Date: 1 Apr 2006 03:28:18 -0000 From: Larry Shiller <marketing@shillermath.com> To: freebsd-chat@freebsd.org Subject: Your ShillerMath Tidbit Message-ID: <20060401032818.27086.qmail@borg.phpwebhosting.com>
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ShillerMath Tidbits: Getting out of the starting gate
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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!
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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,
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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. Visit the
[4]ShillerMath site for all the details on this proven and amazingly
effective product.
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