Posts tagged ‘cookie’
Heavy Cookies, Undervalued Coins, and Misconceptions
Simple question to get us started…
Which is worth more?
And of course the answer is, “The quarters, because 50¢ is more than 20¢,” right? But not to a kindergarten student or a preschooler who hasn’t yet learned how much coins are worth. A young student might argue, “Four is more than two.”
Why didn’t the quarter follow the nickel when he rolled himself down the hill?
Because the quarter had more cents.
Recently, I was asked to review an educational video for kindergarten math that had a similar question.
The video stated, “Can you tell the green, yellow, and orange cookies are heavier? That makes sense, doesn’t it? Because there are more of them!”
Uh, no.
This is the same logic that would lead one to claim that the value of four nickels is greater than the value two quarters because there are more nickels. It’s a huge misconception for students to focus on number rather than value. So it’s very frustrating to see this video reinforce that misconception.
For example, if each green, yellow, or orange cookie weighs 3 ounces, but each blue or purple cookie weighs 5 ounces, then the left pile would weigh 6 × 3 = 18 ounces, and the right pile would weigh 4 × 5 = 20 ounces, so the right side would be heavier. (Then again, are there really 6 cookies on the left and 4 on the right, or are some cookies hidden? Hard to tell.)
As far as I’m concerned, the only acceptable answer is that the pile of green, yellow, and orange cookies must be heavier — assuming, of course, that the balance scale isn’t malfunctioning — because the pans are tipped in that direction.
All of this reminds me of the poem “Smart” by Shel Silverstein.
SMART
My dad gave me one dollar bill
‘Cause I’m his smartest son,
And I swapped it for two shiny quarters
‘Cause two is more than one!And then I took the quarters
And traded them to Lou
For three dimes — I guess he don’t know
That three is more than two!Just then, along came old blind Bates
And just ’cause he can’t see
He gave me four nickels for my three dimes,
And four is more than three!And I took the nickels to Hiram Coombs
Down at the seedfeed store,
And the fool gave me five pennies for them,
And five is more than four!And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head–
Too proud of me to speak!
Oreos, Ratios, and the Perfect Cookie
Okay, first things first. What do you call the following shape?
I call it a pill. My sons call it a racetrack. But is there a formal name for a shape formed by a rectangle with a semicircle attached to each end? If not, I feel like there should be. Place your suggestions in the Comments.
Until I hear a better suggestion, I’m gonna keep callin’ it a pill.
The following trivia question is the reason I ask.
How many pills appear around the circumference of the trademarked design on an Oreo^{®} cookie?
What’s that, you say? You didn’t know that there were little pills along the edge of each wafer on an Oreo cookie? Then you, my friend, need to pay a little more attention.
Because there aren’t just some pills around the circumference. There are 96 of those little buggers, and each of them has a rectangle with a lengthtowidth ratio of approximately 3:2 between two semicircles.
See for yourself.
Ironically, the ratio of 3:2 brings me to the main reason I’m writing today.
The original Oreo represented good design: a single layer of vanilla cream filling trapped between two crisp, chocolate wafers. But it always felt lacking to me. If only it had just a little more cream, then it would be perfect. A potential solution arrived in 1974, when Nabisco released the Double Stuf variety — two chocolate wafers with twice as much filling^{1} as its predecessor. Yet the Double Stuf teetered too far in the opposite direction. It was too sweet.
Which brings me to the delectable treat that I discovered today: the Triple Double Oreo, which is running a strong campaign for the title of World’s Best Cookie. My wife describes it as “the Big Mac of cookies.” Not two but three chocolate wafers with a thin layer of cream filling between each pair. And the pièce de résistance — one layer of vanilla cream filling, the other chocolate.
Now that’s what I call intelligent design.
It absolutely nails the ratio for wafer:filling.
Original 
Double Stuf 
Triple Double 

Wafers 
2 
2 
3 
Filling^{2} 
1 
1.86 
2 
Ratio of W:F 
2 
1.08 
1.5 
The chart above makes it all clear. The ratio is too high in the original, too low in the Double Stuf, and just right in the Triple Double. Indeed, the Triple Double Oreo is the Little Bear’s porridge of the cookie world.
This reminds me of Reese’s Peanut Butter Cups. While I haven’t quantitatively analyzed the peanut butter to chocolate ratio, qualitatively I would say that the original had a little too much peanut butter, the Big Cup was disgusting with far too much peanut butter, but nirvana was captured with the peanut butter to chocolate ratio in Miniature Reese’s Peanut Butter Cups. (Insert smacking lips sound here.)
So if you read this blog and wonder why I’m so hyper sometimes, now you know. I consume an unholy amount of refined sugar.
^{1} There is some debate about the actual amount of filling contained in a Double Stuf Oreo cookie. Although a spokesperson for Nabisco claimed that the cookies indeed contain twice as much filling as a regular Oreo, a math class in upstate New York experimentally found that Double Stuf cookies contain only 1.86 times as much cream filling as a regular Oreo. As I generally trust unpaid high school students more than moneygrubbing corporate types, I’m using 1.86.
^{2} The numbers for “filling” are relative to the amount of cream filling in a regular Oreo^{®}.
Math Fortune Cookies
Today might be Fortune Cookie Day. Hard to say, really, because there are also plenty of references on the web that claim July 20 is Fortune Cookie Day, and the good folks at Holiday Insights claim that there are references to a Fortune Cookie Day in April, May and June, too. But honestly, who cares? No one should lose sleep over an incorrect date for a madeup holiday.
Besides, if you can accept that today is Fortune Cookie Day, well, that gives me a good reason to now tell you two fortune cookie stories.
The first concerns the publication of Math Jokes 4 Mathy Folks. About an hour after Bob Reed called to tell me that he’d like to publish my book, I was dining at a Chinese restaurant. The fortune in my cookie read: Your current plans will succeed. Though I am unwilling to ascribe the success of a book to a fortune cookie, the fortune appears to have been true. Since publication on August 9, 2010, more than 5,000 copies of MJ4MF have been sold. Though I am still holding out hope that it will sell a million copies, I cannot be disappointed in a book of math jokes that reaches 5,000 people.
The second story involves my friend Andy Fielding. The day before he left for Africa to serve two years in the Peace Corps, he and I were dining at a Korean restaurant. After the meal, two fortune cookies were placed on the table. I told him to select one. “No, no, you first,” he insisted.
“But you need the good luck,” I said. “You’re leaving tomorrow.” He repeatedly refused, and the argument continued for 20 minutes. “Oh, fine!” I said finally, and took one. The fortune: You are about to take a long and safe journey. “Dammit,” I said as I showed it to Andy. “This was meant for you!”
“It’s okay,” he said as he showed me his fortune, which read: You are about to take a long and safe journey.
Someday, I hope to open a Chinese restaurant. The portions will be very large, and the existence of leftovers is guaranteed by the Chinese Remainder theorem.
When I do, I look forward to generating creative fortunes to place inside the cookies. Here are a few. (Feel free to add to this list by posting your favorite fortunes in the comments section, or get creative and write one of your own.)
 You are a complex person, and i would like to be your friend.
 When life throws you a curve, calculate the slope of the tangent at the point of inflection.
 You will live a long life. If you marry an actuary, it will feel even longer.
 Some day you will find a useful application for Ceva’s theorem. (Maybe.)
 Your lucky number is the square root of 17.
 Fame and fortune will find you… unless you lock yourself in an attic, trying to prove the Riemann Hypothesis.
 Will you still need me, will you still feed me, when I’m 2^{6}?
 I have found an elegant proof of Fermat’s Last Theorem, but this fortune is too small to contain it.
 You are good at solving problems. Textbooks fear you.
 This cookie contains no fortune.
 Your students secretly agree that your head is not in proportion to your body.
 A foolish man will try to write a better fortune than this, but a mathematician will find it sufficient to know that a better fortune exists.
 When someone finds a counterexample to your proof, look for a different proof.
 A conclusion is your last thought before you got tired of thinking.
 You are so smart that you do not need answer keys.
 The fortune of this cookie is obvious.
 You are good at geometry. Q.E.D.
 Greet new friends with a handshake. At a math social, greet new friends with the handshake problem.
 Do not follow the instructions in this fortune cookie.
 Do not kiss a mathematician on the lips. Ever.