My 7th grader is working on solving equa
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My 7th grader is working on solving equations with parentheses tonight and wrote:
4(2x - 3) - 3(x - 4)
expanded as:
8x - 12 - 3x - 12 = 5x - 24
They missed that distributing -3 across (x - 4) gives -3x + 12, instead writing -3x - 12.
I am sitting at the kitchen table with them. I do not want to just give the correct answer or lecture.
Can you give me:
1. The exact conceptual name of this misconception.
2. Two speakable diagnostic questions I can ask out loud right now, each followed by how I will know the concept landed.
3. One parallel changed-numbers practice problem (withhold the answer).
4. One brief follow-up question that would change our next step.
Answer
Here's what you asked for, in the order you asked for it. Kitchen-table ready.
**1. The misconception**
This is **"negative sign not distributed to every term."** When a minus or a negative number sits in front of parentheses, it has to multiply *every* term inside, not just the first one. Your student multiplied -3 by x correctly (got -3x), then stopped — the -4 inside was treated as if it weren't part of the multiplication.
**2. Two questions to ask out loud**
**Q1:** "Look at -3(x − 4). Does the -3 multiply just the x, or does it multiply every term inside the parentheses?"
- **How you'll know it landed:** they say "every one" out loud, or they count the terms as they go. If they only mention the x, the misconception is still active.
**Q2:** "You wrote -12 there. What two things did you multiply to get that, and why that sign?"
- **How you'll know it landed:** they say something like "negative times negative" or surface the sign rule on their own. If they say "I just copied the -4" or pause on the sign, the sign isn't being tracked through the multiplication.
**3. Practice problem — answer withheld**
Have them expand: **5(x − 2) − 2(x − 6)**
Two negative-coefficient distributions to do, same shape as the homework. After they finish, ask: *"For each set of parentheses, how many terms did you multiply? Did you reach both?"* — that's a process check, not a number check.
**4. One follow-up question**
"Are there other parenthesized expressions on tonight's page, or is this the only one?"
If there are more, we'd want to walk through each before signing. If it's the only one, the practice problem above is enough for tonight and we can revisit later in the week.