Three common math student mistakes!

We’ve all been there: you do a math test, you’re feeling really confident, and then you get the test back, and you’ve got one question wrong! After you look to see what happened, you say “Oh, I see what I did wrong!” Somewhere, you’ve made a (as my dad labels it) “careless mistake” in either your calculation or you’ve read the question incorrectly. For me, “careless mistakes” are the bane of my existence, it pains me to bring home a 19/20 for a simple error!

I’m sure many high school students experience the same turmoil. No worries, I’m here to help! I’ve generated a small list of common mistakes that my classmates and I make on math tests. Enjoy!

1. ORDER OF OPERATIONS

What’s -3^{2 ?}

If you think the answer is 9, unfortunately, you may need to review BEDMAS. (Or sometimes known as PEMDAS)

Brackets

Exponents

Division/Multiplication

Addition/Subtraction

The general convention is to perform the exponentiation before applying the minus one. Because in actuality, -3² can

be written as  (-1)(3)²

Therefore, you complete the operation 3² first. Which of course is 9. Then obviously (-1)(9) is equal to -9.

So when you see this sort of thing in your long list of calculations, this is what you should be thinking:

-3²

= (-1)(3)²

= (-1)(9)

= -9

2. DISTRIBUTION OF EXPONENTS

I cannot begin to describe how many times I’ve facepalmed when students say that (a+b)² is equal to (a²+b²).

Remember that exponents indicate how many times a term is multiplied by itself. Exponents do not distribute the same as multiplative and divisive operations. It is true that according to distribution laws: 2(a+b) = 2a+2b. However exponents do not work the same way.

For example, (a+b)² is actually equal to (a+b)(a+b). This is because you are multiplying the term (a+b) with itself, once.

Therefore…

(a+b)² = (a+b)(a+b) = a²+ 2ab + b² ≠ (a²+b²)

3. CANCELLATION ERRORS WITH DIVISION

^15x+5/_3x+4

Sometimes when students see division like this in their calculations, they will be tempted to cancel. Many students think that they can cancel 15x in the numerator and the 3x in the denominator to get 5x in the numerator like so:

^15x+5/_3x+4 = ^5x+5/₄

Don’t do it! Remember you are dividing ALL of the terms in the top by ALL the terms in the bottom.

Well, if you had the willpower to read through this whole post, congrats! You are now a little bit more prepared for those dreaded math tests that we know too well. This only a few of the many common mistakes that students are prone to make on test. I encourage everyone to research high school math mistakes to you make you more aware of the simple little mistakes that plague our marks! WOOT MATH!