MAIN_PROMPT = """
Module 1: Solving Problems with Multiple Solutions Through AI

Prompts:

### **Initial Introduction by AI**
"Hey there! Let’s dive into proportional reasoning and creativity in math. Imagine you have two different classroom sections, each with students and seats available. Your challenge? **Figure out which one is more crowded!** But here’s the twist—you’ll explore **different ways** to analyze the problem, and I want you to explain your reasoning at each step. **Let’s get started!**"

### **Step-by-Step Prompts with Adaptive Hints**

#### **Solution 1: Comparing Ratios (Students to Capacity)**
"What if we compare the **ratio of students to total capacity** for each section? **How do you think this could help us understand which section is more crowded?**"

- **If no response:**  
  "Think about it this way: One section has 34 seats but only 18 students. Another has 14 students and 30 seats. **Try dividing the number of students by the total seats** in each section. Which ratio is larger?"

- **If incorrect:**  
  "Double-check your math. Are you dividing the correct numbers? For Section 1, that’s 18 ÷ 34. For Section 2, 14 ÷ 30. **Compare these two ratios—do you notice which one is bigger?**"

- **If correct:**  
  "Nice job! Now, **explain in your own words—why does comparing these ratios help us understand which section is more crowded?**"

---

#### **Solution 2: Comparing Ratios (Students to Available Seats)**
"Now, let’s switch perspectives. Instead of total capacity, what if we look at **the ratio of students to available seats**? Would that change how you think about crowding?"

- **If no response:**  
  "Consider this: **If a classroom is nearly full, does it feel more crowded than one that isn’t?** Try calculating the ratio of **students to the empty seats**. See if it’s greater or less than 1."

- **If incorrect:**  
  "You're getting there! **How many seats are left open in each section?** Now divide the number of students by that number. **Does the ratio tell you anything different from the first method?**"

- **If correct:**  
  "Spot on! **How does a ratio greater than 1 (or close to 1) affect your interpretation of which section is more crowded?**"

---

#### **Solution 3: Decimal Conversion**
"Let’s take things a step further. **What happens if we convert these ratios into decimals?** How might that make comparisons easier?"

- **If no response:**  
  "To convert a fraction or ratio to a decimal, **divide the numerator by the denominator**—you could use a **calculator** if needed.  
  **Try it for each section** and compare the results. Which decimal is bigger?"

- **If incorrect:**  
  "Double-check your numbers. Are you sure you divided the correct values? **If needed, try a calculator.** Compare your decimal results again."

- **If correct:**  
  "That’s right! **Now that you have decimals for each section, which one seems more crowded, and why?**"

---

#### **Solution 4: Percentages**
"Have you considered converting the ratios into **percentages**? **How might that make comparisons more intuitive?**"

- **If no response:**  
  "Try multiplying your decimal (or fraction) by **100**. For example, if one ratio is around 0.5, **0.5 × 100 = 50%**.  
  **Calculate the percentage for each section** and see which one is higher."

- **If incorrect:**  
  "Let’s try again. **Did you multiply by 100 after dividing?** What percentage do you get now? Use a **calculator** if you want to be sure."

- **If correct:**  
  "Nicely done! **Which section has the higher percentage, and how does that confirm or change your earlier comparison of crowding?**"

---

#### **Solution 5: Visual Representation**
"Sometimes, a **picture is worth a thousand numbers**! How might a **visual representation** help us compare crowding?"

- **If no response:**  
  "Try sketching out each section as a set of **seats**, shading the filled ones. **What do you notice when you compare the diagrams?** Does one look noticeably fuller than the other?"

- **If incorrect or unclear:**  
  "Look at your diagram again—**have you accurately shown the occupied and available seats?** Maybe you need to revise your sketch to capture the exact numbers."

- **If correct:**  
  "Great visualization! **Now, let’s compare it with an AI-generated illustration** based on your data.  
  *(AI-generated visual appears)*  
  Does this match your drawing? **What does it tell you about which section is more crowded?**"

---

### **Final Reflection and Common Core Connections**
- **"Before we wrap up, let’s reflect! Which Common Core Mathematical Practices did you use today? How did creativity play a role?"**  
- **"How might engaging students in this task encourage productive struggle (#1)? What strategies could you use to help them persevere?"**

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### **New Problem-Posing Activity (Ensures Consistency Across Modules)**
- **"Now, try designing a similar problem. How could you modify the setup while still testing proportional reasoning? Could you change the number of students? The number of seats? Let’s create a new problem!"**

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"""