The 5 Most Common Math Mistakes Students Make on Standardized Tests (and How to Avoid Them)

Math in the classroom and math on a standardized test, whether it is a state assessment or college admissions exam, are not the same experience. 

Yes, the rules are identical—fractions work the same way whether you're at your kitchen table or in a state assessment or college admissions exam—but the conditions are not, and it is that shift of environment where students usually lose points.

Knowing the material is not enough. We’ve met many students who excelled in math class but struggled on a standardized exam for this very reason; they lacked the test-taking skills necessary to navigate the new environment and format, and they make mistakes that were avoidable. 

Today, we’ll look at the most common mistakes students make on these exams and explore strategies to optimize their performance.

Why Knowing the Math Is Not Always Enough on Test Day

Think about how your student does math homework: they have time to think, re-read, ask for clarifications, and work through problems at their own pace. 

A standardized test is notably different, as it usually has a very clear structure, a limited time per section, and no external help. So, even though the rules for solving fractions are the same whether you’re doing them at home or on a standardized test, mistakes tend to crop up due to this change in circumstance.

There is also the mental aspect to consider.

Some students handle the pressure of a ticking clock better than others. And since standardized test results come with consequences, students can get test anxiety regardless of how much they have practiced the material at home.

All of this is to say that a lower score on a standardized math test doesn’t always correlate to knowledge gaps or a lack of practice. In fact, as we will soon see, a lot of the mistakes we see quite often have nothing to do with any one specific math concept, but rather the skill of test-taking in general.

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The 5 Most Common Math Mistakes on Standardized Tests

In our experience, there are five groups of mistakes that students tend to make across all grade levels. These mistakes all have to do with the test environment itself and require students to develop the appropriate habits to properly correct them.

1. Misreading the Question

Standardized tests tend to have more and longer word problems than those students see in class or on a worksheet. And due to the time constraints, they might fly through the problem without reading it carefully.

This then leads to them missing the point of the problem and losing points. The mistake shows up most on problems where the actual question is buried at the end of a long prompt. For example:

• A fourth grader reads a problem about a basket with 15 red and 9 green apples. They correctly add the two groups and write 24 as the answer. However, the question asked how many more red apples there were than green ones. The subtraction was right there in the problem, but the student never got to it.

• A seventh grader solves for x in an equation, gets x = 5, and moves on. Had they stuck around till the end, they would have seen that the question asked for the value of 2x. 

To tackle this problem, we teach students the Underline-Identify-Solve framework. This is basically a three-step framework that helps students take note of all the relevant information in a word problem.

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2. Skipping Steps and Losing the Thread

When a topic feels familiar, writing out every step can feel unnecessary, so students sometimes skip steps to save time. But this is a trap.

They may not fully realize it, but their working memory is likely taxed by time pressure, and mental math can be unreliable. 

Say your student is solving a multi-step problem and they decide to carry the mental math across two operations at once. The individual calculations are ones they know cold. The combination, held in memory under time pressure, produces an error that would never appear on homework.

The solution here is to make it a rule that every step gets its own line. This way, the paper is doing the memory work, so your brain does not have to.

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3. Calculation Errors on an Otherwise Correct Setup

Perhaps one of the errors students find most frustrating: They set up a problem correctly and then get the arithmetic wrong. It is frustrating because the mathematical thinking was sound, still the points disappear.

Mistakes of this kind can be as simple as:

• Correctly identifying that a problem requires multiplication, setting it up properly, and calculating 7 x 8 as 52.

• Solving for x in the proportion \(\Large\frac{3}{4}\) = \(\Large\frac{x}{20}\); cross-multiplying correctly, getting 4x = 60, and then dividing incorrectly, writing x = 12 instead of x = 15. 

The most direct solution here is to calculate the result again and see whether it matches up. However, due to the time constraints, what we usually encourage instead is a plausibility check.

After getting an answer, ask your student whether it is in the right range. 

An answer of 52 for 7 x 8 should feel off: 7 x 7 is 49 and 7 x 9 is 63, so the answer has to land in the middle. That check takes five seconds and catches a surprisingly high proportion of arithmetic errors.

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4. Mismanaging Units

Units are easy to treat as decoration around the real math. But on a standardized test, they are part of the answer, and getting the calculation right while handling the units wrong still costs points.

We typically see these kinds of mistakes show up in two forms: forgetting to include the units at the end or not converting units properly. For example:

• A fifth grader solving a problem about distance converts 2 kilometers to 200 meters instead of 2,000, then uses that number in a calculation that produces a plausible-looking but incorrect answer.

• An eighth grader correctly calculates the area of a rectangle as 48 cm², but writes just 48 as the final answer. The question asked for the area in square centimeters. So, even though the number was right, the answer was incomplete.

We recommend writing the units next to every number from the first line, not just the final answer. If units are visible throughout the calculation, conversion errors become harder to miss, and the final answer naturally includes the unit because it has been present on the page the whole time.

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5. Spending Too Long on Hard Problems and Running Out of Time

Some students, especially those aiming for a certain score, prioritize and spend most of their time on the hardest problems. Even when stuck, they try to stick with it at the expense of other, lower-hanging fruit.

This sometimes results in a shaky answer that ate up 10 minutes of their time. During those same 10 minutes, they could have gotten guaranteed points by skipping ahead and doing the easier material. 

A strategy that works well for most of our students is:

1. Move through the test, answering every question you are confident about.

2. Mark the ones you are unsure of and keep moving.

3. Return to marked questions with whatever time remains.

One important note: this strategy requires practice before it works reliably under pressure. 

If a student tries it for the first time on a real test, they will likely find it uncomfortable to leave a question unanswered and move on. If the next assessment is weeks away, practice the two-pass approach on a timed homework set. 

If the test is in two days, focus on the other four fixes first and come back to this one.

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Mathnasium tutors focus on helping students understand math, which is crucial for catching onto test mistakes.

How Mathnasium Helps Students Perform Their Best on Tests

Mathnasium is a math-only learning center dedicated to helping K-12 students learn and master math at every level, from foundational arithmetic through high school algebra and beyond.

When students come to us, we do not hand them generic test prep materials and move on. Our proprietary approach, the Mathnasium Method™, works differently. It is personalized and designed to build not just content knowledge but the reasoning habits and self-checking behaviors that prevent these common mistakes.

To foster lasting mastery, our approach relies on six core principles:

1. Personalization on a granular level: Each student begins with a diagnostic assessment that identifies their strengths, knowledge gaps, and how they approach problems. Tutors then follow personalized learning plans that target the specific habits and gaps most likely to cost points on assessments.

2. Teaching for understanding: We explain math using clear, everyday language and support each concept with visual, verbal, written, mental, and hands-on techniques so students develop genuine understanding rather than surface familiarity with procedures.

3. Caring instruction: Our tutors provide caring guidance in a fun group environment where students feel supported as they work through challenging material.

4. Independent problem solving and critical thinking: Each session includes time for students to work through problems on their own. Tutors guide them to understand both how and why a concept works, building the deliberate, step-by-step approach that holds up under test conditions.

5. Singular focus on math: Our program spans thousands of pages and has been continuously refined over the past 20 years. This singular focus allows us to take a deep dive into how students best absorb, learn, and retain mathematical concepts across every grade level.

6. Empowering, fun learning environment: Our environment is designed to be both engaging and fun. Our materials are game-based, and students have the opportunity to earn rewards to keep them motivated as they advance to higher levels of achievement.

And the results speak for themselves:

• 94% of parents report an improvement in their child's math skills and understanding

• 93% of parents report an improved attitude toward math after attending Mathnasium

• 90% of students saw an improvement in their school grades

With over 1,100 centers, we bring the Mathnasium Method™ close to your community.

For families in Westminster, Mathnasium of South Westminster is a trusted center with years of experience transforming how children think and feel about math.

Here’s how one parent described their child’s experience at Mathnasium:

Whether your child needs help catching up, wants to stay on track, or is ready to move ahead, Mathnasium can support their journey.

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