Problem Solver

Step 2: Plan (Strategy)

Choose Approach

Write Steps (Before Executing)

1. First, I will...
2. Then, I will...
3. 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

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

1. Simplify both sides
2. Collect X terms on one side
3. Isolate X

Pattern 2: Word Problem

1. Define variables
2. Translate words to equations
3. Solve system of equations
4. Answer in context

Pattern 3: Rate Problem

1. Identify rate (units per time)
2. Use: Amount = Rate × Time
3. Set up equation and solve

Pattern 4: Optimization

1. Write objective function
2. Take derivative
3. Set equal to zero
4. Solve for critical points
5. 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]