If:
2 + 3 = 10
7 + 2 = 63
6 + 5 = 66
8 + 4 = 96
Then: 9 + 7 = ????
It took me, what? 15 seconds? 30 seconds? 3 minutes?. It was fascinating how my subconscious grasped the answer, but then it took 1/4 second to 2 seconds for me to identify explicitly the pattern needed to get the answer and to put the answer into words.
(HT: my brother)
On the Internet there is a plethora of practice material for the math portion (and science, reading, etc.) of the TAKS test. The Texas Education Agency, TEA, has made available pdf files of some recent tests and also has a number of tests archived. This material would be good for preparing for the TAKS test and for practicing algebra and geometry.
Pearson has made available some pdf files of study guides and has some online, interactive study guides. (If those links do not work, start on the TAKS Study Guides page, then click on “Interactive Study Guides,” or click on “Printed Study Guides” followed by “Study Guide PDFs.”)
Mathbits has some good information on how to use the TI-89 and how to use the TI-83/84. Valuable stuff for those taking math or getting ready for the SAT or ACT.
Update (1-21-10, 9:32 AM): I highly recommend that you be fluent with a graphing calculator for the tests. The test makers might say that the calculator might help, might not, and might slow you down, but they are talking to a general audience, including people who do not know how to use a calculator, people who are trying to use one they are unfamiliar with, and people who do not know how to use the graphing calculator effectively on the tests. The fact is that the calculator can make some of the questions, even some of the ones rated “hard,” virtually brainless; it makes it possible to get some easy points on the SAT, ACT, TAKS, and AP exams.
Differentials, an aspect of calculus, are important for working with errors of measurement and the propagation of error.
Dr. Donald Simanek discusses their use in Error Calculations Using Calculus. Dr. Mike Coombes discusses their use in Error Propagation Using Calculus Solutions. And Dr. Rhett Allain uses them in the interesting Error Propagation And the Distance To the Sun.
I have not read the articles/essays closely, so I don’t know if there are any mistakes in them. But they illustrate the general idea.
I received this in an email from a parent of a student I have tutored:
New IEEE standard values:
Non-Conventional Units of Conversion
Ratio of an igloo’s circumference to its diameter = Eskimo Pi
2000 pounds of Chinese soup = Won Ton
1 millionth of a mouthwash = 1 Microscope
Time between slipping on a peel and smacking the pavement = 1 Bananosecond
Weight an evangelist carries with God = 1 Billigram
Time it takes to sail 220 yards at 1 nautical mile per hour = Knotfurlong
16.5 feet in the Twilight Zone = 1 Rod Serling
Half of a large intestine = 1 Semicolon
1,000,000 aches = 1 Megahurtz
On p. 143 of Old textbooks: spelling, grammar, reading, arithmetic, geography, American history, civil government, physiology, penmanship, art, music, as taught in the common schools from colonial days to 1900 ((c) 1961, University of Pittsburgh Press, printed by American Book-Stratford Press, Inc.), author John Alfred Nietz wrote:
The first seven arithmetic textbooks published in the Americas were in Spanish, four in Mexico and three in Lima, Peru. The first mathematics textbook was the Sumario Compendioso (1556) written by Juan Diez Freyle, and the first separate arithmetic was the Arte Para Aprender Todo El Menor Del Arithmetica by Pedro de Paz (1623), both published in Mexico. Incidentally, the first university in America was founded in Mexico by 1554, in which later the first lecturer in mathematics was Juan Negrete.
Wow. Fascinating.
In “Fables of the Reconstruction (Or, How to Make Your Own Hockey Stick),” the blogger Iowahawk says:
What follows started as a comment I made over at Ace’s last week which he graciously decided to feature on a separate post (thanks Ace). In short, it’s a detailed how-to-guide for replicating the climate reconstruction method used by the so-called “Climategate” scientists. Not a perfect replication, but a pretty faithful facsimile that you can do on your own computer, with some of the same data they used.
A good read. And fun with stats. Check it out. (HT: Geoffrey K.)
On a related note, read “The ‘Science’ of Global Warming” (Macleans.ca, Thursday, December 3, 2009 10:00am) by Mark Steyn. He writes:
Yet perhaps the most important revelation is not the collusion, the bullying, the politicization and the evidence-planting, but the fact that, even if you wanted to do honest “climate research” at the Climatic Research Unit, the data and the models are now so diseased by the above that they’re all but useless. Let Ian “Harry” Harris, who works in “climate scenario development and data manipulation” at the CRU, sum it up. Mr. Harris was attempting to duplicate previous results—i.e., to duplicate all that science that’s supposedly settled, and the questioning of which consigns you to the Climate Branch of the Flat Earth Society. How hard should it be to confirm settled science? After much cyber-gnashing of teeth, Harry throws in the towel:
“ARGH. Just went back to check on synthetic production. Apparently—I have no memory of this at all—we’re not doing observed rain days! It’s all synthetic from 1990 onwards. So I’m going to need conditionals in the update program to handle that. And separate gridding before 1989. And what [#%] happens to station counts?
“OH [#&] THIS. It’s Sunday evening, I’ve worked all weekend, and just when I thought it was done I’m hitting yet another problem that’s based on the hopeless state of our databases. There is no uniform data integrity, it’s just a catalogue of issues that continues to grow as they’re found.”
You cannot do good statistics with bad data. Nor can you do science. (HT: Harry B.)
In stats and science, reality must come first.
I tutored a fifth grader on 11-17-09. We did some work on numbers and the decimal system.
Me: “So do you understand this about the way decimals work?”
Student: “I do the way you explain it.”
Logic. Gotta love it. Theory and practice unite.
One of my favorite phrases is “Q.E.D.” It means:
which was to be shown or demonstrated (used esp. in mathematical proofs).
1810–20; < L quod erat dēmōnstrandum
QED. Dictionary.com. Dictionary.com Unabridged. Random House, Inc. http://dictionary.reference.com/browse/QED (accessed: November 16, 2009).
Breakfast (October 30th) at 10:45 AM: a pound of shrimp sauteed in lots of butter (then sprinkled with chipotle powder and black pepper) and some homemade guacamole. I ate 30 to 45 minutes after 15 to 30 minutes of “hunting and gathering:” a little kettlebell work, some sit-ups, jumping up the stairs, and crawling (bear, crab, and push-up).
Exercise that week: made it to the gym Tuesday for a good half hour, then went for a mile to mile and a half walk outside (without a shirt, to get some good vitamin D; and barefoot, to maintain a good posture and reinforce good body dynamics); Wednesday I rode my horse for an hour and a half; Thursday I went to the gym for a good half hour.
Powered by WordPress
