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MAIN_PROMPT = """ |
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Module 7: Understanding Non-Proportional Relationships |
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Task Introduction |
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"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!" |
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🚀 **Problems:** |
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**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? |
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**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? |
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**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? |
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💡 **Before receiving guidance, solve each problem and explain your reasoning.** |
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🚀 **Let's start with Problem 1. What do you think—Is the relationship between speed and time proportional? Why or why not?** |
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""" |
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def get_prompt_for_problem(problem_number): |
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if problem_number == "1": |
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return """ |
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### **Problem 1: Ali's Driving Speed** |
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Great! Let’s analyze the relationship between speed and time. |
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📌 **Before we discuss, solve the problem and explain your reasoning:** |
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- How do you determine if a relationship is proportional? |
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- What happens to travel time when speed increases? |
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- Does the ratio between speed and time remain constant? |
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🌊 **Describe your thought process first. I will ask follow-up questions before offering hints or solutions.** |
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""" |
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elif problem_number == "2": |
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return """ |
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### **Problem 2: Tugce's Cell Phone Bill** |
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Nice choice! Let’s break this down step by step. |
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📌 **Before we discuss, solve the problem and explain your reasoning:** |
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- What is the fixed charge in the bill, and why does it matter? |
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- How does the cost per text affect proportionality? |
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- Does doubling the number of texts double the total bill? Why or why not? |
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🌊 **Describe your thought process first. I will ask follow-up questions before offering hints or solutions.** |
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""" |
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elif problem_number == "3": |
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return """ |
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### **Problem 3: Ali and Deniz's Running** |
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Good thinking! Let’s explore the relationship between their distances. |
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📌 **Before we discuss, solve the problem and explain your reasoning:** |
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- If both run at the same rate, why does their distance differ? |
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- How can we determine the pattern in their distances over time? |
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- Is there a constant ratio or a constant difference between their distances? |
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🌊 **Describe your thought process first. I will ask follow-up questions before offering hints or solutions.** |
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""" |
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return "I didn’t understand your choice. Please select Problem 1, 2, or 3." |
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def get_feedback_for_problem(problem_number, teacher_response): |
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if problem_number == "1": |
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return """ |
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Great observation! Since speed and time vary inversely, increasing speed decreases time. However, does the ratio between speed and time remain constant? How would you verify it? |
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""" |
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elif problem_number == "2": |
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return """ |
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You're on the right track! The fixed charge prevents proportionality. How does the per-text charge fit into this? Can you compute the total cost for 60 texts? |
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""" |
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elif problem_number == "3": |
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return """ |
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Good thinking! The key here is the additive nature of their distances. Since Ali started earlier, his lead remains constant rather than proportional. Can you determine the difference in distance at another point in time? |
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""" |
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return "Interesting approach! Could you clarify your reasoning a bit more?" |
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def additional_discussion(): |
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return """ |
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### **Extending the Discussion: Common Core and Creativity** |
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Now, let’s reflect on the broader connections. **Before I provide details, what Common Core Practice Standards do you think we covered in this module?** |
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Now that you've shared your thoughts, here are some key Common Core Practice Standards we engaged with: |
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- **MP1: Make sense of problems and persevere in solving them.** You analyzed and worked through non-proportional relationships. |
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- **MP2: Reason abstractly and quantitatively.** You interpreted relationships and represented them mathematically. |
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- **MP4: Model with mathematics.** You created equations to describe real-world scenarios. |
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- **MP7: Look for and make use of structure.** You identified patterns in proportional and non-proportional relationships. |
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🌈 **Now, what creativity-directed practices do you think we covered?** |
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Some creativity-directed practices we explored include: |
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- **Problem-Solving:** Approaching non-proportional problems with different strategies. |
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- **Modeling Real-World Situations:** Translating problems into mathematical equations. |
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- **Connecting Concepts:** Linking ideas across different mathematical representations. |
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- **Generating and Testing Hypotheses:** Predicting relationships and verifying solutions. |
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### **Posing a Similar Task** |
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Now that you’ve analyzed these problems, it’s your turn! **Can you create a non-proportional problem similar to the ones we explored?** |
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- Describe the situation and explain why it is non-proportional. |
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### **Final Summary: CK, PCK, and MC** |
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To wrap up, let's summarize what we learned in terms of: |
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- **Content Knowledge (CK):** Understanding and distinguishing non-proportional relationships. |
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- **Pedagogical Content Knowledge (PCK):** Strategies for teaching proportional vs. non-proportional relationships. |
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- **Mathematical Creativity (MC):** Using real-world modeling, problem-solving, and alternative representations. |
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""" |
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