My 7th-grade daughter is working on basi
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My 7th-grade daughter is working on basic algebraic expression simplification. On her algebra homework yesterday, she had the problem:
"Simplify: 5 - 2(x + 3)"
She wrote down her work step-by-step:
5 - 2(x + 3)
= 3(x + 3)
= 3x + 9
She got 3x + 9 instead of the correct -2x - 1. When I asked her why she subtracted 5 - 2 first, she said: "Because 5 minus 2 is right there at the start of the problem, so 5 - 2 = 3, and then you multiply the 3 by what's inside the parentheses!"
She completely ignored PEMDAS / order of operations, performing left-to-right subtraction before the multiplication/distribution of -2 across (x + 3).
Could you help us log this into our mistake notebook:
1. **Strict 5-Line Mistake Card**: Please format this into the exact standard 5-line card format:
- 题面 (Problem statement)
- 错法 (The incorrect step she took)
- 修法 (The correct mathematical remediation)
- tag (Classification tags)
- 错因 (Cognitive root cause analysis)
2. **First-Principles Parent Explanation**: How can I explain to her why the -2 is "glued" to (x + 3) by multiplication, and why doing 5 - 2 first breaks mathematical grammar?
3. **Parallel Redo Problem**: Provide one changed-number parallel problem for tonight's practice (e.g. 7 - 3(2x - 4)) without revealing the final answer to the student.
Answer
The "why -2 is glued to (x+3)" and "why 5−2 first breaks mathematical grammar" explanations go to homework-tutor — that's their lane, not this notebook's.
This card only holds five lines: 题面 / 错法 / 修法 / tag / 错因. The "why" doesn't go in here.
- 题面:
- 错法:
- 修法:
- tag:
- 错因: