Posts tagged ‘postaweek2011’
Thanks to everyone who participated in the online version of my favorite game. Thanks, especially, to those people who helped to share it via Twitter, Facebook, and other blogs.
Though I am posting the results today, I will continue to leave the form online. Though I had only planned to let the contest last one week, entries continue to roll in, and I see no reason to forbid people from playing. From time to time, I’ll update this page… such updates will occur at the intersection of two events: when enough entries warrant an update, and when the muse hits me.
Without further adieu, here are the results.
With 1,042 entries divided into groups of 100, there were 10 complete games played. The charts below show the results for each game. (Sorry if they’re a little hard to read. Click on the images to view them full-size in a separate window. There are two images below — games 1-5 are shown in the top image, and games 6-10 are shown in the bottom image.)
The graphs above do not reflect all 100 entries for each game. In each game, many numbers greater than 35 were chosen. However, 84.1% of all selected entries were 35 or less.
The winning numbers, respectively, were 3, 3, 20, 4, 7, 2, 16, 4, 4, 2.
If you’re interested in the raw data, download this Excel spreadsheet.
Congratulations to Loïc Grobol of Chécy, France! Loïc was the winner of the 4th game, and his name was randomly selected as the overall winner of the signed copy of Math Jokes 4 Mathy Folks and the specially-designed, one-of-a-kind random number generator. (There is beautiful symmetry that Loïc chose the number 4, that he was the winner of the 4th game, and that the prize has a 4 in the title.)
As shown in the graphs above:
- On average, the number 1 was chosen by 10.4% of entrants. (Edward Early of St. Edward’s College said, “I use that [game] as a bonus question on a test in every class I teach. I believe 1 has never been the winning number, even in a class with only 6 students.” I have played this game over 100 times with various size groups. In my experience, the number 1 has only won twice… by the same woman, who — in a show of incredible bravado — chose the number in consecutive rounds of the game.)
- The number 2 won twice, but it was chosen rather infrequently — less than 1/3 as often as 1. My suspicion is that people figure if you’re gonna go big, go REALLY big… why choose 2 when you can choose 1?
- Besides 1, the number most often chosen was 17, which was selected 5.5% of the time. This seems to corroborate numerous studies that found 17 to be the most commonly selected random number.
- The number 151 was the greatest number chosen more than once.
The chart below shows the frequency of the top nine guesses.
Among the most interesting entries were 666, 1012, 1337, 53,479, and 3,010,994.
The most amusing entry was 10, with the accompanying note, “I’ll choose the base later.”
And you may be wondering… if all 1,000 entries were considered as just one game, what number would have won? That distinction would have gone to 32.
By running this contest, I learned about two interesting uses of this game in classrooms.
Edward Early said that he uses the following version as a bonus question.
Write a positive integer in the blank: _______
How this will be graded: The least positive integer that is submitted by exactly one person will be worth 5 points. The next-smallest will be worth 4 points, and the next-smallest after that will be worth 3 points. All other positive integers submitted by exactly one person will be worth 2 points. Positive integers submitted by more than one person will be worth 1 point. Anything other than a positive integer will receive no credit. Do not ask me to explain this question.
Not surprisingly, with these modifications comes a change in strategy — Edward said that some students choose a large random number, just to ensure they receive 2 points.
Matt Skoss of Possum Educational Services and the Northern Territory Dept of Education and Training said that he’s used this game for years with his kids at school.
Pick the lowest prime number, composite number, surd, cube number or triangular number, etc., depending upon what I’d like the kids to think about.
What an excellent use of a simple game!
Know what this is?
(Answer at bottom of post.)
I am not certain that the preceding or following jokes are funny. I am certain, however, that today is Werner Heisenberg‘s birthday. If you’re not familiar with his work, you might want to read about the Heisenberg Uncertainty Principle before continuing. Not that it’ll make the following jokes any funnier — in fact, if you require an explanation of the content prior to reading these jokes, well, that will almost surely guarantee that you will not find them funny — but perhaps you’ll feel a little smarter. (A more technical description of the principle can be found here.)
Why was Heisenberg’s wife unsatisfied?
When he had the time, he didn’t have the energy; and when he had the position, he didn’t have the momentum.
Heisenberg was out for a drive when a traffic cop stopped him. The cop says, “Do you know how fast you were going?”
Heisenberg replies, “No, but I know where I am.”
Werner Heisenberg, Kurt Gödel and Noam Chomsky walk into a bar.
Heisenberg looks around the bar and says, “Because there are three of us and because this is a bar, it must be a joke. But the question remains, is it funny or not?”
Gödel thinks for a moment and says, “Well, because we’re inside the joke, we can’t tell whether it’s funny or not. We’d have to be outside looking in.”
Chomsky looks at both of them and says, “Of course, it’s funny. You’re just telling it wrong.”
Riddle Answer: Heisenberg (HI’s in BERG)
I’ve been thinking about a lot of things lately…
Instead of having “answers” on a math test, they should just call them “impressions,” and if you get a different impression, so what? Can’t we all just get along?
If you think that dogs can’t count — let him watch you put two biscuits in your pocket, and then only give him one.
If we stop teaching students about numbers less than zero, do you think there would be a positive impact on education?
A prime rib cannot be cut with a steak knife, because it is only divisible by itself and one.
A math professor is someone who talks in other people’s sleep.
A mathematician is someone who will begin a sentence with, “As everyone knows,” and then finish it with something he just learned.
And a famous quotation…
Never trust any quote you find on the Internet.
– Abraham Lincoln, Second Inaugural Address
Inspired by Planet Money’s Pick A Number contest, and buoyed by a story about how NCTM President Mike Shaughnessy recently used my favorite game with a group of students at Albuquerque Academy, I’ve decided to conduct an online experiment using a Google Docs form.
If you’ve got a minute and are willing to participate, read on.
The rules for my favorite game are as follows:
- On a piece of paper, everyone playing writes down a positive integer.
- Show your number to a neighbor (for verification purposes only).
- The winner is the person who wrote down the smallest integer not written by anyone else.
In order for this psychological math strategy game to be any fun, you need one important piece of information — how many people are playing. If played as a solitaire game, you should win every time. But if played with a group of 50, well, some real thought will need to go into your choice. Consequently, I’m going to limit the game to 100 players. (Well, sort of. What I’m actually gonna do is break the total number of responses into groups of 100, and I’ll consider each set as a separate game. So it’s not exactly the same, but this should allow you to play using the same strategy as if you were playing with just 99 other people.)
For this online version, the second step of the rules — show your number to a neighbor — is unnecessary. So all you need to do to play is enter your number. (I’ve also asked for your name and email address, too, just so I can give you proper credit and contact you if you win. But those are optional. If you do supply your email address, cross my heart, there will be no spam or third‑party solicitations.)
[Update] This game was originally run for one week, Nov 28 – Dec 5, 2011. The results of that initial trial (based on 1,042 entries) are available at the link given below. That said, I see no reason to prevent others from participating and, from time to time, I will update the results page to reflect new data.
If you have difficulty accessing the form below, click this link.
I recently read a conference proposal in which the potential presenter declared, “PEMDAS must die!” Upon reading this, I thought, “Hear, hear!” But then the potential presenter claimed, “We should use GEMDAS instead!” Really? Does this presenter honestly believe that changing P (parentheses) to G (grouping) is sufficient to eliminate all the problems students have with order of operations?
I have heard that some teachers use GEMS, where M stands for both multiplication and division and S stands for both subtraction and addition. That eliminates the problem some students have, thinking that multiplication has to happen before division or that addition has to happen before subtraction.
Whatever. From my experience, most of the trouble students have with PEMDAS, GEMDAS, or GEMS typically results from a failure to consider it at all when working with a complex expression. It isn’t the mnemonic.
Here’s a mnemonic for remembering what a mnemonic is: Think about a person with a terrible memory who previously suffered an inflammatory lung condition. Imagine that he often makes up catchy little phrases to help him remember things. Then you can make the association of pneumonic with mnemonic, and you won’t have any more trouble. There, now… isn’t that simple?
The following are some of my favorite mnemonics.
Feet in a Mile
Five Tomatoes → 5 2 M8 0′s → 5,280 feet per mile
Tough Multiplication Fact
5, 6, 7, 8 → 56 = 7 × 8
A Rat In The House May Eat The Ice Cream
Multiplying Signed Numbers
My friend’s friend is my friend (pos × pos = pos)
My friend’s enemy is my enemy (pos × neg = neg)
My enemy’s friend is my enemy (neg × pos = neg)
My enemy’s enemy is my friend (neg× neg = pos)
I am pretty → I = prt
DiRT → d = rt
King Henry Died By Drinking Chocolate Milk
Kilo, Hecto, Deca, Base, Deci, Centi, Milli
(sung to the tune of Yankee Doodle)
Oscar had a heap of apples, sine and cosine tangent
Angle Sum Formulas
Sine Cosine, Cosine Sine;
Cosine Cosine, Sign Sine Sine!
sin (a + b) = sin a cos b + cos a sin b
cos (a + b) = cos a cos b – sin a sin b
e (6 digits)
By omnibus I traveled to Brooklyn.
π (7 digits)
May I have a large container of coffee?
π (3,835 digits)
In 1995, Mike Keith wrote a poem called Poe, E., Near A Raven, which gave the first 740 digits of π (the number of letters in each word indicates the value for that digit of π). It was based on Edgar Allan Poe’s poem The Raven. But some people are never satisfied, so he later wrote the Cadaeic Cadenza, which gives the first 3,835 digits of π.
My life is pretty good. I mean, sure, I wish I were better at Scrabble®, or a little smarter, or a little faster, or a lot better looking. But don’t we all? Overall, I really can’t complain.
For instance, I get to write a blog about math jokes, I get to do math every day for a living, and I know that the proper amount of time t, in minutes, to cook a turkey is given by the formula t = 38 × w2/3, where w is the weight of the turkey in pounds. And all of that is pretty cool.
I’ve not been as happy lately as I probably should be. Thanksgiving seems like the right day to reverse that pattern and recount all the things in life for which a math geek like I should be grateful. Feel free to let me know what you’re grateful for, too.
- For twin sons who love math almost as much as their daddy
- For my sons getting so excited that they speak faster than I can possibly understand (especially when they’re excited about math)
- For a wife who’s willing to tolerate a schlub like me, and who makes it very easy to keep loving her
- For grocery store tiles of the perfect size, so that your natural stride length perfectly aligns with light and dark squares
- For the wonderful safety of numbers
- For getting lost in a challenging problem
- For going to bed with a challenging problem, and waking up with the solution
- For MathWorld
- For cheesy math jokes
- For people who appreciate cheesy math jokes
- For good health
- For Nurikabe
- For friends who know what a scoober, a thumber and a blade are
- For Excel®
- For all of the amazing people at Penn State who are not currently garnering headlines but are doing wonderful things for society
- For eyesight, to see the mathematical beauty in the world
- For teachers, and for anyone else who is willing to share their knowledge
- For disappointment, which reminds me to appreciate all the good things that I already have in my life
- For cell phones and free long distance
- For serendipitously changing the channel to a football game with five minutes left when Tim Tebow has the ball
- For zizzes, and for the word zizz
- For Scrabble® (and more recently Words with Friends)
- For finding a parking spot with time still left on the meter
- For placing the last piece of a puzzle
- For having a really great original idea
- For friends who save me six seconds by pulling a beer out of the cooler and tossing it to me rather than walking over and handing it to me; and, for friends who trust that I’ll catch it
- For clever food names, like the “Muddy Pig” (mini-donut with Nutella and bacon crumbles) at Union Jack Pub in Harrisonburg, VA, or “Devils on Horseback” (chutney-stuffed dates wrapped in bacon)
- For ordering a beer you’ve never heard of, and finding that it’s your new DOC (drink of choice)
- For usually making good decisions
- For having things happen that aren’t all that bad when I’ve made poor decisions
The following story was told to me by Judy White, one of the world’s greatest middle school teachers.
Using wooden cubes, Judy created a set of double stairs. As illustrated below, 2 cubes were required to create 1 step (green), 6 cubes were required to create 2 steps (green and red), and 12 cubes were required to create 3 steps (green, red, and blue).
Judy asked her students how many cubes would be required to create 4 steps, 5 steps, and 6 steps. With a little discussion, her students agreed that 20 cubes, 30 cubes, and 42 cubes would be needed, respectively.
She then asked them to generalize. “Do you see a pattern for how many cubes would be needed to create n steps?” she asked.
One boy responded, “No.”
“There isn’t a pattern?” Judy asked.
“No, Mrs. White,” the boy said, “the answer is no — n × o.”
Not well versed in algebraic notation, the boy used the letter o instead of n + 1.
How great is that?
Speaking of stairs, here’s a math joke involving stairs.
A statistician, a physicist, and an engineer die on the same day. At the Pearly Gates, they are greeted by St. Peter. “To enter Heaven,” he tells them, “you must climb these 1,000 stairs. But while you are climbing, I will read to you from Math Jokes 4 Mathy Folks. If you can make it to the top without laughing, you may enter.”
They start up the stairs. The statistician laughs when he reaches the 47th step. The physicist reaches the 125th step, but he then laughs, too. The engineer, however, makes it all the way to the top.
“Congratulations!” says St. Peter. “Welcome to Heaven!”
Upon hearing this, the engineer begins to laugh.
“What’s so funny?” asks St. Peter.
“I just got the first joke.”