If honor, prestige, and academic satisfaction aren’t enough to coerce you into studying for the SAT, maybe some cold hard cash will. Colleges hand out a huge percentage of their endowment money to award merit, talent, and accomplishments of those students who have dedicated themselves to be great at something. Generally speaking, they do this because they feel that the value of money they invest in you will be returned through alumni donations, enhanced student body, and your telling 10,000 people over your lifetime that you went to XYZ College.

One of the money stats colleges look at is your SAT score. There’s no question about it: Students who have higher GPAs and test scores receive more money. How much would you have to improve your SAT score to be considered one of those students who gets the hook up? What if you made the decision that for 100 days before the SAT you would study 1 hour every day no matter what. Don’t you think you could improve your reading comprehension? Don’t you think you could advance your mental arithmetic skills beyond the norm? Couldn’t you learn all of the math and algebra equations inside and out?

If your combined efforts were able to earn an extra $5,000 per year toward college, that’s worth $20,000 over the course of a 4-year run. Let’s do the math: $20,000/100 hours = $200/hour. Sign me up for that any day! Folks that’s a tremendous amount of value for a very minimal time commitment. There’s not much you can do to earn that kind of money in high school. Somehow spending 20 hours every week earning $8.50/hour (bagging groceries, being a lifeguard, babysitting, being a hostess, etc.) just sounds really unintelligent when you could maximize your time doing other things. If you make $170 (before taxes) in 20 hours, and I earn $200 in one hour – one of us is stupid.

There is nothing wrong with getting a summer job, gaining work experience, or the jobs in and of themselves. But I would question your priorities if you don’t already have the stats to go with the job. Money aside, the benefits of academic pursuit far outweigh learning the PLU codes for broccoli and asparagus – but that is another discussion entirely.

– Andrew Turner

www.thinkarchimedes.com

I just checked today’s College Board Question of the Day (like all of you should be doing on a daily basis) and at first I was overjoyed because I saw what appeared to be a new, non-SAT-esque type of question of which I have not previously seen. For those of you who have been to my first SAT session you know that the entire class is focused on being able to talk about mathematics in plain English. For a moment it looked as though College Board was thinking about beginning to test your mathematical repertoire:

“If equals y squared, which of the following must be equivalent to x?”

They listed five options to choose from, but the answer isn’t the important element of this discussion. The reason I thought this was such a great question is because it forces you to think about mathematics in terms of language. They do not provide a mechanical setup so you cannot solve it mechanically (yet). You have to actually understand what the words mean to even set it up.  In fact, Page 252 in the incredible College Board: Official SAT Study Guide attempts to get this idea across.

Much to nothing, I then realized that I needed to “display images” in the screen settings and up popped a picture of all of the thinking already done for me. I didn’t even have to set up anything – which is all too typical of most SAT Math questions. (Remember, it’s a timed test so they will nearly always give you an easy way out.) Without a doubt those of you who are willing to invest the time to do this in your head will be much farther along than the person who spends five seconds, guesses, gets it wrong, and moves on. Master being a student and you will, yourself, become a master.

– Andrew Turner

www.thinkarchimedes.com

Last year I happened upon a book entitled, Proust and the Squid: The Story and Science of the Reading Brain by Maryanne Wolf. If you have ever thought about how amazing it is that lines and squiggles on paper can transmit ideas and communicate, then this book will take you on an amazing journey through the human development cycle. In reading this book I was reminded how difficult the English language really is. I am going to let Maryanne Wolf lead into one of the most clever and spirited poems I have ever read:

“I take it you already know
Of touch and bough and cough and dough?
Others may stumble, but not you
On hiccough, thorough, slough, and through?
Well done! and now you wish, perhaps,
To learn of less familiar traps?

“Beware of heard, a dreadful word
That looks like beard and sounds like bird.

“And dead; it’s said like bed, not bead;
For goodness sake, don’t call it deed!
Watch out for meat and great and threat,
(They rhyme with suite and straight and debt).
A moth is not a moth in mother.
Nor both in bother, broth in brother.

“And here is not a match for there,
And dear and fear for bear and pear,
And then there’s dose and rose and lose-
Just look them up – and goose and choose,
And cork and work and card and ward,
And font and front and word and sword.
And do and go, then thwart and cart.
Come, come, I’ve hardly made a start.

“A dreadful language? Why, man alive,
I’d learned to talk it when I was five.
And yet to read it, the more I tried,
I hadn’t learned it at fifty-five. “

This doesn’t even touch the tip of what she covers. Definitely get a copy of this book! I found it very relevant and insightful to today’s current education system and as long as you have any sense of appreciation for history you won’t be disappointed.

– Andrew Turner

www.thinkarchimedes.com

Recently our company has been compiling a lot of research and data for a study related to college planning, and today we began to synthesize that data. College planning has only begun to hit the news stands, but over the past 10 years it has managed to creep in under the radar. With tuition inflation rates reaching 16% in some cases, it only takes a few years to crescendo taking most families off guard.

I do not believe the colleges are at fault – to their defense new buildings, technology, and beautification for your sake costs a great deal of money. It is a moot point by now anyway, and the fact of the matter is that we really did go from easily affordable to retirement-hindering in one generation; and now it is an issue that families really ought to deal with. Through even some simple planning strategies they are able to save thousands of dollars today so they can earn hundreds of thousands at retirement.

Anyway, in establishing the framework of our study one of the points we wanted to consider was the actual size of the student body graduating high school and entering college. I know in school often times you wonder why you are even having to learn about even basic mathematics. Like really, if you are going to be a a painter, or a brick-layer, or a writer – why do you even need to know percents? Well, in real life pretty much any project involving business will necessitate the use of fractions to describe the growth or decline of something.

In this case, we really have three groups of students we must study to make this piece complete. We want the number of students in a senior class, the number of students of that senior class who are awarded diplomas, and of those how many move on to college. I won’t go into all the details but to say that according to the United States Census, we are able to construct the following chart (numbers in Millions, “Sen” represents the total seniors in the senior class, “Grad” represents how many graduate, and “Col” represents how many moved on to college.):

Year    Sen    Grad    Col
2004    —-    —-    1.8
2005    —-    2.8     —-
2006    3.18   —-    —-
2007    3.45   —-    —-
2008    —-    —-   —-

There really is nothing I can go on except to see that from 2006 to 2007 the number of seniors rose by 8.5%  (3.18 * 1.085 = 3.45).  In looking at the population rates, they have remained relatively similar from year to year, so I factored the same population growth moving into the future and into the past:

 Year    Sen    Grad    Col
2004    2.70    —-    1.8
2005    2.93    2.8     —-
2006    3.18   —-    —-
2007    3.45   —-    —-
2008    3.74    —-   —-

This gave me a scaling factor that relates the number of students that make it to their senior year without dropping out to the number of diplomas awarded. (95.53%), which ultimately led me to a scaling factor relating to the 2004 number of students who entered college as a freshman (69.74%):

  Year    Sen    Grad    Col
2004    2.70    2.58    1.8
2005    2.93    2.8     1.95
2006    3.18   3.04    2.12
2007    3.45   3.30      2.3
2008    3.74    3.58      2.49

Wow!  This year you will be entering college with 2.5 Million other students!  That’s more than double what I graduated with!  Is it any wonder that colleges are able to charge the astronomical rates that they do?  Your competition is as steep as ever, and this is a real world example (that even relates to you) on why percents might matter.  Study hard and stay right with school.  Life isn’t easy street and your competition is going to include the hundreds of millions of China and India by the time you graduate college.  Good luck.

– Andrew Turner

www.thinkarchimedes.com 

A large part of understanding mathematics is knowing what words mean. There’s no doubt about it, we even explain mathematics using plain ol’ English. I was reminded the other day that the same word can have different meanings to different people. In fact, while I may have an idea clear in my mind, I can be explaining a concept to a student who “knows” the same words that I do, but we are having two entirely different conversations.

As an example I recently heard somebody tell me that he was paid “biweekly.” But I really knew that he was not paid twice per week because that was not the context used. Interestingly enough the word “biweekly” actually does hold dual meanings. It can mean, “twice a week,” or it can mean, “every two weeks.” There are really two things to say about this.

The first is that this is a classic example of where social-wide ignorance has created ambiguity. Truly it is rare to come across a well-spoken individual: One skilled in oratory and definition. Rare indeed is the person who actually says something (just listen to any politician). I am sure all of you can remember a time when you have had a conversation with somebody for several minutes and walked away wondering what it was you just spent all that time talking about. The world is filled with people who can tell you all about something they have no real knowledge of.

Secondly, don’t assume that just because you have heard a word before or seen it in a book that you own the word in your repertoire. One of the only dangers of reading is that when you see a word repetitiously you can get a false sense of confidence in its meaning. The band 311 has a song entitled, “Reconsider Everything” which really sums up the idea here:

“What if the truth is that there is no truth
The only thing I can prove is there is no proof
Don’t be so sure that your source is correct
People believed it before, before they had checked”

Since the foundation of mathematics is arithmetic, it would be great to have an understanding of the different types of numbers that you will be working with in the first place. For lack of a word that actually exists, let us call this realm of all possible numbers the Numberverse.

For the SAT, the Numberverse is only as large as Real Numbers (you will never be tested on imaginary/complex numbers on the SAT). The following diagram I found at wlonk.com:

I like it because it is simple and does a great job at showing examples within each set. However, you will notice that in Natural Numbers it contains the value zero. I picked this as an example because it makes the assumption that zero is a Natural Number. I have always been taught, and continue to teach, that zero is NOT a Natural Number because I cannot actually possess zero of something. I simply do not have it. I have always called the set containing zero, “Whole Numbers” and showed Natural Numbers as a subset of Whole Numbers.

Even in mathematics there are philosophical debates at every level about simple things like this. All I can tell you is to assume nothing and Reconsider Everything.

– Andrew Turner

www.thinkarchimedes.com

The SAT is unlike any other test students are asked to take. While some of the same ideas from mathematics and English may apply, those ideas are not, necessarily, what students are being tested on. The College Board is not so concerned about a student knowing thousands of Latin roots or all of the formulas associated with finding area, volume, or distance; but rather they are interested in knowing how well a student understands an equation or algebraic concept. Memorization of equations alone will not help students raise their scores into the 1200+ range on the SAT.

A more accurate description of what is being tested on the SAT would be: Logic, Deductive Reasoning, and Reading Comprehension. Obviously these are typically not class titles offered in high school since they are actually intelligences and not simply subjects – more a way of thinking, like knowledge in motion rather than a regurgitation of facts.

Howard Gardner has shown that each of these intelligences can be grown and developed just like physical muscles. If a man wants to get stronger, he has but to make the decision that he will workout regularly and take control of his diet. If he commits to this end then he will, most certainly, get stronger and increase his muscle mass. As the adage goes, “No pain, no gain.”

Students will find it very beneficial to put down the xBox, shut off the boob tube, and begin to actively engage their minds in logical exercises such as chess, Minesweeper, MENSA puzzle books, spades, or any other game that requires logic, strategy, or probability to win. Obviously if a man desires to build muscle mass but chooses to not workout he will remain small, weak, and fragile. Intelligence, like ignorance, is a decision.

– Andrew Turner

www.thinkarchimedes.com

Three hours and forty-five minutes is a long time to go without food if you are exerting yourself physically or mentally. Food is the fuel we use to move ahead and the SAT certainly takes a lot of mental energy. You should definitely plan ahead to ensure you have a nutritious breakfast and some sort of energy snack handy during the SAT.

I suggest waking up early after going to bed early the night before the test. Having a breakfast that isn’t loaded full of sugar, grease, or fats is absolutely essential to supercharging your body with the right stuff. I suggest having a bowl of oatmeal with raisins, yogurt and granola, a veggie omelet, fresh fruits, whole grain cereals, eggs and toast, or anything of the like. You will want to avoid pancakes, french toast, syrup, deep fried foods, or anything that a tree-hugging hippy wouldn’t eat. Granulated sugars are not what your body needs first thing in the morning.

Also, don’t go crazy with the coffee! I highly recommend having a weak or dilluted cup of coffee or tea, but nothing very strong where you will be running to the restroom every ten minutes. You want to have just enough to waken the mind, but not so much that you burst your bladder. Be sensible and you won’t have anything to worry about.

Once you are in the test it might be a good idea to bring a trail mix or a couple granola bars. You want to avoid sugary foods and greasy snacks like chips or anything of similar nature. Moderate to high amounts of caffiene and sugar are two major contributors in the lack of ability to pay attention.

It wouldn’t hurt to go for a morning jog or bike ride either. There are been many studies relating exercise to increased brain function and in my personal experience I have found that exercising regularly helps me to clear my mind and get ready for the next project.

– Andrew Turner

www.thinkarchimedes.com

Typically you will be taking the SAT at your high school or location college. Regardless of where the SAT is offered, however, you will want to pick a site where the people running the show are on top of their game and they know exactly what they are doing. Don’t be afraid to ask around and find out if people have had problems at the testing site you are thinking about attending. Also, you will want to be absolutely certain that you know where your testing site is located. It might even be a good idea to visit a testing site before test day if you have never been before.

Once you arrive (which, of course, will be early) and you walk into your room you will want to avoid seats that are near windows or have overhead vents blowing air directly onto your seat. Also, there is something to be said for reducing the amount of visual distractions you might encounter. Sitting in the front of the room will help you to avoid checking out the the dude with the six pack or the chick wearing booty shorts. Remember, you want a seat where you have the best chance to focus all of your attention every second on the questions at hand.

Make sure you know where the restrooms are located in the event of an emergency, and if the only seats available are unacceptable to you do not be afraid to request an alternate room or that the physical location of the desk within the room be changed. You want to give yourself every opportunity to succeed.

– Andrew Turner

www.thinkarchimedes.com

There is nothing more distracting than chilly air sweeping across your face from the overhead vent while you are taking the SAT. Temperatures in the room are supposed to be around 70 degrees, but the temperature is measured and adjusted based upon the location of the thermostat and may actually vary depending upon where you sit in the room. You may want to consider each of the following when picking out your seat:

- Sitting near a vent may be a disadvantage if the airflow is pointed in your direction.
- Taking a window seat might be a great idea during a normal class, but in the summertime the sun may beat on your desk causing you to be too warm, and in the wintertime windows provide poor insulation from the outside cold.
- Wearing sandals should be frowned upon. Wear comfortable tennis shoes or something of the like that will keep your feet covered, but that you could easily kick off if you wanted your feet to breathe easy during the test.
- Wear layered clothing! You want to be able to easily take off a jacket or pullover in the event that you suddenly get too warm in the event that you get nervous, the AC breaks, or any other reason.
- Avoid itchy clothing like wool pants or something of that nature that might cause any sort of irritation. Although these clothes might look great, your goal is not to win a fashion show – it is to be very comfortable and give yourself every advantage possible during the SAT.

Keeping these small things in mind may save you some irritation and give you the every opportunity to focus all of your attention on the question at hand.

– Andrew Turner

www.thinkarchimedes.com 

Ask 1,000 students if they know what a number is and you will get 1,000 affirmatives. Ask the same students to tell you what a number is and you might get 500 correct answers. Now ask those students if they can properly dissect a number and explain it piecewise…Sadly, in the modern school curriculum’s race to Calculus many students cannot answer the most fundamental questions about mathematics. This will serve as the second step in understanding the nature of fractions and why they cannot be done away with.

Every number has five components: a base (b), a coefficient (c), a divisor (d), a power (p), and a root (r).

As a simple example, 24 is a number: It exists as an independent, specific, and unique value and has eight “factors” or “numbers that are evenly divisible” into 24: 1, 2, 3, 4, 6, 8, 12, and 24. The amount of 24 is the same as 1 x 24, and this is such an important idea in mathematics that we have a name for it: The Multiplicative Identity. So whereas we started with 24, now we have:

We call a number that sits just out front of the a set of parenthesis a “coefficient”. If you break down that word it gives you more of a clue to what it means: “with” + “efficiency”. It is a simplified way of dissecting and thinking of a number. As an example, rather than thinking of the number 24 as a solid, concrete value of “24″ it might be better to think of it as 8 x 3. In this case, I could think of it two different ways: 8(3) where 8 is my coefficient and 3 is the base number or 3(8) where 3 is my coefficient and 8 is the base number. This is all, of course, very simple – and that is exactly the point. This is the first step in understanding what numbers are. We have covered 2/5 of the components of a number which brings us to our third idea: the divisor.

Any number you can imagine is a fraction, because at the very least every imaginable value is always “over 1″. The number 5? It’s really 5/1. The number 14? It’s really 14/1. -8? You guessed it: -8/1. Even fractions (i.e. 3/5 = (3/5)/1), constants (i.e. π = π/1), imaginary numbers (i.e. 2i-3 = (2i-3)/1), or even algebraic variables (i.e. x = x/1) may ALWAYS be written as [insert every number you can imagine]/1. In the case of our number 24, it is equivalent to write it as:

1(24)
—–
1

Symbolically I might code this as:

c(b)
—–
d

where d = divisor

Even the obelus (“old school” division sign: ÷) looks like a fraction! Mathematicians are so literal, but that is the advantage of mathematics! There really is no guessing involved. The study is filled with very simple ideas which, when put to use on a test like the SAT can turn out to be very powerful…which reminds me.

The last two components are the power and root. These deserve their own discussion so I won’t get into them right now, but the general philosophy is that powers are a quick way to multiply in the same way that multiplication is a quick way to add. Roots are not the “opposite” of powers because the statement, “roots are a quick way to divide in the same way that division is a quick way to subtract” is not correct. Roots are better defined as “inverse roots” than “rooted in subtraction.

What is important is to walk away understanding another reason why not teaching fractions in school is just a bad idea. Contained within the very definition and understanding of a number is the fraction.

– Andrew Turner

www.thinkarchimedes.com