Problem Solver
Structured problem-solving with step-by-step explanations.
Problem-Solving Framework
flowchart LR
A[Understand] --> B[Plan]
B --> C[Execute]
C --> D[Verify]
D -->|Error| B
D -->|Correct| E[Explain]Step 1: Understand (Identify)
Questions to Ask
- What is given? List all known information
- What is asked? Clearly state what to find
- What type of problem? Categorize (algebra, kinematics, etc.)
- What are the constraints? Any restrictions or conditions
Template
**Given:**
- [List all known values with units]
**Find:**
- [What we need to calculate]
**Type:**
- [Problem category]Step 2: Plan (Strategy)
Choose Approach
| Problem Type | Common Strategies |
|---|---|
| Equation solving | Isolation, substitution, factoring |
| Word problems | Define variables, write equations |
| Physics | Draw diagram, identify forces/energies |
| Proofs | Direct, contradiction, induction |
| Optimization | Take derivative, find critical points |
Write Steps (Before Executing)
- First, I will...
- Then, I will...
- Finally, I will...
Step 3: Execute (Solve)
Show All Work
**Step 1:** [Action]
[Mathematical work]
= [Result]
**Step 2:** [Action]
[Mathematical work]
= [Result]
**Step 3:** [Final calculation]
[Work]
= [Final answer with units]Best Practices
- One step at a time
- Include units throughout
- Box or highlight final answer
- Keep work organized vertically
Step 4: Verify (Check)
Verification Methods
| Method | How to Apply |
|---|---|
| Plug back in | Substitute answer into original equation |
| Units analysis | Check dimensions match expected result |
| Estimate | Is the magnitude reasonable? |
| Alternate method | Solve differently, compare results |
| Edge cases | Does answer work at extremes? |
Template
**Check:**
- Substituting x = [answer] into original equation:
[show substitution] = [expected value] ✓
- Units: [unit analysis]
- Reasonableness: [is the answer logical?]Teaching Modes
Hint Mode
Give progressive hints, not full solutions:
Hint 1: "What type of problem is this?" (Identification) Hint 2: "What formula relates these quantities?" (Direction) Hint 3: "Try isolating variable X first." (Specific guidance)
Socratic Mode
Guide through questions:
- "What do you notice about the given information?"
- "What principle applies here?"
- "What would happen if you tried...?"
Full Solution Mode
Complete step-by-step solution with explanations.
Common Problem Patterns
Pattern 1: Solve for X
- Simplify both sides
- Collect X terms on one side
- Isolate X
Pattern 2: Word Problem
- Define variables
- Translate words to equations
- Solve system of equations
- Answer in context
Pattern 3: Rate Problem
- Identify rate (units per time)
- Use: Amount = Rate × Time
- Set up equation and solve
Pattern 4: Optimization
- Write objective function
- Take derivative
- Set equal to zero
- Solve for critical points
- Test for max/min
Answer Template
## Problem
[State the problem]
## Solution
### Understanding
- **Given:** [knowns]
- **Find:** [unknown]
### Approach
[Brief strategy explanation]
### Work
**Step 1:** [action]
[calculation]
**Step 2:** [action]
[calculation]
### Answer
**[Final answer with units]**
### Verification
[Check work]