Found by Timon Piccini:
Any questions?
Well of course there are. He sets up the 3-act #wcydwt structure here. Check it out. Great stuff.
Obfusticated Mandelbrot Set
Coolest thing I’ve seen in a while: High Resolution Mandelbrot code in Python.
The following Python script, on the other hand, begins as ASCII art:
It renders the Mandelbrot set as a full-color, anti-aliased, 1500×1000 image.
Fantastic. Notice that the code also looks likes the mandelbrot set. A true accomplishment with python being so fussy with indentation. Also neat posters with the Mandelbrot set and the code on one poster are available.
Little Gauss and the Dividing Time Puzzler
I gave this problem to the Precalc Honors class, right before their lunch (the block is split into two parts). A couple of them came back with the solution, but most had chosen to eat and socialize (how dare they!). An epiphany hit me when I saw how a student had started to solve the problem. He added 1 + 2 + 3 + 4 + 5 + … + 11 + 12 to find out if the sum is divisible by 3 or 4.
My brain found the link to one of my very favorite math tricks / math stories: Little Gauss finding the sum of all the integers from 1 to 100.
So I put the following up on the board:
S = 1 + 2 + 3 + 4 + 5 + ... + 98 + 99 + 100. Find S.
Naturally a couple of the kids take the calculators out, so I go over and swipe the calculator out of their hands. I go through the whole story: An elementary teacher needed some quiet time to get stuff done, so the teacher asks the class to add all the integers between 1 and 100. Little Carl Gauss walks up in under a minute with the answer. Teacher is losing patience with this know-it-all, and asks him to add all the integers between 1 and 1000. Gauss strolls up in under a minute with the answer again. (Yes I dramatize the story. Sue me.)
So how’d he do it?
“You guys agree that I can write the numbers backwards and the sum will be the same right?”
S = 1 + 2 + 3 + 4 + 5 + ... + 98 + 99 + 100
S = 100 + 98 + 97 + 96 + 95 + ... + 3 + 2 + 1
What about if I add from top to bottom, what do I get?
2S = 101 + 101 + 101 + 101 + 101 ... + 101 + 101
How many 101’s is that?
2S = 101 x 100
…
S = 5,050
Go on to ask them what is the sum of all integers between 1 to 1,000 and find the following sum: 2 + 5 + 8 + 11 + … + 98 + 101.
Dividing Time Link
So back to the puzzler. Find the sum of the clock digits:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 (then reverse them)
12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
How many pairs (after you divide by the 2)?
6 pairs.
So how many divisions of the clock by the two lines?
4 divisions wouldn’t work, so 3 divisions.
What are the divisions? Lets keep the pairs together so the sums are equal in each section.
Neat:
Cartalk Puzzler – Dividing Time
From Cartalk.
Dividing Time
RAY: Draw a clock face on a piece of paper. Using Arabic numerals put the appropriate numbers at 12, 1, 2, 3 and so on.Now, somewhere on the clock face, draft two lines. In doing so, you’re going to divide the clock face into segments, which contain numbers.
TOM: Do the lines have to go from one edge of the clock face to another?
RAY: Yes. So, when you draw the lines, you will wind up with either three or four segments of clock face. If the lines intersect someplace, you will wind up with four sections. If they don’t intersect, you will wind up with three sections.
The question is: Where do you draw the lines so that the sum of the numbers in each section is equal?
This one should get your students watching the clock that much closer.
Twitter Graph Story #anyqs
To no one surprise, [removed] was lowest on Monday afternoons and through Tuesday, the beginning of the work week, and rose later in the week, peaking on Saturday and Sunday. The pattern on weekend days was shifted about two hours later — the morning peak closer to 9 a.m. and the evening one past 9 p.m., most likely because people sleep in and stay up later — but the shape of the curve was the same.
What subject were they studying?
Original image and article.
Cartalk Puzzler: An Interesting Series of Numbers
When my kids were in school, they, like all the other kids I guess, had to learn their numbers. So each day for homework, they would bring home a list of numbers on a piece of paper, and they were asked to write out the letters that spelled that number, right next to each of them. So the number seven would be there, there’d be a blank space, the kids would have to write S – E – V – E – N. And of course they were also asked which numbers were spelled out by the various combinations of letters, so they’d see S – I – X – T – Y and write Sixty, etc.
One day, son number two presented me with a list of numbers and he said, “These numbers are different. There’s something special about them.” Here are the numbers:
Four, Six, Twelve, Thirty, Thirty Three, Thirty Six, Forty, Forty Five, Fifty, Fifty Four, Fifty Six, Sixty, Seventy, Eighty One, Eighty Eight, Ninety, and a Hundred.
Now there are no other numbers between one and a hundred inclusive that share this same characteristic. There’s something unusual about these numbers that son number two figured out. And I’ll give you an additional hint that order does not matter. The best hint is that he determined that these numbers should be on the list perhaps from his homework assignment.
What is special about this list of numbers?
Well?
Update (9/25/11): Answer is up.
Drag Race #wcydwt
Act 1
http://vimeo.com/29051572
What questions do you have?
Act 2
- Talk about why the highest horsepower might not be that fast (10,000 horsepower vehicle that you could beat with a Toyota Prius).
- Ask what other things are important for going fast. Is the lightest vehicle always the fastest (Would you want this 326 pound vehicle in a drag race)?
-
Have the students record the type and horsepower for each car.
Make sure they make a prediction of the fastest car by putting their initials next to their guess.
- Have the students do some research to find the curb weight for each car.
- Discuss how we could use this information to make a prediction of the fastest car. How do we compare numbers (+,-,*, or / ?). Do we want horsepower or weight on top of the fraction? Is a higher or lower number better?
Act 3
http://vimeo.com/29054710
1st Day for Intro to Programming: Lightbot
I forget who introduced the Light-bot game to me, but thank you.
I got the link from Hélène Martin. Much thanks!
First day went excellent in Introduction to Programming class. “We get to play a game?”
Introduction to loops, functions (methods), and debugging all on the first day, without me saying a word? Yes please.
Side-question: Are there were parts of math that are this easy to introduce through a fun game?
Cartalk Puzzler: License Plate
Deep Tanning
RAY: You’re driving past a high school parking lot on a fine spring afternoon in Our Fair City, watching the kids try to do wheelies with their parents’ station wagons. You happen to notice a car with an interesting license plate. It reads TAN 270. What make of car is it attached to?
Love it.
Responses to NYT article on “How to Fix Our Math Education”
Original on How to Fix Our Math Education article is found here.
Some great responses were mailed in.
Sol Garfunkel and David Mumford are right to observe that the everyday usefulness of our high school math curriculum leaves much to be desired. But since when did practicality become the only goal of our educational system?
Should English classes dispense with classic literature in favor of company annual reports? Should music and art be jettisoned to make way for classes in accounting and tax?
DANIEL ALTERBAUM
New Haven…
Examples of applied mathematics are critical, but to gear education toward any outcome is coercive and damaging. Instead, teachers should aim to give children all the tools they need to apply mathematics, and knowledge in general, in the way they choose.
JESS COLEMAN
New York…
Just as we teach students the beauty of poetry, we should teach students the beauty of mathematics — a beauty that does not depend on calculating a gear ratio or estimating a marginal profit.
ANDREW M. H. ALEXANDER
Oakland, Calif.…
You do not study mathematics because it helps you build a bridge. You study mathematics because it is the poetry of the universe. Its beauty transcends mere things.
JONATHAN DAVID FARLEY
Orono, Me.
Some important thoughts to keep in mind for the upcoming school year.