Are you a student who is tired of getting points taking off their assignments or high percentage assessments because of one simple mistake? Do you spend hours study only to end up on the losing end of grades just because you made one simple mistake? Do you hate when teachers mark the whole problem wrong just because you forgot to put the negative sign down in your final answer? Been there and done that. No matter if you are a student, parent, or life learner, everyone has made one or all five of the most common mistakes in math at one point in their lives. I am here to show you how to approach and identify these math problems prior to submitting your work.
My name is Mrs. Audrey Codner-Gibson and I am the owner of ACG Math Tutoring and I am a 19-year Secondary Math teacher and tutoring coach who decided to leave the classroom to help students all over the world to see math as a possible goal to achieve as well as a feat that they can accomplish.
I was not always this great teacher you “see” before you. When I was growing up in Philadelphia, PA, I was not at all as confident in math as I am today. I HATED MATH because I did not understand the purpose of math. Yes, I understood the basic concepts of adding, subtracting, multiplying, and dividing, but when algebra kicked my world into a rapid downward spiral I had no idea how I was going to making it to survive middle school. No matter how hard I tried, Algebra was right there taunting me and leaving me emotionally empty.
It was not until high school; I had the best teacher who taught the class how to see Algebra for what its worth and how we could connect its ideal through step-by-step instruction. I hope that everyone has a teacher like this at least once in their lives, but until now allow me to show you the 5 most common mistakes that students make and teachers what to scream every time they see them.
Subtracting Negative Numbers
After learning about integers and how they work in algebraic expressions and equations, students from various academic levels will always make the common mistake of subtracting negative numbers. When encountered with subtracting negative numbers, many students will either make the minus sign longer or just ignore the negative sign completely.
For example, x - -2 = 6 would either give a student an answer of 4 or 8 depending on what the student sees. One way that could simplify the situation is to place a set of parentheses around the negative two to see the separation between the minus sign and the negative two. When you are subtracting a negative number, you are actually multiplying the negative number with the minus sign which causes you to think of the multiplying negative numbers rule (a negative times a negative is a positive). Or simply, when you move down the negative direction of a number line you change direction twice which cause you to move in the positive direction. It’s like you going out of the door then returning back in the house to get something you forgot.
Simplifying exponents using their properties seems to the be the second most anticipated error secondary teachers experienced through their careers. When I ask a student to simplify 4^2, for example, I most always get an answer of 8. There are times, I cut a student off at the pass and tell them “don’t say eight”. Of course, this puts students in a state of confusion because 4 * 2 is equal to 8. But that is not what the expression is asking. 4^2 can be extended out to 4 * 4 because the expression is telling you how many times the base (which is 4) is being multiplied to itself (you get that answer from the exponent. So save your teachers sanity and try to remember that when dealing with exponents, please extend the base out and don’t simplify multiply the base with the exponent.
Order of Operations
No matter where you are from and how old you are, everyone knows the acronym for the process of Order of Operations: Please Excuse My Dear Aunt Sally (PEMDAS) or (BEMDAS-in Canada). When simplifying algebraic expressions, there is a process you must perform to get the correct answer. It’s like making a PB&J sandwich or getting dressed, everything has an order to stay within social norms. Each letter represents a step in the process. P represents the parentheses (or B represents the brackets or braces), E represents the exponents, Now here is the kicker, the M and D come next and they represent Multiplication and Division; however, there is a rule within the rule. After you deal with the exponents, you are either doing multiplication or division first based on what comes first from the left to right. This is where many students go wrong. It is not just you. In fact, there was a huge push on Facebook for a simple expression where the answer could be either 16 or 1that made the national news! As long you remember that you must do multiplication/division prior to addition from left to right, you will be on the right track. Therefore, the rule is designed this way:
Now you have seen the 5 most common mistakes students make in math and learned how you can fix them prior to submitting your assignments, what are you going to do next? Hopefully, this article made you think about how you can do math just by tweaking a few things instead of redoing everything in your thought process. Remember, in math, there are patterns and rules to everything. I know that it is hard to remember all these and many more rules but through practice and taking things for what they are in a step-by-step sequence, you will have a better chance to raise your grades and expand your content knowledge compared to someone who sits and complain about how they will never “get it”. By taking the first steps towards bettering yourself and wanting to make a chance in your current mindset, I want to say that I am so proud of you and keep moving forward in your academics. Because the world needs you and what you can bring to the table of life…YOU!
Even after all of this and you feel that you need more support in your math abilities, I do have FREE (yes Free) algebraic foundation skills videos on Youtube (https://www.youtube.com/channel/UC9j_8oJSGV3Od_IvDZqjiJw/videos?view=0&sort=da&flow=grid). If you would like more of a personalized one-to-one or small group tutoring, you can go to my website acgmathtutoring.com and sign up for a FREE Meet & Greet (YES, we LOVE FREEBIES!) to talk more about how I can help you achieve your math goals with little stress and more confidence.
In closing, I want you to remember that you can do math! Just take your time and learn to adjust to the given situation. You can do it!