How to Stop Making Careless Mistakes on Math

Initially relaxed, you get back your math test but there are red marks on the page. You are shocked because you didn’t expect to lose points on the easiest parts of the test. How often does that happen to you? If this is not unusual, then this article is probably very helpful for you. Careless mistakes on math tests result in losing a few points, which may ultimately put a student’s grade on the border between an A and an A-. What was said previously may have been an exaggeration, but these small actions may have a big impact on a student’s grades or score on a standardized test. Without further ado, the process used to prevent making careless mistakes will be revealed. The process doesn’t guarantee all the future careless mistakes will be eliminated. However, the process will lessen the chance of careless mistakes to occur by a substantial amount. Using this method ever since high school has really helped me notice what I did wrong on math tests before time is called.

The method I use is the numbered box method. This method is not created out of my own imagination; in fact, the numbered box method was mentioned in a popular Art of Problem Solving article. My article will be different from the one on AOPS as I will include other details.

Before I start the numbered box method, I read the question carefully line by line and circle or underline what I am being asked. Reading the question carefully is pretty crucial on SAT math because they ask you very specific values. I may need to write down briefly what is the concept that is being tested. Then, I write down equations that are related to the concept. Writing down formulas are pretty helpful because it prevents you from doing mental math. For visual math problems, drawing a graph or picture is highly recommend because it isn’t good to do all the thinking in the brain.

In the numbered box method, you number the steps for solving a problem with a brief description in 1-3 words about the step. Then, write neatly line by line for solving the problem that involves calculations. When you complete the first step, you should box the first step and then make a new box for your second step. Keep doing this until you finished the math problem. Although it may sound tedious to box your work and write the steps, I find it to be a very good way of organizing your work and forcing yourself to not have messy handwriting. If I write messy, the xs look like ys, and then the 0s look like 9s. Another important thing about handwriting is to not have small handwriting that is crammed together. Maybe I am wrong (as I cannot speak on behalf for people with small handwriting), but I think spacing out your work really helps see things more clearly.

Here is an example of using numbered box method:

While doing your calculations or arithmetic, you cannot skip steps and do mental math. I have tried that many times and learned that it is kind of risky because you end up making some stupid mistake. For instance, I suddenly realized while double checking I made a calculation mistake because I thought n*0=n. Why did this happen? Because I did not write it down on paper! Another good habit while you are doing the steps is internally talking about how to solve a problem as if you were a teacher. I don’t really do this all the time, but lecturing it in your head makes you be more aware of each step.

For double checking, I personally find it ineffective to simply stare at your paper until time is called. You are not actively checking. What you are doing is passively checking. Again, my steps sound like I waste a lot of time, but here’s the paradox: the best way to be fast is to not be fast. What do I mean by this? What I mean is that when you are thorough and meticulous, you avoid a lot of potential careless mistakes, so you don’t have to waste time resolving the whole thing from the start. If you have enough time, double check by repeating the process that I described above. Reread the question carefully, do the numbered box method, and see if your answer matches the previous one.

In a nutshell, one method of performing better on math tests is changing your approach to the tests and establishing a good work habit. Sometimes, studying more doesn’t necessarily guarantee a higher score. How you take the test matters just as much as how you study. 

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