5 Common Math Mistakes Students Make | MGL Math Center Glenview IL
After working with hundreds of students across Glenview and the Chicago North Shore, I’ve seen the same math mistakes come up again and again — from 3rd graders just building their foundations to 10th graders deep in Algebra 2.
The good news? These mistakes are fixable. Most of them aren’t signs of a student who “isn’t a math person.” They’re signs of a student who hasn’t been shown the right way to think through a problem yet. That’s exactly what we do at MGL Math Center.
Here are the 5 most common math mistakes I see — and what your child can do about them starting today.
Mistake #1: Skipping the Problem Setup
This is the #1 mistake I see across every grade level. A student reads the problem, jumps straight to calculating, and makes errors before they even get to the math.
Good math starts before you write a single number. Students need to slow down and ask: What is this problem actually asking? What do I know? What do I need to find?
At MGL, we teach students to write out what they know, label their unknowns, and identify the operation before they start. It adds 20 seconds to the process and eliminates a huge percentage of careless errors.
The fix: Before solving, have your child write: “I know ___. I need to find ___.” This simple habit changes everything.
Mistake #2: Misapplying the Order of Operations
PEMDAS is taught in every middle school classroom in Glenview — but knowing the acronym and knowing when to apply it are two very different things.
The most common version of this mistake: students see 2 + 3 × 4 and calculate left to right, getting 20 instead of 14. Or they forget that multiplication and division are evaluated left to right as equals — not multiplication always before division.
This mistake shows up constantly in Algebra, and it causes students to lose points not because they don’t understand the concept, but because the foundation was never made concrete.
The fix: Practice order of operations with expressions that are designed to trip students up — not just the easy ones. Work through problems that have parentheses inside parentheses, or that mix division and multiplication. If your child hesitates, that’s the signal to drill deeper.
Mistake #3: Treating Fractions Like Whole Numbers
Fractions are the first major conceptual hurdle in math, and for many Glenview students, they’re where confidence starts to waver. The most common error: adding fractions by adding both the numerators and the denominators.
1/2 + 1/3 = 2/5 — this is wrong, but it feels logical to a student who is pattern-matching from what they know about whole numbers.
The fix isn’t just memorizing “find a common denominator.” It’s understanding why you can’t add fractions with unlike denominators — what you’re actually doing when you add fractions — so the rule isn’t arbitrary.
The fix: Use visual models. Draw the fractions as pieces of a whole (pizza slices work great). Once a student sees that 1/2 and 1/3 are different-sized pieces that can’t simply be combined, the rule makes sense and sticks.
Mistake #4: Sign Errors in Algebra
Ask any math teacher in the Glenview area what the most frustrating mistake is to grade, and they’ll tell you: sign errors. A student does everything right and loses the answer because of a negative sign they dropped in the middle of the work.
This usually comes down to one of two things: rushing, or a shaky understanding of how negative numbers actually behave. The student knows the process but hasn’t internalized why −(x − 3) becomes −x + 3, not −x − 3.
The fix: Slow down the distribution step. Write it out explicitly every time. −1 × (x − 3) = −1 × x + (−1 × −3). It looks tedious, but students who do this build the intuition fast — and then they can skip the step once it’s automatic.
Mistake #5: Not Checking the Answer
This one hurts the most, because it’s the most preventable. A student works hard, gets the right method, makes one arithmetic slip, and never checks — so a 90% becomes a 75%.
Checking an answer isn’t just running through the problem again. It means asking: Does this answer make sense? If a problem asks how many students are in a classroom and the answer is 0.3, something went wrong. If a distance comes out negative, something went wrong. Number sense — the ability to know roughly what an answer should look like — is one of the most valuable skills we develop at MGL.
The fix: Teach your child to estimate before they solve. “This should be somewhere between 10 and 20.” Then check the final answer against that estimate. This habit catches errors and builds mathematical intuition at the same time.
Why These Mistakes Keep Happening
Here’s the honest answer: most of these mistakes happen because students have been shown what to do, but not why it works. When the rule is arbitrary — just a thing to memorize — it doesn’t stick. When the concept is understood, the rule is obvious.
That’s the difference between math instruction that produces short-term results and math instruction that actually builds a student’s capability. At MGL Math Center, we focus on the second kind.
Our students improve an average of 1.8 letter grades in 12 weeks — and the reason they improve isn’t that we work them harder. It’s that we teach them how to think through problems, not just solve the ones they’ve already seen.
Is Your Child Making These Mistakes?
If you recognized your child in any of these five mistakes, that’s actually a good sign — it means there’s a clear path forward.
MGL Math Center serves students in grades 2–11 in Glenview and the surrounding North Shore communities, including Northbrook, Wilmette, Evanston, and Skokie. Our small-group sessions (max 6 students per tutor) are designed to give every student the individualized attention they need to move past these exact kinds of roadblocks.
We’re so confident in our approach that we back it with a satisfaction guarantee: if your child doesn’t improve in 12 weeks, the next month is on us.
Ready to get started? Contact us at 847-220-4242 or visit mgltutor.com to learn more about our Spring enrollment. Spots are limited.
MGL Math Center is located at 4350 Di Paolo Center, Suite H, Glenview, IL 60025. We serve students in grades 2–11 from Glenview, Northbrook, Wilmette, Evanston, Skokie, and throughout the North Shore. Follow us on Facebook for weekly math tips and student wins.
