Math Misconception Library

The specific wrong beliefs that hold students back — and exactly how to fix them.

These aren't just “mistakes.” They're logical conclusions from incomplete understanding. Each guide explains what the misconception is, why it makes sense to the child, and step-by-step remediation.

Find your child's misconceptions

Early Math

Counting without one-to-one correspondence

Saying numbers without matching each count to exactly one object.

Pre-K to Grade 1

Zero means nothing (so it doesn't matter)

Ignoring zeros or treating them as meaningless in place value.

Grades K-3

Subtraction

Always subtract smaller from bigger

Flipping digits in subtraction to always subtract smaller from larger.

Grades 1-4

Multiplication

Multiplication is just repeated addition

Only understanding multiplication as adding groups, which breaks with fractions.

Grades 3-5

Fractions

Adding denominators

Believing 1/2 + 1/3 = 2/5 by adding tops and bottoms separately.

Grades 4-6

Bigger denominator = bigger fraction

Thinking 1/8 is larger than 1/4 because 8 > 4.

Grades 3-5

Multiplication always makes bigger

Expecting 6 × 1/2 to be larger than 6.

Grades 5-6

Invert both when dividing fractions

Flipping both fractions instead of just the divisor.

Grades 5-6

Decimals

Decimal place value confusion

Thinking 0.45 > 0.5 because 45 > 5.

Grades 4-6

Integers

Negative × negative = negative

Believing two negatives multiply to a negative.

Grades 6-7

Algebra

Equals means "answer comes next"

Seeing = as an operator rather than a balance.

Grades 4-7

Percents

Percent = just remove the %

Converting 25% to 25 instead of 0.25.

Grades 5-7

Misconceptions hide in plain sight

Your child might be getting answers right for the wrong reasons — or wrong for reasons you'd never guess. Our diagnostic finds the hidden gaps.

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