My 7th-grade daughter is doing two-step
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My 7th-grade daughter is doing two-step linear equations. For 4x - 9 = 15, she wrote 4x = 6 (she subtracted 9 from 15 instead of adding 9 to undo the subtraction).
I need to sign her homework tonight, but I want her to discover the error herself without me giving the answer key.
Can you provide:
1. The exact misconception name.
2. 1-2 diagnostic questions I can ask aloud, plus how I will know if each landed.
3. One parallel problem with changed numbers (withholding the final answer) to try tonight.
4. One clarifying question if anything would change our approach?
Answer
Tonight's job: she moved the −9 across the equals sign but kept the minus instead of flipping it to a plus. The rule she's missing is "undo the last operation" — when the left side has *subtract* 9, the move is *add* 9.
**1. Misconception name (to say aloud):**
"Moves the number across the equals sign but doesn't flip the sign." Not a careless slip — she's treating the move as a copy, not as an undo.
**2. Diagnostic questions (each with how you'll know it landed):**
- **Q1 — the undo idea:** "On the left side of `4x − 9 = 15`, someone *subtracted* 9. To undo a subtraction, do you subtract again or add?"
- *How you know it landed:* she says "add, because we're undoing it" — or any phrasing where "undo" and "add" are linked. If she just says "add" without the undo frame, ask the next one; she may have remembered a rule but not the reason.
- **Q2 — both sides, not one:** "If the equation is a balance, and you want to take the −9 off the left side, what do you have to do to the right side at the same time, and why?"
- *How you know it landed:* she says "add 9 to both sides so they stay equal" — or sketches it on a balance. If she only says "add 9 to the right," she has the inverse but not the balance; that's tomorrow's talk, tonight still works.
Either question, not both, is enough. Start with Q1; use Q2 only if Q1's answer was rote.
**3. Parallel problem (no answer from me — she does it):**
`6x − 7 = 17`
Same shape as hers: a multiple of x, minus a number, equals another number. After she solves it, ask her to **put her answer back into the original** (`6·(her x) − 7`) and check it equals 17. The check is the part that catches the sign-flip — if she gets the same wrong answer as last time, the substitution will not balance.
**4. Clarifying question (would change our approach):**
Is this the only equation she got wrong on tonight's page, or are there others? If two or more share this shape (a number being moved across with its sign unchanged), we treat them as **one cluster** and she just does the new one; if it's the only one of its kind, tonight's redo is enough either way, but it tells me whether the lesson tomorrow needs to revisit the inverse rule or just one bad habit.
One side note for your signature line: the cause name above is enough on her paper — teacher Monday reads "kept the sign when moving across the equals" and knows what to come back to. No need to write the right answer next to her work.