My 8th grade daughter keeps making this
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My 8th grade daughter keeps making this error on algebra tests:
When evaluating -4^2, she writes +16.
When evaluating -5^2, she writes +25.
She reasons: "A negative times a negative is a positive, so (-4) times (-4) is 16."
The issue is she doesn't see that without parentheses, the exponent only attaches to the 4, not the negative sign: -4^2 = -(4^2) = -(16) = -16. Only (-4)^2 = +16.
I want to create a mistake-notebook card for her so this stops costing her test points.
Format requirement: exactly 5 lines, no academic jargon, no explanatory lecture rules in the card fields.
Please generate the exact 5-line mistake notebook card for:
-4^2 = 16 (wrong) vs -4^2 = -16 (correct).
Answer
Two misses, same cause (exponent binds only to the number it sits on, not a sign in front) → one card, not two.
**Card written** — id `c17a1898d83aeb6f`:
| line | field | text |
|---|---|---|
| 1 | prompt | Evaluate −4². |
| 2 | wrong move | She wrote +16, treating it as (−4) × (−4). |
| 3 | right move | −4² means −(4²) = −(16) = −16. The exponent binds to the 4 only. Same-type: −3² = −9. |
| 4 | tag | exponents, negative base, order of operations |
| 5 | cause | _(empty — pick an A1–G9 id if you want, or leave blank)_ |
The card holds only what ties to this one item. Why the rule works (operator precedence, why − isn't "inside" the base without parentheses) is a teaching question — `homework-tutor` is the right place to walk through it; I won't write the explanation into the card.
Want me to set a nightly reminder so she re-tests this card on its due day?