Category: Math Around Us

  • A Human Interest Story Involving Math: The $100 Battery Charger

    A Human Interest Story Involving Math: The $100 Battery Charger

    My day job colleague told a beautiful story yesterday. He had been washing his car late at night, in the dark, and was approached for assistance. He is generous beyond belief, and apparently he made a real impact.

    Oh, and it involved a little math.

    I was washing my car the other night and really getting after it. I had the scrubbing brush going and was really making progress on getting the car clean. I was totally focused and I felt a tap on my shoulder. It startled me and I turned around to be faced with a large African-American woman who said, “I’m sorry, I don’t mean to interrupt, but we’re having car problems. Is it possible you can help us? I think we need the battery jumped.”

    I looked down the street and saw no other people and no car. Within a split second I remembered my latest purchase: a wireless battery charger that needs no people, no cables and no extra car to jump a battery. I got it out of my garage and handed it to her.

    “I’m in the middle of washing my car. Why don’t you borrow this? It should help.”

    She thanked me and walked away with the charger. I got back to washing my car.

    Five minutes later there was another tap on my shoulder. Another African American woman was standing there holding a five dollar bill. She offered it to me.

    “Oh my goodness, no,” I said. “I’m not taking your money. I’m just glad I could help.”

    Another 5 minutes went by and I saw one of the ladies put the battery charger close to my garage. I was really getting into the car washing at this point – suds everywhere – so I didn’t pay much attention.

    When I was returning my carwash supplies to the garage, I saw a crisp new $100 bill on top of the battery charger!

    That thing was only $40 – and they just gave me $100 to borrow it!

    This is a wonderful and touching story. These ladies were having difficulty finding someone to help them. Not only did my friend help, he also freely gave them something to use and trusted without question that they would return it.

    They, too, were moved by his generosity.

    The numbers don’t work.

    It looks like this:

    • Battery charger cost: $40
    • “Rental fees” offered: $5
    • Shown gratitude: $100

    The numbers don’t make sense. And in a way they shouldn’t. The $100 bill wasn’t really money. It was the biggest, fattest, loudest thank you note ever written. There’s no value you can place on someone being free and generous and trusting.

    It still goes in as $100 in the eyes of the bank. But what do they know?

    Notice the math and share the story.

    When you share this story, point out the math. Especially if you tell this in front of (or to) children. Making the connection of generosity and emotion to math will help everyone see how integral math is in our lives.

    How about you? Do you have a story of generosity that you’re just now realizing involves math? Share it in the comments!

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  • The Math in Credit Card Security

    The Math in Credit Card Security

    We had a fun little discussion via email at the day-job. Someone changed the code on the combination lock and the discussion around combinations, permutations, cryptography and all things sneaky-math cranked up.

    It reminded me of this neat fact I learned about credit card security.

    Not all digits on a credit card are created equally!

    A credit card is made up of 16 numbers. But only the first 15 are “random,” according to NRich Math. The last number – the 16th number – is the “check digit.” It’s calculated using a fancy formula using the first 15 digits.

    This check digit helps a computer system quickly determine if a credit card number is fake. Now, it can’t confirm that it’s real – it just can help determine if it is fake.

    The digit is created using a method called Codabar.

    First, let’s define some things.

    An odd digit is a digit in the credit card number that is in an odd position. For the photo of the card here, the number is: 5184 8204 5526 6423:

    The odd digits are 5, 8, 8, 0, 5, 2, 6, 2

    An even digit is a digit in the credit card number that is in an even position. For the photo of the card here, even digits are 1, 4, 2, 4, 5, 6, 4, 3

    The check digit is the last digit – it gets calculated and isn’t considered in either odd or even position. It’s a super special digit.

    The method is weird – and kinda fun!

    Here’s what you do:

    1. Add up all the odd digits, or the digits in the odd positions: 5 + 8 + 8 + 0 + 5 + 2 + 6 + 2 = 36
    2. Double that number: 36 × 2 = 72. Save this number, 72, for later…
    3. Add the even digits together, or the digits in the even positions: 1 + 4 + 2 + 4 + 5 + 6 + 4 + 3 = 29. Save this number, 29, for later…
    4. (This is a freaky step.) Count the number of odd digits that are greater than 4. The odd digits are 5, 8, 8, 0, 5, 2, 6, 2. Of these, 5, 8, 8, 5 and 6 are bigger than 4. There are 5 of those total. Save this number, 5,  for this next step…
    5. Add up the results you saved from steps #2, #3 and #4. 72 + 29 + 5 = 106
    6. Take the answer from step #5 and figure out how many you need to add to get it to the next multiple of 10 (or the next number that ends in zero). The number after 106 that ends in zero is 110. So we need to add 4. 106 + 4 = 110. 4 is the super important number.
    7. That final super important number – well, that’s the check digit! That’s the last number that should be on the credit card – if it were a real card!

    For the picture, the check digit should be a 4. And it’s a 3. So I can tell instantly that this is a fake credit card number.

    You can use this to teach your children!

    Stuck in a waiting room with a 10-year-old? All you need is a pen, piece of paper and any credit card in your wallet.

    Teach them the method and have them check all of your credit cards. Or tell them you can guess the last digit of any credit card number.

    Either way, you’ve got an instant source of entertainment wrapped in a ball of education!

    What do you think? Are you racing to your purse right now to check your cards? Share your thoughts in the comments.

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  • Back to School Math Clothes

    Back to School Math Clothes

    For many across the  world, today is the first  day of school. For after schooling families, or blended homeschoolers going to a co-op,  you’ve probably been shopping for new clothes for a few weeks. For those in areas that offer tax-free back-to-school weekends, you no doubt have taken advantage of that. Even if you unschool on a sailboat hopping around the coast!*

    And why should the children have all the fun? Why not do a little back-to-school shopping of your own?

    And of course, don’t just buy any clothes, buy math clothes!

    Math accessories dress up a business or formal look.

    At a fancy business meeting, or a full tilt gala, show your  affinity for math with your jewelry. This Fibonacci sequence necklace is a beautiful addition to the little black dress or business suit:

    Notice the Fibonacci sequence: 1, 1, 2, 3, 5

    This artist is working with me to create some really neat Fibonacci earrings and matching bracelet. We’re also working on other patterns and concepts for jewelry that says, “Math is cool, and it’s pretty too!”

    Business casual means t-shirt with a blazer.

    My favorite outfit is a math T-shirt with a blazer over the top. I wear some slacks and modest heels and I’m ready to take on the world. Here’s a T-shirt that I found that’s on its way to me now:

    This “obtuse” shirt is created by Matt at ExBoyfriend Collection (now BoredWalk), who is generous enough to give one to me! I’ll post a photo in full dress when it arrives.

    It reminds me of what my Ma used to tell us: “Quit being so obtuse!”

    Matt creates other math t-shirts too! We’re looking at collaborating on some – so keep your eyes peeled.

    Take it to the limit with casual wear.

    You can also wear a t-shirt as just a t-shirt, with shorts or capri pants.

    This infinity shirt is from Mike who publishes MathFail, Spiked Math Comics and Math Shirts.

    What’s your favorite math outfit? Are you hitting the stores for yourself this back-to-school season? Share with us in the comments!

    * BTW, that’s my homeschooling dream – on a sailboat, unschooling around the coast!

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  • Cheesy Math – No, Really. Math & Cheese!

    Cheesy Math – No, Really. Math & Cheese!

    Last night was taco night and my job was to grate the cheese.

    I didn’t get too far in before I noticed some math.

    For some reason I always start grating on a corner. Then I rotate the block so I’m grating on another corner. After doing this a few times I noticed the angles I was creating:

    And what exactly are the shapes, anyway? What is the shape of the grating holes of the grater? And what is the resulting shape of the cheese sliver?

    How much cheese is in the pile after you “fluff” it by grating it? What’s the volume of fluffed cheese compared with stuck-together-in-a-block cheese?

    More importantly, is there enough for two grownups and a toddler? (When one of the grownups loves cheese!)

    What are your math curiosities in the kitchen?

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  • Unrecognized Math Conversations

    Unrecognized Math Conversations

    I had the pleasure of assisting Sarah Shah in her appearance on Great Day Houston yesterday.

    While preparing for the show, I observed Sarah and the host, Deborah Duncan, in the makeup room having a conversation about math.

    When I said to Sarah later, “that was an interesting math conversation,” she looked at me with anticipation, encouraging me to share what I heard. She had no idea I was referring to her conversation!

    The math conversation was fully on-topic.

    It was national thrift store day, and Sarah was going to share with GDH viewers some tips on shopping at resale shops. The topic of the show inspired their kibitzing behind-the-scenes about buying gold jewelry.

    Deborah was talking about how there’s a difference (sometimes big) between the cost of the gold in a piece of jewelry, and the sale price.

    The cost of craftsmanship should be close to its value.

    Deborah was making the point that there’s value on the design of an object based on the workmanship that went into it. And this goes only so far.

    Right now gold prices are around $1700 per ounce. Since an ounce is around 28 grams, gold is valued at about $60 per gram.

    The QVC bracelet in the picture is 9 grams. It’s selling for $530 – pretty much exactly the value of the gold contained within.

    If the value of gold for a 9 gram bracelet is around $530, charging $3000 for it means you’re paying about $2500 for the craftsmanship!

    Unconscious math is all around.

    Aqua And Gold Fractal by Sharon Apted

    It was a wonderful experience to see two intelligent, educated women having a lively and entertaining conversation about math. It was quite disheartening, though, that Sarah didn’t even recognize it. In a previous life she was a physicist.

    How many other conversations about math are ignored? How many people who claim they aren’t good at math have these conversations every day?

    Look around at your conversations this week. How many of them are about math? Share your conversations in the comments. And with your kids!

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  • “Let’s NOT divide the pizza equally” – A Hard Lesson in Fractions

    “Let’s NOT divide the pizza equally” – A Hard Lesson in Fractions

    Our discussion on fractions and pizza on #mathchat yesterday reminded me of a story.

    A cooked Totino's pizza. Perreroni variety, with a little added garlic.
    Image via Wikipedia

    My best friend lost on this deal back in 1978. But she gained a valuable lesson.

    My friend, let’s call her Linda…

    She was a terribly terribly slow eater. Like annoyingly so.

    We would sit down to a Totino’s pizza on a summer afternoon. I would finish my half while she was still working on her first piece!

    One day I suggested a different method.

    “Let’s NOT divide the pizza in half – equally,” said I in my sweetest voice. “We’re best friends, and dividing food up is so primal. Let’s just eat like normal people.” (Okay, I’m sure I didn’t say, “primal,” but you get the point.)

    She agreed. Even though she could manipulate the heck out of me, I certainly had my share of the talent.

    She got two pieces.

    A whopping 1/4 of the pizza.

    She still tells this story.

    And guess what? She totally knows the difference between her 1/4, our 1/2 and my 3/4.

    What about you? Do you have any lessons you learned from friends in math? Share them in the comments.

    Please note that my bottom still reflects this bad pizza eating habit. Perhaps writing it down for the world to see will help me knock of the over-pizza-eating habit. That and the LoseIt! iPhone app.

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  • How to Integrate Math into Geography

    How to Integrate Math into Geography

    Everyone’s getting back into the schooling groove. So twitter is filled with questions like Cara’s:

    And since my world revolves around math, here are my thoughts.

    Use the Four Color Theorem (but don’t say it out loud).

    The Four Color Theorem says that if you only have four crayons, you’re good to color your map and not have any colors touching. (That’s the he kiddo version of the theorem.)

    So get out your google and print out some map coloring pages. Choose ones with lots of borders. (As fun as it is to color Texas as a whole, use a map of Texas’s counties.)

    Caution: don’t tell the children they’ll be using math. Let them figure it out.

    Now it’s coloring time!

    And here’s the challenge: color the map with as few colors as possible so that no two touching territories have the same color.

    While they color, you can talk about the names of the locations and some of the details. Even have them label them.

    Once they finish coloring, have them remember how few colors they used.

    Next time you talk about this map, ask them to use one less color than they did before. Continue labeling and discussing the locations.

    After a while they’ll figure out that they can’t do it with three, but they can do it with four.

    Shower, rinse, repeat.

    From the Texas Environmental Education Providers (how cool is that!)

    Kids are experimental. And they don’t believe that what works once, automatically works again (that’s why they drop Cheerios on the floor over and over and over again).

    So you can do this with the next map when you’re ready to go to another part of the world.

    Indeed, they’ll eventually figure out that four is the magic number. Then they can google it and learn all about the theorem!

    How about it? Did it work? Share your experiences in the comments.

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  • How to Quit Saying “I Hate Math”

    How to Quit Saying “I Hate Math”

    Is changing how you feel about math like changing who you are?

    My Little Brother is a licensed professional counselor. He often tells me that you can change your attitude by changing your behavior.

    Apparently the behavior-attitude door swings both ways. If you don’t want to do something because you feel frustrated, do it anyway and that will clear up the frustration.

    So that’s how you can get your attitude and your child’s attitude aligned with positive feelings of math.

    Stop saying angry math things.

    I’ve pointed out that the real place kids learn math is at home. And I’ve discussed why grown-ups should quit talking about hating math. But until now, I’ve never said how to do this.

    Because it’s easier said than done right? When you’re frustrated, or your children are frustrated, you’ve gotta say something. So you can’t “just stop.”

    HOW do you quit saying “I hate math” (when you really do hate math)?

    First, make a list of all the math things you do (download the handy helper here). Here’s a starter list for both you and your children:

    • I know how long it takes to get dressed and so I can calculate when I have to wake up in the morning.
    • I can figure out if our car is getting good gas mileage.
    • I can figure out if I have enough money saved to by a nice toy.
    • I know what I have in savings and if that’s enough to buy the fancy shoes I want.
    • I know how many minutes it takes me to walk to my friend’s house.
    • I know that riding my bike to my friend’s house is faster than walking.
    • I know that in the past I couldn’t reach the middle of the dinner table, and now I can – because my arms are longer.
    • I can figure out how much I’ve grown in the past year by looking at my growth chart.

    Copy your list and put it on the refrigerator, in the bathrooms, on the front door and next to your bed. When you find your child or yourself wanting to say, “I hate math,” instead say, “I can do math because __” and fill in the blank with something from the list. If you need to, continue like this:

    This particular math problem I’m working on is more challenging than what I already know, but it isn’t hard. I just have to figure it out. And since I’m smart enough to do all that other math, I can figure this out!

    The behavior of changing what you say will have a positive affect on how you and your children feel about math!

    Try it. Let me know how it goes!

    This article was previously part of a We Are That Family “Works for Me Wednesday” post.

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  • How Adding Evens and Odds is like Multiplying Positives and Negatives

    How Adding Evens and Odds is like Multiplying Positives and Negatives

    I was playing cribbage with Husband when I found my hand to be 8, 4, 2, 2 and the cut card was also a 2. I focused hard to see if I could come up with 15. (If any group of cards add to 15, you get two points.)

    My resolve was strong. Then I remembered that for any group of numbers to add up to an odd number, one of them must be odd.

    While shuffling for the next hand, I started thinking about adding evens and odds:

    • Even + Even = Even
    • Odd + Odd = Even
    • Odd + Even = Odd

    This looked familiar. Then I remembered the rules of multiplying positives and negatives:

    • Pos x Pos = Pos
    • Neg x Neg = Pos
    • Neg x Pos = Neg

    I was so excited to notice this. Alas, I’m pretty sure I’ve noticed it before. I love rediscovering patterns as much as discovering them!

    Look for patterns everywhere.

    Always keep your eyes peeled for similarities. When you see them, if your children are old enough, use leading questions to get them to observe the same thing. If they aren’t old enough, keep a journal to share things with them later. Encourage your kids to look for patterns in everything. Use toys and manipulatives to improve this, but also use nature and everyday activities. What patterns or nifty things in math have you noticed recently?

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  • Birthday Math: How to Celebrate with Math

    Birthday Math: How to Celebrate with Math

    Do you try to integrate math in everything? Would you like to? How about integrating it into birthdays?

    It’s Husband’s birthday today. He’s 42. But instead of just saying, “Husband’s 42,” I can say he’s 13.37pi years old. (At that site you can also find an “exact” pi birthdays in case you want to celebrate at some other time.)

    He’s also 15,340 days old! This site calculates months, hours and seconds too.

    He’s 2×3×72 \times 3 \times 7 years old. His age is also the second sphenic number. What’s that? I’m not sure – but if you click on your child’s age on this Wikipedia page, you’ll get some fun sounding words for their number that they can use all day! Here are some for your kids:

    He can go here to find out that he was born in MCMLXIX. This nifty birthday math trick will result in the number 4.22 (April 22 – his birthday!). Or this one which will result in 42269 (also his birthday).

    For some fun birthday math, he (and you) can check out The Birthday Problem – also known as the birthday paradox.

    How will you celebrate a family member’s next birthday? Will you use birthday math? Share your thoughts in the comments.