Algebra Problem-Solving Framework

Help me teach algebra problem-solving strategies:

Topic Focus:
[Specific algebra topic: linear equations, quadratic equations, systems of equations, word problems, inequalities, etc.]

Student Profile:
- Grade/Course: [Grade and Math Course]
- Foundation Strength: [Strong/Adequate/Weak in prerequisite skills]
- Main Struggle: [Where they get stuck - setting up, solving, checking, etc.]
- Type of Problems: [Textbook, word problems, application problems]

Sample Problem:
[Include a specific problem they're working on or struggling with]

Please provide:

1. PROBLEM-SOLVING FRAMEWORK
- Universal steps for this problem type
- Checklist students can follow
- Decision points and what to do at each

2. PREREQUISITE CHECK
- Skills needed for this problem type
- Quick diagnostic questions
- Review resources if gaps exist

3. STEP-BY-STEP DEMONSTRATION
- Worked example with think-aloud commentary
- Explanation of WHY each step
- Common branching points

4. ERROR ANALYSIS
- Typical mistakes at each step
- How to catch and correct them
- Warning signs of going wrong

5. PRACTICE PROBLEMS (Tiered)
- Level 1: Basic application (3 problems)
- Level 2: Standard complexity (3 problems)
- Level 3: Challenge level (2 problems)
- Full solutions with explanations

6. WORD PROBLEM STRATEGIES
(If applicable)
- Translation guide (words to symbols)
- Organizing information
- Identifying what's being asked
- Setting up equations from context

7. SELF-CHECK STRATEGIES
- Verification methods
- Estimation to check reasonableness
- Substitution checking

8. INDEPENDENCE BUILDERS
- Questions to ask themselves
- Reference sheet for process
- When to move to next difficulty