My 7th grader is working on pre-algebra
Ask
My 7th grader is working on pre-algebra distributive property homework tonight.
On this problem:
3(2x - 4) - 2(x - 5)
He wrote down:
= 6x - 12 - 2x - 10
= 4x - 22
I see where he made the error distributing the negative sign over the parentheses.
Please:
1. Name the exact error cause/misconception.
2. Give me a diagnostic question I can ask him so he spots it himself, with the landing signal (how I know it clicked).
3. Give one changed-number parallel problem (withhold the answer so he works it out himself).
Answer
Cause: **negative sign not distributed to every term inside the parentheses.** In his second line the −2 in front of (x − 5) only flipped the x — the −5 inside stayed negative. That's why `−2(x − 5)` came out as `−2x − 10` instead of `−2x + 10`. The first group `3(2x − 4)` is fine; the mistake lives on the second term.
**Diagnostic question (you ask him):**
"Watch the −2 sitting outside (x − 5). It has to multiply *both* things inside, not just the x. Show me what −2 does to the x, and what −2 does to the −5, each with its new sign."
**Landing signal — how you know it clicked:**
- He can say out loud "minus times minus is plus" and point to the +10, **or**
- He redoes the second line on paper and the second term is `−2x + 10`, not `−2x − 10`.
If he just rewrites `6x − 12 − 2x + 10` because you hinted it, that isn't a click — you want him to derive the +10 himself.
**Changed-number problem (he works it, you don't):**
`5(3x − 2) − 4(x − 6)`
Same trap on the second group. After he's done, ask him to circle the two new signs he had to write — the one after the −10, and the one between the −4x and 24.
You gave me the problem, his work, and the grade — that's enough. Go.