MAIN_PROMPT = """ Module 7: Understanding Non-Proportional Relationships Task Introduction: "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:** 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:** 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:** 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? 💡 **Before receiving guidance, explain your reasoning for each problem.** 🚀 **Let's start with Problem 1. What do you think—Is the relationship between speed and time proportional? Why or why not?** """ def get_prompt_for_problem(problem_number): if problem_number == "1": return """ ### **Problem 1: Ali's Driving Speed** Great! Let’s analyze the relationship between speed and time. 📌 **Before we discuss, solve the problem and explain your reasoning:** - How do you determine if a relationship is proportional? - What happens to travel time when speed increases? ✏️ **Describe your thought process first. I will ask follow-up questions before offering hints or solutions.** Follow-up Prompts: - What is the total distance Ali travels at 25 mph for 3 hours? - If the distance remains the same, what happens when his speed increases? - How does this affect the relationship between speed and time? - Would you like to move on to Problem 2 now, or discuss more about Problem 1? """ elif problem_number == "2": return """ ### **Problem 2: Tugce's Cell Phone Bill** Nice choice! Let’s break this down step by step. 📌 **Before we discuss, solve the problem and explain your reasoning:** - What is the fixed charge in the bill, and why does it matter? - How does the cost per text affect proportionality? ✏️ **Describe your thought process first. I will ask follow-up questions before offering hints or solutions.** Follow-up Prompts: - How much does Tugce pay for 30 texts? - How would the bill change if she sent 60 texts? - Does the bill start from zero, or does it have a fixed cost? - Do you see why this relationship is non-proportional? - Would you like to attempt solving it yourself before I provide guidance? """ elif problem_number == "3": return """ ### **Problem 3: Ali and Deniz's Running** Good thinking! Let’s explore the relationship between their distances. 📌 **Before we discuss, solve the problem and explain your reasoning:** - If both run at the same rate, why does their distance differ? - How can we determine the pattern in their distances over time? ✏️ **Describe your thought process first. I will ask follow-up questions before offering hints or solutions.** Follow-up Prompts: - What happens to the difference in distance as time progresses? Does it remain constant or change? - If Ali had run 3 miles while Deniz had run 2 miles, how much more does Ali run compared to Deniz? - Now, when Ali reaches 6 miles, what pattern do you notice in their distances? - Can you explain why this is an additive relationship rather than a proportional one? - Would you like to attempt solving it yourself before I provide guidance? """ return "I didn’t understand your choice. Please select Problem 1, 2, or 3." def get_ccss_practice_standards(): return """ ### **Common Core Practice Standards** Before moving forward, let's reflect on the problem-solving process: 📌 **Which Common Core Practice Standards do you think we covered?** - Think about reasoning, problem-solving, and mathematical modeling. - Once you've shared your thoughts, I will provide a breakdown of the relevant standards. """ def get_problem_posing_task(): return """ ### **Problem Posing Activity** Now that we've explored non-proportional relationships, let's extend our understanding: 📌 **Create a similar non-proportional problem.** - Think about situations where a fixed cost, an additive relationship, or an inverse relationship might appear. - Explain why the relationship is non-proportional. """ def get_creativity_discussion(): return """ ### **Creativity-Directed Practices** Before we conclude, let’s reflect: 📌 **How do you think creativity played a role in solving these problems?** - What aspects of problem-solving required flexibility or new ways of thinking? - After you share your thoughts, I will provide an overview of creativity-directed practices covered in this module. """ def get_summary(): return """ ### **Summary of Learning** Let’s wrap up what we covered today: 📌 **Content Knowledge (CK):** Understanding non-proportional relationships through real-world contexts. 📌 **Pedagogical Content Knowledge (PCK):** Strategies for teaching these concepts to students. 📌 **Mathematical Creativity (MC):** Problem-solving, reasoning, and connecting concepts in innovative ways. """