| 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 attempt solving it yourself before I provide guidance? | |
| """ | |
| 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_problem_posing_prompt(): | |
| return """ | |
| ### **Problem Posing Activity** | |
| Now that we have analyzed different non-proportional relationships, let’s extend our thinking by creating our own problems. | |
| 📌 **Write a similar problem that involves a non-proportional relationship.** | |
| - Can you think of a real-world situation where there is an additive relationship, a fixed starting cost, or an inverse relationship? | |
| - How will you describe the relationship mathematically? | |
| Would you like to share your problem and discuss how it differs from the ones we explored? | |
| """ | |
| def get_ccss_and_creativity_prompts(): | |
| return """ | |
| ### **Common Core and Creativity Discussion** | |
| Before we go over what standards and creativity-directed practices were covered, what do you think we addressed in this module? | |
| 📌 **Think about the problem-solving strategies, reasoning, and mathematical principles we used.** | |
| - Which Common Core Practice Standards do you think we applied? | |
| - How did creativity play a role in understanding non-proportional relationships? | |
| ### **Now, let’s go over the key standards covered:** | |
| **Common Core State Standards (CCSS) Covered:** | |
| - **CCSS.MATH.CONTENT.7.RP.A.2** - Analyzing proportional relationships and distinguishing them from non-proportional ones. | |
| - **CCSS.MATH.CONTENT.8.F.A.3** - Understanding how functions describe relationships between quantities. | |
| - **CCSS.MATH.CONTENT.8.EE.B.5** - Graphing proportional relationships and understanding unit rates. | |
| **Common Core Practice Standards Applied:** | |
| - **MP1:** Making sense of problems and persevering in solving them. | |
| - **MP2:** Reasoning abstractly and quantitatively. | |
| - **MP3:** Constructing viable arguments and critiquing reasoning. | |
| - **MP4:** Modeling with mathematics. | |
| **Creativity-Directed Practices:** | |
| - **Mathematical Reasoning:** How do you explain non-proportionality to students in a creative way? | |
| - **Exploring Multiple Representations:** What other representations (e.g., graphs, tables) could be used? | |
| - **Applying Problem-Solving Strategies:** How did you approach solving and creating problems in this module? | |
| Would you like to reflect on what you learned in this module and how you might apply it in your teaching? | |
| """ | |
| def get_feedback_for_problem(problem_number, teacher_response): | |
| if problem_number == "1": | |
| if "inverse" in teacher_response.lower(): | |
| return "Good observation! Since speed and time vary inversely, increasing speed decreases time. Can you verify if the ratio stays constant?" | |
| return "Think about what happens to travel time when speed increases. Does the ratio between speed and time remain fixed? Can you calculate the new travel time?" | |
| elif problem_number == "2": | |
| if "fixed charge" in teacher_response.lower() and "$22.50" in teacher_response.lower(): | |
| return "Great insight! The fixed charge prevents proportionality. How does the per-text charge fit into this? Can you compute the total cost for 60 texts?" | |
| return "What happens if the number of texts is zero? Does the total cost still change? Why? Can you calculate the total bill if she sends 60 texts?" | |
| elif problem_number == "3": | |
| if "constant difference" in teacher_response.lower(): | |
| return "Nice thinking! The key here is the additive nature of their distances. Can you determine the difference at another point in time? How far has Deniz run when Ali reaches 6 miles?" | |
| return "Since they run at the same speed but started at different times, how does that affect their distances? Can you compute how far Deniz has run when Ali reaches 6 miles?" | |
| return "Interesting approach! Could you clarify your reasoning a bit more?" | |