Naming the Numbers

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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…

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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.

Why?

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?

 Happy Labor Day (It’s a Milestone)!

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On the first Monday in September, Americans celebrate Labor Day. It’s a day to celebrate work and workers. It’s a time to pause, and then get back to work.

For students it’s often the first day off in the school year, or a last hurrah before school starts. For most of America it’s regarded as the unofficial end of summer.

For many people Labor Day is a milestone day. It’s a way that we mark time and keep track of its passage. And milestone days are important.

In your progress toward your test you undoubtedly have one milestone day on the calendar: test day. However, there’s definitely room for others. Milestones are important because they help you set goals and monitor your progress. Here are 5 examples of milestone days you should consider adding to your study calendar:

1. Goal-Setting Days- One of the most important days to put on your schedule is a goal-setting day. It’s a time to sit down and access what it’s going to take to get you where you want to go. It’s a day to be excited about what’s to come.

2. Review Days- The companion to every goal-setting day is a review day. It’s a chance to give yourself accountability and see whether you’re making the progress you set out to make. If you’re not meeting the standards you set out for yourself, it’s a chance to make changes so that your next review day is more satisfying.

3. Practice Test Days- You need to test yourself on a full scale test before the real thing. These are dates you want on your calendar so you can look forward to them, anticipate them, and feel a little bit of the anxiety that test day will bring. It’s healthy!

4. Rest Days- It’s important to take a break every once in a while to make sure that you’re keeping good balance in your life. Rest days are a great motivator because they can keep you going strong knowing that relief is in sight!

5. Dress Rehearsal Day- One week before the test it’s important to have a practice test that you treat like the real thing. Get up at the same time, wear the same clothing, eat the same foods, etc. Simulate the real test day experience as much as possible. It helps prepare you for the real things.

Put these milestones on your calendar to give you something to look forward to and keep working hard!

 Bloody Lips and Second Chances

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I had my biggest parental fail yet last week. I was in the process of unbuckling my son out of his high chair when I got distracted and turned my head. When I turned back, he’d tumbled forward and taken a spill. He and I were both pretty shaken up by the whole experience, but he’s on the mend and will be just fine.

In the days following, I’ve been a little paranoid and extra careful. But I wonder: had I left him in that dangerous position before? It could be that this was the first lapse I’d had and it turned out poorly, or it could be that I’d made this mistake before and gotten lucky because nothing bad had happened.

I don’t have a nanny cam running in my home 24-7 to monitor my parental performance, so I can’t really know the answer to that question. But if I did, this accident might not have happened. There’s a benefit to being able to review your performance, even if the end result turned out just fine.

Let’s carry that lesson over to the test prep world. Sure, it makes sense to spend most of your review time going over problems you missed so that you’re better able to understand what went wrong and how you can do better next time. However, it does make sense to spend some time going over the questions you get correct as well. At minimum it can reinforce good habits, and potentially you may spot mistakes that didn’t end up costing you a correct answer on this problem. However, you may not be so lucky next time.

For instance, if asked for the square root of 9, and given an answer choice of 3 you won’t be penalized for forgetting that -3 was also an option. However, if you review that correct answer and realize your mistake you’re less likely to make the same mistake where your error is the difference between a right answer and a wrong one.

As I’ve seen this week it’s helpful to learn from a wrong choice, but it’s even better if you can learn without suffering the consequences.