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!)
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!
Our discussion on fractions and pizza on #mathchat yesterday reminded me of a story.
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.
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.
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.
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!
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?
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 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.
I’ll bet the first answer you have is, “in school.”
In my recent research of different types of math teaching, including dancing, literature and gaming, it’s occurred to me that I didn’t learn math in school. I learned arithmetic, I learned algorithms, but math?
My dad is an engineer, and by nature not a teacher. But we did puzzles. Cryptograms from GAMES magazine, computer-based role-playing games and TV-based video games. He wasn’t one for shoot-em-up or beat-em-up games (although swords were essential). Everything we did had logical thinking.
My mother was an English major. She encouraged memorization of both prepositions and multiplication facts. And she played word games with me.
Puns have a special kind of logic to them. As she was punning around with me, I was learning a unique set of skills.
Of both of them, I was allowed to ask questions. Any questions. And I did. And they answered them.
Everyone learns math at home.
As a parent, your daily actions impact your child mathematically. It’s not your skills with pencil and paper that help you teach math, but who you are.
You connect with your children and understand them because of your similarities to them. Remember how you learned math. Not how you learned arithmetic and algorithms, but math. The art of math.
That’s your key to helping your kid learn math.
How did you learn math? Can you use this to help your children? Teachers – how can you help parents tap into this side? Share your thoughts in the comments.
You’re at a a party. Someone asks you what you do. You say, “I’m an undertaker’s assistant. And what do you do?”
They say they teach English.
You say, “Oh wow. I have always HATED English. I can’t even read the street signs!”
The guy a few feet away overhears this and joins in the conversation: “I know, right! I tried to read and write stuff in high school, but it just never worked for me. I finally decided that English wasn’t my thing.”
You respond with: “Yeah, when I go to a restaurant I ask the waiter to explain everything. So many letters! I don’t understand how you teach such a dreadful subject. I’m so sorry for you.”
Have you ever done that? Seen it? No doubt you’ve seen with with math.
Why can you say, “I hate math” but not “I can’t read”?
Why is it acceptable, even cool, to be “bad at math” but those who can’t read or write stay in the proverbial closet?
It’s time to come out, y’all. If we can’t get people to stop saying “I hate math” then let’s water it down by saying “I hate <anything else>.”
The next time you’re at a party and someone tells you what they do, respond with, “Wow, I’m so sorry for you. I’ve always hated <field/career>. You must be miserable!”
The more we all do this, the more people will stop giving credence to the words “I hate…” Soon the phrase “I hate math” will be extinguished.
What do you think? Can you do it? Will it work? Share your thoughts in the comments.
I remember being allowed in Jr. High to use the calculator to “check my work.” Soon after I learned that the books in High School had the answers in the back! It was like condoned cheating!
How could I go wrong with the magic box and the answers given to me straight from the publisher?
And then I became addicted.
Sometime after Geometry I lost my multiplication facts. I wasn’t just checking my work on the calculator.
Subconsciously I figured there was no reason to trust my potentially faulty memory of math facts if I had the absolute sure thing right there next to me.
For years I stopped doing arithmetic.
And my dad chastised me. Every time some quick calculation came up in the kitchen, garage or grocery store, I would stare at him blankly. Then I would reach for my calculator.
The way he looked at me, you’d think I had reached for a bong, ripped off my bra, sang Kumbaya and spat on the pope.
I ignored him.
For years.
Until one day I realized that I had absolutely no memory of . Yep – was what did it. I started watching myself. I always did simple arithmetic (even addition of single digits) on the calculator!
Then I watched other people. I saw the clerks in the grocery store reach for the magic box to figure out 10% off something. I saw an older man at McDonald’s send the girl into a tizzy because he modified his cash payment after the girl had already typed it in.
“There’s a problem here,” I thought. Maybe Paps was right.
I put it on my syllabi that calculators were strictly prohibited (unless expressly invited by me – in the case of probability and statistics). I growled at anyone who reached for one.
And I taught them arithmetic.
And we were all better off.
Are you a calculator addict? Share your story in the comments.
