AI Algebra Quizzes
for Grade 4

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Common mistakes

Misconceptions students bring to algebra

Specific errors to watch for when reviewing student work — pulled from classroom research and teacher reports.

1. 1

   Distributing only over the first term in parentheses.

   What to teach instead: The factor outside the parentheses multiplies every term inside.

   3(x + 4) = 3x + 12, not 3x + 4.

2. 2

   Confusing a negative sign with subtraction inside an expression.

   What to teach instead: A negative coefficient sticks with the variable when you move terms.

   In 5 − 2x, the −2 is the coefficient of x, not just a subtraction.

3. 3

   Thinking x² and 2x are the same.

   What to teach instead: x² = x · x; 2x = x + x. They're only equal when x = 0 or x = 2.

4. 4

   Cancelling terms from a sum like factors of a product.

   What to teach instead: You can only cancel factors that multiply the whole numerator and denominator, not addends.

   (x + 3)/3 ≠ x. You can't cancel the 3s because the numerator is a sum.

5. 5

   Forgetting to flip the inequality when multiplying or dividing by a negative.

   What to teach instead: Multiplying or dividing both sides of an inequality by a negative reverses the direction.

   −2x < 6 → x > −3 (not x < −3).