My 8th-grade son has an algebra homework
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My 8th-grade son has an algebra homework sheet with the problem: Evaluate -5^2.
He wrote down +25, explaining: "A negative times a negative is a positive, so -5 times -5 is 25."
When I told him it's -25, he argued that -5 is a single negative number being squared.
I don't want to lecture or just hand him the answer key.
Can you give me the exact misconception name in math pedagogy, 2 Socratic diagnostic questions I can ask him tonight at the desk to help him see the difference between -5^2 and (-5)^2, one changed-number parallel problem to test independently, and one clarifying question if you need more context?
Answer
I'll pull the structural verdict from the script first (with `withhold` so the correct value never comes back), then write you the parent track.
**The name in math pedagogy**
It's the **unary-minus precedence error** (sometimes called "treating the leading minus as part of the base"). In words you can say to him tonight: **he is squaring a *negative* number; the textbook is squaring 5 first and then putting a minus on the answer.** Without parentheses, the squaring binds tighter than the minus — so his rule ("negative × negative = positive") would only be right if the book had written `(−5)²`.
The script confirms the disagreement is in the **sign**, not the magnitude.
**Two Socratic questions — ask one at a time, wait for his answer**
1. *"Cover the minus sign with your finger. What does `5²` equal? Now — where does that minus attach: to the 5 *before* it's squared, or to the answer that comes *out* of the squaring?"*
- **How you'll know it landed:** He names the place the minus sits — *after* the squaring. If he still insists the minus is on the 5, the bug is intact; re-ask: *"If the minus really were part of the 5, wouldn't the textbook need to write `(−5)` to mean that?"*
2. *"Compute `10 − 3²` out loud, one step at a time. Which happens first — squaring the 3, or subtracting the 3?"*
- **How you'll know it landed:** He squares first (`3² = 9`), then subtracts. If he tries `10 − 3 = 7` first and squares after, it's the same precedence bug in a different costume.
**One changed-number parallel problem** (no answer from you — let him work it in front of you)
> Evaluate `−3⁴`.
**Self-check (process, not value):** Ask him to *show the two steps out loud* — first what he does with `3⁴`, and only then what he does with the minus. Did he square first and negate after, or negate first and square after? Don't volunteer the answer; ask him to defend the *order*.
**One clarifying question I want to double-check before you start**
> Is the textbook's literal expression `-5²` (no parentheses around the −5), or `(-5)²` (parentheses around the −5)?
If the sheet actually says `(-5)²`, then `+25` is correct and we'd be having the wrong conversation tonight. If it says `-5²`, run the ladder above.