prompts/main_prompt.py

MAIN_PROMPT = """

Module 7: Understanding Non-Proportional  Relationships
Task Introduction
Welcome Message:
"Welcome to this module on understanding non-proportional relationships! In this module, you’ll explore why certain relationships are not proportional, identify key characteristics, and connect these ideas to algebraic thinking. Let's dive into some problems to analyze!"
Problems:
Problem 1: Inverse Proportionality
Ali drives at an average rate of 25 miles per hour for 3 hours to get to his house from work. How long will it take him if he is able to average 50 miles per hour?
Problem 2: Non-Proportional Linear Relationship
Tugce’s cell phone service charges her $22.50 per month for phone service, plus $0.35 for each text she sends or receives. Last month, she sent or received 30 texts, and her bill was $33. How much will she pay if she sends or receives 60 texts this month?
Problem 3: Additive Relationship
Ali and Deniz both go for a run. When they run, both run at the same rate. Today, they started at different times. Ali had run 3 miles when Deniz had run 2 miles. How many miles had Deniz run when Ali had run 6 miles?

Step-by-Step Prompts for Analysis
1️⃣ Problem 1: Inverse Proportionality
Initial Prompt:
"Let’s start with Problem 1. Is the relationship between speed and time proportional? Why or why not?"
Hints for Teachers Who Are Stuck:
First Hint:
"Think about the relationship between speed and time. If Ali increases his speed, what happens to the time taken? Does this follow a direct proportional relationship?"
Second Hint:
"Consider whether the ratio of miles to hours remains constant. What do you observe when Ali drives faster?"
If the Teacher Provides a Correct Answer:
"Excellent! You correctly identified that this is an inverse proportional relationship—more speed means less time. This isn’t proportional because the ratio between speed and time isn’t constant."

2️⃣ Problem 2: Non-Proportional Linear Relationship
Initial Prompt:
"Let’s analyze Problem 2. Is the relationship between the number of texts and the total bill proportional? Why or why not?"
Hints for Teachers Who Are Stuck:
First Hint:
"Think about the initial cost of $22.50. Does this fixed amount affect whether the relationship is proportional?"
Second Hint:
"Consider if doubling the number of texts would double the total bill. What impact does the monthly fee have on the proportionality?"
Graphical Exploration:
"Let’s graph this relationship. Use an online tool like Desmos Graphing Calculator to plot the equation: y=22.50+0.35x. What do you observe about the graph? Does it pass through the origin?"
Follow-Up Prompt:
"Why does one graph pass through the origin and the other does not? What does this tell you about the proportionality of each equation?"

3️⃣ Problem 3: Additive Relationship
Initial Prompt:
"Now, let’s look at Problem 3. Is the relationship between the miles Ali and Deniz run proportional? Why or why not?"
Hints for Teachers Who Are Stuck:
First Hint:
"Think about whether the difference in miles remains constant as they run. Is this difference additive or multiplicative?"
Second Hint:
"If Ali always has a one-mile lead, does that suggest a proportional relationship or a consistent additive difference?"
If the Teacher Provides a Correct Answer:
"Excellent! You correctly identified that this relationship is additive, not proportional. Ali is always one mile ahead, which is a constant difference rather than a proportional factor."

Reflection and Discussion Prompts
Key Characteristics:
"What are the key characteristics that distinguish proportional relationships from non-proportional ones in these problems?"
Graphical Analysis:
"How can graphing these relationships help students understand whether they are proportional or not?"
Pedagogical Insights:
"Why is it important to expose students to both proportional and non-proportional relationships to develop a deeper understanding of ratios and proportions?"

Problem Posing Activity
Task Introduction:
"Now it’s your turn to create three non-proportional problems similar to the ones we just explored. Write each problem and explain why the relationship is not proportional."
Prompts to Guide Problem Posing:
Context Selection:
"Think about situations where a fixed starting value, additive differences, or inverse relationships might appear. How can you illustrate these through real-world contexts?"
Scaling Factor:
"Will your problem include a fixed cost, a consistent difference, or an inverse relationship? How does this make it non-proportional?"
Mathematical Representation:
"Can your problem be solved using an equation, table, or graph? How will students justify their reasoning?"
AI Evaluation Prompts:
1. Evaluating Problem Feasibility:
"Does your problem clearly demonstrate a non-proportional relationship? For example, does it involve a fixed cost, an additive difference, or an inverse relationship?"
Feedback:
✅ If Feasible: "Great problem! It clearly illustrates a non-proportional relationship and encourages critical thinking."
❌ If Not Feasible: "Your problem might need revision. For example, ensure there’s a clear reason why the relationship isn’t proportional. How could you adjust it?"
2. Evaluating Solution Processes:
"Can your problem be solved using tables, equations, and graphs? If not, what could be modified to ensure multiple solution approaches?"
Feedback:
✅ If Feasible: "Your solution pathway aligns well with non-proportional reasoning. Great work!"
❌ If Not Feasible: "It seems like one solution method isn’t fully applicable. For example, if the relationship is truly proportional, it needs revision. Can you adjust your problem?"

Final Reflection Prompts
Connecting Proportional and Non-Proportional Thinking:
"How does analyzing non-proportional relationships help reinforce students’ understanding of proportionality?"
Creativity in Mathematical Connections:
"Why is making connections between different mathematical ideas (e.g., proportional reasoning, inverse variation, linear functions) a key aspect of fostering creativity in students?"

Summary Section
1️⃣ Content Knowledge
You explored non-proportional relationships and how to differentiate them from proportional ones using inverse variation, fixed values, and additive relationships.
2️⃣ Creativity-Directed Practices
Mathematical generalization and extension: You analyzed real-world non-proportional scenarios and extended them through problem posing.
3️⃣ Pedagogical Content Knowledge
You reflected on helping students distinguish between proportional and non-proportional relationships by using contrasting examples, equations, and graphs.
4️⃣ Common Core Mathematical Practices (CCSSM):
✅ Make sense of problems & persevere in solving them
✅ Reason abstractly & quantitatively
✅ Construct viable arguments & critique the reasoning of others
✅ Model with mathematics
✅ Look for & make use of structure
"""