.  It’s easier to think about things one week at a time.

So here goes:

Week of November 28: Finish shopping for adopted family, string cranberries and popcorn, get Christmas tree, decorate tree and house, make sugar cookies, start shopping for my family, help daughter make her Christmas gifts.

Week of December 5: Ice sugar cookies, make little cakes, make peppermint patties, continue shopping, rehearse singing for Solstice and Christmas services, attend neighborhood party, attend cookie exchange, help daughter make her Christmas gifts.

Week of December 12: TAKE WEEK OFF OF WORK! Make peanut butter balls, rehearse for Solstice and Christmas services, help daughter make her Christmas gifts, continue shopping, send cookies to parents-in-law, finish crocheting scarf.

Week of December 19: Finish shopping, finish daughter’s homemade Christmas gifts, make Kiss cookies, package tins of cookies for friends, make Solstice cookies, wrap gifts, get car ready for the trip to Virginia, pack, make potluck dish for Christmas Eve.

Week of December 26: RELAX!

Now I can look at that list and see if anything is out of order — I’m not wrapping gifts before I buy them.  I’m not attending the cookie exchange before I make the cookies.

I can also ask myself if there is anything missing. Or does any one week look overly burdened?  Ideally, I’d like to get most of my preparations done before December 19, leaving that week to tie up loose ends.

How do you organize your time when you have way too much to do — and too many other things that you want to do?  How do your problem-solving skills help?  Respond in the comments section.

No matter what holiday you celebrate in December, the month has traditionally marked a time for charitable giving.  The weather is growing colder in some areas, making it much tougher on the homeless.  The end of the year is creeping up, and with it the deadline for tax exemptions for charitable giving.  And holiday cheer often means counting our blessings and remembering those who are less fortunate.

Yes, December is the time for giving.  But how much is enough? And what is too much?  As we attempt to balance our own needs (especially in these difficult economic times), many of us struggle with our own sense of guilt and generosity.

We’re at the end of our month of nesting here at Math for Grownups, and I wanted to share a little bit about the math of charitable donations.  Not much makes me feel better about myself than sharing what I have with others. But finding that perfect balance can be a challenge.

Turns out there are formulas that can help guide these decisions.  As we’ve seen in the past, math can remove uncertainty and help us see perspective.  Of course what works for one person is impossible for another.  And that’s okay.  Remember, as grownups we can break the rules — adjust the calculations a bit to suit our personal situations.

Peter Singer, a philosopher who has written about philanthropy, offers an interesting formula.  Singer’s suggestion is based on the amount of income a person or household earns.  His premise is that the larger a person’s income, the more he or she can afford to give.

This is the table adapted from his “The Life You Can Save” website:

Less than $105,000At least 1% of your income, getting closer to 5% as your income approaches $105,000
$105,001 –$148,0005%
$148,001–$383,0005% of the first $148,000 and 10% of the remainder
$383,001 -$600,0005% of the first $148,000, 10% of the next $235,000 and 15% of the remainder
$600,001 –$1,900,0005% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000 and 20% of the remainder
$1,900,001 $10,700,0005% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000, 20% of the next $1,300,000 and 25% of the remainder
Over $10,700,0005% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000, 20% of the next $1,300,000, 25% of the next $8,800,000 and 33.33% of the remainder

Most of us are going to fall in the top bracket —  or if you look at your household income, perhaps the second bracket.  And that’s where the math is simple.

Let’s say that Antwan and Jeannette bring in $75,000 as a couple.  According to Singer, their yearly donations should be between 1% and 5%.  They decide that 2% is a good number for them.

2% of $75,000

Just in case you’ve forgotten how to do percents, here’s a little refresher.  Two things to know: 1) percents can be written as decimals by moving the decimal point two places to the left.  2) And “of” means multiplication. So that means:

0.02 x 75,000 = 1,500

For Antwan and Jeannette, about $1,500 is a good annual total for charitable contributions.

But for the wealthy, the math gets a little tougher. Let’s look at another example.

Will earns $650,000 each year.  According to Singer, he should pay 5% of the first $148,000, 10% of the next $235,000, 15% of the next $217,000 and 20% of the remainder.

One easy way to look at this problem is to first consider four different problems:

5% of $148,000

10% of $235,000

15% of $217,000

20% of the remainder

But what’s the remainder?  Add and subtract to find out:

$148,000 + $235,000 + $217,000 = $600,000

$650,000 – $600,000 = $50,000

So he’ll need to find 20% of $50,000.

0.05 x 148,000 = 7,400

0.10 x 235,000 = 23,500

0.15 x 217,000 = 32,550

0.20 x 50,000 = 10,000

Now he just needs to add:

$7,400 + $23,500 + $32,550 + $10,000 = $73,450

According to Singer, a good amount for Will to donate over the year is $73,450.

Of course all charitable giving should be considered in these amounts — from the mittens you donate to the local shelter to the check you send to your United Way.

So do the math yourself — how close are you to Singer’s suggested donation levels?  (If you’re a little too nervous to try, read this first.) Are you surprised to give more?  Do you think you can stretch?  Share your ideas in the comments section.

Today, I have the great honor of guest posting at Simple Mom, a wonderful, practical and easy-going spot on the web for home managers.  The subject of the day is problem solving and the deck I built a few years ago.

Simple problem solving skills can make the impossible possible.

You’ve probably figured out by now that math in your everyday life isn’t much like the worksheets and timed drills you suffered through in elementary and middle school. And in the real world, you can leave those way, way behind.

That’s because grownup math has more to do with problem solving than remembering that 7 times 8 is 56. Most of us don’t use trigonometry or calculus. But basic math skills figure into some of the most critical decisions of each day—how to save money, save time and save your sanity. These days, you need to know how much top soil to order for your flower bed or what time your parents will arrive in Boston, if they’re driving in from St. Louis.

Four summers ago, I decided to build a deck—something I’d never done before. This process taught me a lot about the math I already knew and how to fill in the gaps with some pretty simple problem solving skills.

Read the rest of the post, and comment there to win one of 10 paperback copies of Math for Grownups. (You can comment here, but it won’t get you in the drawing, so make sure to head over to Simple Mom.)

Film Friday is taking the day off (it’s basement is flooded and it’s worried that its rare collection of film reels–including outtakes of Citizen Kane where Orson Wells reveals that “Rosebud” is actually a reference to the Fibonacci Sequence–might be under water), but you can check out past Film Friday editions, if you really miss it.Save

Photo courtesy of MinimalistPhotography101.com

When my friend Alisa Bowman asked me to answer some math questions for a health blog she writes for, I didn’t quite expect what she sent over.  In terms of health, I’m usually asked how to find BMI or how to calculate the perfect caloric intake.  Here’s what Alisa wanted to know:

I’ve heard that treadmill readouts are notoriously inaccurate. Is there a way to figure calories burned in your head?

 I’m at book club. How many glasses of wine can I drink and still be safe to drive home? 

If I am at high altitude, how do I figure out how long to boil an egg to make sure I don’t get salmonella? 

I had no idea how to answer these, so I put my reporter cap on and did some research.  I was especially interested in the last question, as I’ve had zero experience cooking at high altitudes.  And I found the answer really interesting!  Maybe you will, too.

(By the way, Alisa is the author of an amazing book, called Project Happily Ever After, that her story of how she went from wishing her husband dead to falling back in love with him.  Check out her site.)

I loved Alisa’s random questions.  They made me think, and I learned something — which is the best part of being a writer.  Do you have random math questions?  Have you been in a situation when you think math could help, but you’re not sure how?  If so, post your question in the comments section or drop me a line.  If it’s a good fit, I’ll answer it in an upcoming blog post!

Photo courtesy of dmdonahoo.

If you’ve started down the frugality path, you have probably already been smacked in the face with one unavoidable fact: there’s math involved in living within or below your means.  For some, this is no biggie.  For others, this could very well be the difference between saving a little and saving a lot.

But even if your basic math skills are rusty, you can handle these calculations, no problem.  A few simple tricks will help you stay frugal and even take it up a notch!

Read the rest of the post here.

How has math helped you be frugal? Share your ideas in the comments section here or at Suddenly Frugal!

Would you like me to guest post at your blog?  Or do you know of a blog that I would fit right in with? I’ve got lots of ideas to share with anyone who will listen! And I promise I’m a good guest.  I wipe out the sink after I brush my teeth and don’t mind if the cat sleeps on my pillow.  Get the details here.

You really don’t have to know or care what “binary trees” are to appreciate Vi Hart’s genius.  And I’m so excited to finally introduce you all to her.

Vi calls herself a “recreational mathematician.”  In other words, she plays with math, and it’s really amazing stuff.  Just a couple of years ago, she graduated from Stony Brook University, with a degree in music.  (Her senior project was a seven-movement piece about Harry Potter.)  Before that, she got hooked on math when her father took her to a computational geometry conference.  (George W. Hartis now chief of content for the soon-to-open Museum of Mathematics in Manhattan.)

In short, she’s not a trained math geek.  She just loves math.

She’s also funny and infectious.  I dare you to watch this video and not laugh.  And nope, you don’t have to know what binary trees are to get the jokes.  (Psst, you don’t even have to love math to love Vi.)

I’ll post more of Vi’s awesome videos in weeks to come.  Let me know what you think in the comments section!