Key Elements:

• Exact terminology usage
• Unit specification
• Variable definition
• Notation clarity

Components:

• Given information
• Required calculations
• Expected format
• Solution steps

Sample Prompt Template:

"Generate a step-by-step solution for this [calculus/algebra/etc.] problem:

• Show all work clearly
• Explain each step
• Include relevant formulas
• Highlight key concepts

Problem: [Insert problem]"

Sample Prompt Template:

"Create a physics problem solution that includes:

• Initial conditions
• Relevant equations
• Step-by-step calculations
• Unit analysis

Problem: [Insert problem]"

Sample Prompt Template:

"Develop a design solution that addresses:

• Technical requirements
• Constraints
• Calculations
• Implementation considerations

Problem: [Insert scenario]"

Framework Steps:

1. Problem Analysis
   • Identify known variables
   • Define unknowns
   • List constraints
   • State assumptions
2. Solution Planning
   • Select methods
   • Outline steps
   • Choose equations
   • Plan verification
3. Implementation
   • Show calculations
   • Track units
   • Document process
   • Check results

Structure:

• Concept introduction
• Mathematical foundation
• Application examples
• Common pitfalls

Original Prompt:

"Explain derivatives."

Enhanced Prompt:

"Explain the concept of derivatives in calculus, including:

• Basic definition and notation
• Geometric interpretation
• Basic rules with examples
• Real-world applications
• Common student misconceptions

Use clear mathematical notation and provide visual description where helpful."

Original Prompt:

"Create physics problems."

Enhanced Prompt:

"Generate three physics problems about projectile motion that:

• Progress in difficulty
• Include real-world scenarios
• Require multiple concepts
• Have complete solutions
• Include common error warnings

Provide step-by-step solutions with clear explanations."