When I used to tutor SAT prep, it was nails on a chalkboard to me when students said with despair, “I’m just bad at math.”
“Right,” I would say. “You’re probably also bad at building bridges, dancing the lead in Swan Lake, and performing open heart surgery. Why? Because you haven’t properly learned and practiced how to do those things. Just because you don’t excel at something now does not mean that you are incapable of doing so. Math can be really tricky, but I know that if you change your attitude and put forth the effort, it will get a lot easier for you. Besides, the cool thing about the SAT is that it really has little to do with how good you are at math. Rather, the SAT tests your math habits.”
I have worked with several students in the McLean and Great Falls areas who are phenomenal math students, taking the most challenging courses offered and garnering top grades, but who started out really struggling on the math sections of the SAT. The reason for this is quite simple. SAT math is not difficult, but determining which math you need to do on the SAT is hard, and it takes a lot of practice to perfect.
Consider the following problem to illustrate this idea:
Each of 5 people had a blank card on which they wrote a positive integer. If the arithmetic mean of these integers is 15, what is the greatest possible integer that could be on one of the cards?
Right away, the math prodigy student taking multivariable calculus begins formulating equations at near calculator speed to maximize one of five variables. Utter madness.
Rather, a question such as this requires a bit of logical thinking and proper setup. Good SAT students contemplate before acting. They figure out exactly what is being asked of them before they jump in to start solving an imaginary math problem of their own creation.
For this problem, a great SAT student would think like this:
1. Ok, I have 5 different positive integers whose average equals 15.
2. This means that when these 5 integers are added together and divided by 5, the result is 15. (A+B+C+D+E) / 5 = 15
3. By multiplying both sides of this equation by 5, I now know that my 5 integers added together equal 75. A+B+C+D+E = 75
4. I need to figure out the highest value that one of these integers can be. Let’s say I want E to be my highest value.
5. What I know about this simple addition equation (A+B+C+D+E = 75) is that if I want to make E as high as possible, then A, B, C, and D need to be as low as possible.
6. The problem tells me that each card contains a positive integer. It does not, however, say “different” integer.
7. The lowest positive integer is 1. Therefore, I will make A, B, C, and D all equal to 1. 1+1+1+1+E = 75
8. Now I have a simple algebra problem where I need to solve for one variable. I subtract 4 from both sides to arrive at E = 71.
This process was not difficult. There are no differential equations or advanced number theory involoved. Students often get caught up in the idea that they need to be using specific formulas to solve problems and that plugging in numbers and assigning variables are taboo. However, these beliefs will do more harm than good. You need to have the right systems in place and you need to train yourself to avoid math in favor of logical reasoning, counter-intuitive as is may be.
To improve your math score, stop worrying about math! Instead, focus on SAT math (there is a difference!) and the strategies you need to conquer it. There are countless materials and resources available to help you accomplish this. Should you need guidance, please email me at firstname.lastname@example.org.