Snap a Picture, Get a Result


There’s a new app out there that allows you to take a picture of an equation with your smartphone, and the app will solve it. Before you start grabbing your phone to download it, here are three important things to consider.

1. It’s a Tool, Not a Magic Cure- Much like a calculator, this app is a tool that can be very useful when used correctly and under the right circumstances. Need to figure out whether the giant TV you want to buy will fit on the wall space you have? Sure, jot the equation and solve away.Trying to figure out how many jelly beans are in the jar to win a prize at the local fair? Write out an equation for your volume estimates and snap the picture. Trying to learn how to solve quadratic equations? Stop right there. If you don’t have the proper underlying knowledge first, you aren’t just taking a shortcut, you’re potentially setting yourself up for disaster.

2. Technology isn’t Perfect- Neither are we! The problem with that combination is that we often expect technology to be perfect and that can lead to bad consequences. If you attempted to type 9 + 2 into your calculator and the result came up 101 you wouldn’t take that answer as truth. You’d recognize that the sort of answer you should get should be around 10, and you might even be able to work backward to find that the mistake you made was entering 99 + 2 on accident. However, if you’re snapping a picture of an equation you don’t really understand and the software interprets the numbers wrong, or you don’t take the picture correctly, you may end up proceeding off a bad result!

3. You’re Never Going to Be Able to Use That on Your Test- We want to test the processor that’s mounted above your shoulders, not carried in your pocket. Using a shortcut when time is of the essence makes sense, but knowing that you don’t need the shortcut when it comes right down to it is even better.

 A Note on Perspective


I know that we spend a lot of time here talking about improving your scores as much as you possibly can and pushing small advantages as much as you possibly can. But sometimes it pays to get a little perspective.

I was recently over at my parents’ house cleaning out the last of my old stuff from the garage. I came across the printout of my PSAT results. This immediately triggered two thoughts:

1. I can’t believe I saved this

2. I wonder what I got

That second thought is the one I want to focus on right now. It’s interesting that someone who is immersed in the test-prep industry doesn’t even know what he got on the PSAT. And that’s completely okay. That score and that number didn’t define my life. It was merely a means to an end. A stepping stone toward the next phase of life. Fifteen years later those results have become irrelevant in my life.

I have some students who obsess about every question, every point, every wrong answer. Sometimes you just need to step back and take a wider view. Absolutely you should make every effort to do your very best work. But occasionally you need to consider what’s really going to matter 10 years down the line.

Keep working hard, but keep perspective!

 Naming the Numbers


When getting back to math-based questions after it’s been a while since math class, many of us need a refresher on some key terms that are used and what they mean. Here are five that you’re likely to come across and a quick definition to refresh your memory.

1. Integer- Probably the most commonly used number term, integer is a commonly confused term. I like to say that if you were going to draw a number line, an integer is anywhere you would draw a dash, including zero and negatives. So, -2, -1, 0, 1, 2, and 3 are all integers, while 1.4 and 2/3 are not.

2. Whole Number- While this term isn’t commonly used in tests, it’s one you’ve heard before and it can easily be confused with the term integer. While there is a great deal of overlap between the two groups, the group of whole numbers does not include negative numbers. So, while 0, 1 and 2 are both integers, -3 is an integer but not a whole number.

3. Multiple- A number is a multiple of another number– for instance 8– if it is the product of that number and an integer. So, 24 is a multiple of 8 because 24= 8 * 3 and 3 is an integer. Similarly, 0 and -16 are multiples of 8 because they are the product of 8 and an integer (8 * 0 = 0, 8 * -2 = -16). 4 is not a multiple of 8 because it is the product of 8 and a non-integer (8 * 0.5 = 4).

4. Factor- A factors are the integers you multiply together to get a number. They come in pairs. For instance, if we were  factoring 18 we would see that 6 * 3 = 18, so both 6 and 3 are factors. So are 9 and 2, and 18 and 1. Factors can be negative as well, although that is rarely tested.

5. Prime Numbers- A prime number is a number whose positive factors are only 1 and itself. Since no integers other than 1 and 13 divide evenly into 13, it is prime. Common misconceptions about prime numbers are than 1 is prime (it isn’t), and that all prime numbers are odd (2 is a prime number).

Hopefully that served as a good refresher!

 You’re Smart, But…


I was watching American Ninja Warrior with my wife the other night. It’s the American version of a Japanese show that has contestants race through a ninja-inspired obstacle course. The obstacles require incredible amounts of upper body strength, balance, agility, grip strength and creativity. No one has been able to complete all four stages of the course over the several seasons the American version has been on the air.

The difficulty of the task and the possibility of big prize money attracts competitors from all walks of life. From the enthusiastic fan, to the experienced rock climber to the gym owner or the professional free runner, they all bring their experiences and hopes to the course.

In a recent episode, some of the top rock climbers in the world came to take a shot at the course. These are guys that have all of the physical tools that it takes to complete the course. They have amazing upper body and grip strength, and the kind of agility and athleticism it takes to be world-class. And yet, they struggled on some areas of the course.


Even though these athletes had amazing skills, they hadn’t yet adapted those skills to the particular techniques and challenges that the course put in front of them. Sure, rope climbers spend a lot of time on ropes, but the rope jungle maze was trouble because they weren’t used to ropes that moved or dropped in the certain ways that these ropes did.

Standardized tests like the ACT, SAT, GRE and GMAT offer their own types of rope jungles. You can have every single skill that would be necessary to conquer the test, but if you don’t have the particular techniques necessary that might not be enough.

You’re smart, but are you ready for this jungle?