| 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, solve the problem and explain your reasoning first.** |
| 🚀 **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 I provide guidance, solve the problem and explain your reasoning:** |
| - What assumptions do you make about the problem? |
| - How does changing speed impact time? |
| ✏️ **Describe your thought process first. I will ask follow-up questions before offering hints.** |
| |
| 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? |
| - Does this relationship follow a proportional pattern? Why or why not? |
| - Would you like to create a similar problem related to speed and time? |
| """ |
| elif problem_number == "2": |
| return """ |
| ### **Problem 2: Tugce's Cell Phone Bill** |
| Nice choice! Let’s analyze the billing structure. |
| 📌 **Before I provide guidance, solve the problem and explain your reasoning:** |
| - What components make up the total bill? |
| - Does the bill start at zero, or is there a fixed charge? |
| ✏️ **Describe your thought process first. I will ask follow-up questions before offering hints.** |
| |
| Follow-up Prompts: |
| - How much does Tugce pay for 30 texts? |
| - How would the bill change if she sent 60 texts? |
| - Is this a proportional or non-proportional relationship? Explain why. |
| - Can you create a similar problem involving fixed and variable costs? |
| """ |
| elif problem_number == "3": |
| return """ |
| ### **Problem 3: Ali and Deniz's Running** |
| Let’s explore how distance changes over time. |
| 📌 **Before I provide guidance, 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.** |
| |
| Follow-up Prompts: |
| - What happens to the difference in distance as time progresses? Does it remain constant or change? |
| - Can you explain why this is an additive relationship rather than a proportional one? |
| - Would you like to create your own running-related problem? |
| """ |
| 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?** |
| - Look at reasoning, problem-solving, and mathematical modeling. |
| - Once you've shared your thoughts, I will provide a breakdown of the relevant standards and how they connect to creativity. |
| """ |
|
|
| def get_problem_posing_task(): |
| return """ |
| ### **Problem Posing Activity** |
| Now that we've explored non-proportional relationships, let’s extend our understanding: |
| 📌 **Create a non-proportional problem based on real-world scenarios.** |
| - Think about situations where a fixed cost, an additive relationship, or an inverse relationship might appear. |
| - Explain why the relationship is non-proportional and how it differs from proportional relationships. |
| """ |
|
|
| def get_creativity_discussion(): |
| return """ |
| ### **Creativity-Directed Practices** |
| Before we conclude, let’s reflect: |
| 📌 **How did creativity play a role in solving these problems?** |
| - What problem-solving strategies required flexibility or new ways of thinking? |
| - How did posing your own problems deepen your understanding? |
| - After you share your thoughts, I will summarize the 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 and engaging students in reasoning. |
| 📌 **Mathematical Creativity (MC):** Encouraging problem-solving, reasoning, and generating new mathematical questions. |
| 📌 **Common Core Standards:** Applying mathematical modeling, attending to precision, and making sense of problems. |
| """ |
|
|
