On Saturday 01 April 2006 08:04, Brett Glass wrote: > Why is this spam on the list? > > Also, it's worth noting that the author gives the wrong answer to his > sample SAT question below. The only correct answer is 4 (D), not 5 (E). > I wouldn't pay $29.95 for a book from an author who couldn't give the > correct answer to his own sample problem! > > --Brett
It probably requires Shiller transformations to be applied :) > At 02:12 PM 3/31/2006, Larry Shiller wrote: > > ShillerMath Tidbits: Getting out of the starting gate > > > > [parentzone.gif] > > What to do when you have no idea what to do! > > > > A 1,000 mile journey begins with but a single step... > > Have you ever looked at an SAT question and felt like saying, "Help! > > I'm clueless!"? You're not alone. Even the brightest and best have > > felt the same way. Should this ever happen to you, this sure-fire tip > > will get you on your way to math success. > > An overwhelming problem typically has a lot of information to process, > > and it's not clear how all that information leads to the answer. So > > instead of worrying about how to get the answer, start with the answer > > and work backwards. Let's see how this might work using a sample > > multiple-choice SAT test question: > > If x and y are integers and 5x + 2y = 13, which of the following could > > be the value of y? > > A. 1 > > B. 2 > > C. 3 > > D. 4 > > E. 5 > > This problem falls into an interesting branch of mathematics called > > Diophantine Equations. > > Since this is a multiple-choice problem, one strategy is to try each > > answer to see what happens. For example, if y=1 (choice A), 5x + 2(1) > > = 13; 5x = 11; x = 11/5. But x must be an integer ("If x and y are > > integers..."). So choice A is incorrect. > > If y=2 (choice B), 5x + 2(2) = 13; 5x = 9; x = 9/5. But again, x must > > be an integer so choice B is incorrect. > > After repeating this process for choices C, D, and E, we find that > > only choice E satisfies the condition that x is an integer. > > If the problem requires a student produced response, you know the > > answer will be a number because only numbers can be answers to student > > produced responses: You may try the strategy of picking a number (pick > > a number, any number!) and working backwards as you did above. As you > > work through the problem you'll likely find a way to get the correct > > answer. > > By working backwards you always have a place to start. And that makes > > it more likely you'll have a happy ending! > > > > In the next ShillerMath Tidbit we have another installment in our math > > biography series. In the meantime help yourself to [1]Free Downloads > > on our web site! > > [funnybone.gif] > > > > They Said It... > > "There is no royal road to geometry." Euclid > > "Mathematics is the queen of the sciences and number theory is the > > queen of mathematics." Carl Friedrich Gauss > > "...the greater part of our happiness or misery depends on our > > dispositions and not on our circumstances." Martha Washington > > > > I hope you enjoyed this short math break. > > Sincerely, > > [lssig.jpg] > > Larry Shiller > > Publisher > > Been thinking about ShillerMath but just wanted to start with just one > > year's worth of material? [2]YES! Get individual lesson plan books for > > as low as $29.95! > > Did you enjoy this Tidbit? Please tell your friends, family, and > > fellow parents, teachers, librarians, and local homeschool groups. > > Thank you for [3]spreading the word! > > _________________________________________________________________ > > > > What is ShillerMath? > > ShillerMath publishes research-based homeschool math curriculum, > > music, and manipulatives for ages 4-12, with beautifully designed > > lessons, diagnostic tests with answer keys, catchy math songs, and > > Montessori-based manipulatives. No Montessori or math knowledge is > > required and there's zero lesson preparation - just read what's in > > quotes and you're good to go! Students using this approach > > consistently outperform their peers. Larry Shiller, ShillerMath > > founder and President, has a math degree from MIT. The ShillerMath > > curriculum includes authoritative materials and lessons used by > > thousands of Montessori schools worldwide and is the math curriculum > > of choice for thousands of homeschoolers nationwide. 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