My 7th grader is simplifying expressions
Question
My 7th grader is simplifying expressions with parentheses:
Expression: 3(2x - 5) - 2(3x - 4)
He wrote: 6x - 15 - 6x - 8 = -23
He distributed 3(2x - 5) into 6x - 15, but for -2(3x - 4) he wrote -6x - 8 instead of +8.
I don't want to give him the answer.
Can you give me:
- The exact name of this algebraic misconception.
- Two Socratic questions I can ask him so he catches the sign error himself?
- One parallel problem with changed numbers for him to test tonight?
Answer
This is "negative sign not distributed to every term in parentheses" (algebra card, L3).
He distributed the *magnitude* (2) to both terms but only let the *negative* attach to the first term. The inside `–4` got treated as if it had been multiplied by `+2` instead of `–2` — so it stayed negative instead of flipping to `+8`.
Two Socratic questions, with what "landing" looks like:
- *"When you distributed, the –2 reached the 3x and turned it into –6x. Did the same –2 also reach the –4? What is –2 × –4?"*
— *You'll know it landed if* he says "–2 × –4 = +8, so that term becomes +8." If he hesitates on the double negative, step back to a pure number: *"What is –2 × –6?"* Have him answer that first, then come back to the term.
- *"If your answer –6x – 8 were right, factor it back: put the –2 outside again and divide each of your terms by –2. What do you get inside the parentheses?"*
— *You'll know it landed if* he sees that –8 ÷ –2 = +4, so the inside would be `(3x + 4)` — not the `(3x – 4)` he started with. The mismatch is the sign error.
Parallel problem (no answer for him):
`5(3x - 2) - 4(2x - 6)`
Same trap sits in the second parentheses: –4 × –6 should flip to +24, not stay as –6. If he nails this one, try `-3(2x + 4) + 5(x - 1)` to vary the sign pattern.
*For your own check only:* `5(3x - 2) - 4(2x - 6) = 15x - 10 - 8x + 24 = 7x + 14`.