The Math Mistake Library
Most apps hand your kid the answer and move on. Bija does the opposite — it reads the actual work and names the specific misconception behind a wrong answer, then points to the one skill that fixes it. Here are 30 of the ones we diagnose, in plain words. This library grows as real students practice.
The negative-sign slips that quietly break everything above them.
Didn't flip the sign of every term when multiplying a negative across parentheses — e.g. −(x − 3) became −x − 3 instead of −x + 3.
🌱 the fix: The Distributive Property
Lost a minus sign partway through, so the final answer has the wrong sign.
🌱 the fix: Adding & Subtracting Negatives
Mixed up the rules for adding positive and negative numbers (e.g. −5 + 3).
🌱 the fix: Adding & Subtracting Negatives
Got the sign wrong multiplying or dividing negatives — two negatives make a positive (−6 × −5 = 30).
🌱 the fix: Multiplying & Dividing Negatives
Shifted a term across the equals sign but forgot it should switch from + to − (or the reverse).
🌱 the fix: Variables on Both Sides
Did the steps out of order — e.g. added before multiplying instead of following PEMDAS.
🌱 the fix: Order of Operations (PEMDAS)
The answer is one more or one less than it should be — often from miscounting terms or steps.
The method was right; a small computation error (like 7×8) threw off the final number.
Combining, distributing, and moving terms — the grammar of algebra.
Added terms that don't match — e.g. treated 3x + 2 as 5x. Only like terms can be combined.
🌱 the fix: Combining Like Terms
Multiplied the outside factor by just the first term in the parentheses instead of every term.
🌱 the fix: The Distributive Property
Didn't reverse the < or > sign after multiplying or dividing both sides by a negative.
🌱 the fix: One-Step Inequalities
Where 'flip and multiply' and 'reduce' go wrong.
Divided fractions without multiplying by the reciprocal ("flip and multiply").
🌱 the fix: Equations with Fractions
Flipped the fraction upside down at the wrong moment.
🌱 the fix: Multiplying & Dividing Fractions
The answer is correct but not simplified to lowest terms (e.g. left 6/8 instead of 3/4).
Reading a power as a product, and the rules that follow.
Treated an exponent as multiplication — e.g. read 2³ as 2×3 = 6 instead of 2×2×2 = 8.
🌱 the fix: Order of Operations (PEMDAS)
Treated a power as a product — e.g. read 2³ as 2×3 = 6 instead of 2×2×2 = 8.
🌱 the fix: Intro to Exponents
Slope, coordinates, and what 'parallel' really requires.
Read the slope with the wrong sign — a line going down should have a negative slope.
🌱 the fix: Slope from a Graph
Used run-over-rise instead of rise-over-run, so the slope came out flipped (e.g. 1/3 instead of 3).
🌱 the fix: Slope from Two Points
Read a point's coordinates with the wrong sign — e.g. plotted (−3, 2) as if it were (3, 2).
🌱 the fix: The Coordinate Plane
Called two lines parallel when their slopes differ — parallel lines must have equal slopes.
🌱 the fix: Parallel & Perpendicular Lines
Formulas, units, and the logic of if-then statements.
Used the perimeter formula where area was needed, or vice versa.
Used the wrong angle unit for the calculation.
Chose the wrong triangle-congruence rule (e.g. used SSA, or confused SAS with ASA).
Mixed up the contrapositive of a statement ("if not-B then not-A") with its inverse ("if not-A then not-B").
Swapped the converse ("if B then A") for the contrapositive ("if not-B then not-A").
Swapped the converse ("if B then A") for the inverse ("if not-A then not-B") of a statement.
The two-solution nature of quadratics, and the ± that gets dropped.
A quadratic usually has two solutions — stopped after finding one and missed the other.
🌱 the fix: Solving by Graphing
Took the square root of both sides but kept only the positive root, dropping the negative solution.
🌱 the fix: The Quadratic Formula
Got the signs wrong inside the factors (e.g. (x−2)(x+3) instead of (x+2)(x−3)), so the roots came out wrong.
🌱 the fix: Factoring x² + bx + c
Slipped a sign substituting into −b ± √(b²−4ac) / 2a — often the −b or the 4ac term.
🌱 the fix: The Quadratic Formula
Take the free 3-minute Math Checkup. No answers given — just the exact misconception, and where it first broke.
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