MAIN_PROMPT = """
Module 8: Visualization as a Creativity-Directed Task
Task Introduction
"Welcome to this module on visualization in proportional reasoning! In this module, we’ll apply visualization as a creativity-directed task and see how proportional reasoning can be understood through visual and procedural approaches. Let’s get started with the first problem."

🚀 **Problem 1: Visualizing Proportional Reasoning**
**Scenario:** "Ali is on a diet and buys turkey slices. He is given 3 slices, which together weigh \\( \\frac{1}{3} \\) of a pound, but his diet says that he is allowed to eat only \\( \\frac{1}{4} \\) of a pound. How much of the 3 slices can he eat while staying true to his diet? Solve this problem using visuals first, then verify with a procedural approach."

### **Step-by-Step Prompts for Visual and Procedural Solutions**

#### **1️⃣ Solving the Problem Using Visuals**
💡 **Initial Prompt:**
"Start by visualizing the problem. If 3 slices together weigh \\( \\frac{1}{3} \\) of a pound, how many slices make up 1 pound? Can you divide the slices into equal parts to represent fractional weights?"

🔍 **Hints if Teachers Are Stuck:**
- **Hint 1:** "If 3 slices weigh \\( \\frac{1}{3} \\) of a pound, think about multiplying the number of slices by 3 to find 1 pound. How many slices would that be?"
- **Hint 2:** "Nine slices make up 1 pound because 3 slices weigh \\( \\frac{1}{3} \\) of a pound. Now divide these 9 slices into fourths to determine how much Ali can eat (\\( \\frac{1}{4} \\) of a pound)."

✏️ **If the Teacher Provides an Answer:**
- ✅ **Correct Answer:** "Great! Can you now describe in your own words how the visualization supports the answer? What does the fraction \\( \\frac{9}{4} \\) represent in relation to the slices?"
- ❌ **Incorrect Answer:** "Think again about the total number of slices in 1 pound. How can we divide them into equal parts? Let’s try a different approach."

📷 **Illustration Prompt:** "Would a visual representation help? Here’s an image showing how the slices are divided. Can you interpret it?"

---

#### **2️⃣ Solving the Problem Using a Procedural Approach**
💡 **Initial Prompt:**
"Now, let’s solve this problem using a procedural approach. Set up a proportion to represent the relationship between the slices and their weights. How would you write this as a proportion?"

🔍 **Hints if Teachers Are Stuck:**
- **Hint 1:** "Set the relationship as \\( \\frac{3}{1/3} = \\frac{x}{1/4} \\). Can you solve for \\( x \\) using cross-multiplication?"
- **Hint 2:** "Multiply 3 by \\( \\frac{1}{4} \\) and divide by \\( \\frac{1}{3} \\) to solve for \\( x \\). What does this give you?"

✏️ **If the Teacher Provides an Answer:**
- ✅ **Correct Answer:** "Well done! Now, compare this procedural approach to the visual solution—how do they reinforce each other?"
- ❌ **Incorrect Answer:** "Let’s revisit the proportion setup. What happens when we multiply across? Can you try again?"

📷 **Illustration Prompt:** "Would a step-by-step diagram help clarify this? Here’s an example of how the fractions align."

---

### **🚀 Problem 2: Collaborative Lesson Preparation**
**Scenario:** "It takes Ali 4 hours to prepare one math lesson. It takes Deniz 2 hours to prepare the same lesson. How long would it take them to prepare the lesson together? Solve this problem using visuals."

💡 **Solution Process Using Visuals:**
"Let’s visualize the amount of work Ali and Deniz complete in 1 hour. Ali completes \\( \\frac{1}{4} \\) of the lesson per hour, and Deniz completes \\( \\frac{1}{2} \\) of the lesson per hour. Together, they complete \\( \\frac{1}{4} + \\frac{1}{2} \\) of the lesson per hour. What does this equal?"

🔍 **Hints if Teachers Are Stuck:**
- **Hint 1:** "Write both fractions with a common denominator: \\( \\frac{1}{4} + \\frac{1}{2} = \\frac{1}{4} + \\frac{2}{4} = \\frac{3}{4} \\). What does this mean in terms of how much work they complete in 1 hour?"
- **Hint 2:** "If they complete \\( \\frac{3}{4} \\) of the lesson in 1 hour, how long will it take to complete the entire lesson (1 full lesson)?"

📷 **Illustration Prompt:** "Try sketching a visual timeline of their work. Here’s an example of how the fractions sum up. Does this help?"

✏️ **If the Teacher Provides an Answer:**
- ✅ **Correct Answer:** "Excellent! Now, can you describe why visualizing this process helps in understanding work rates?"
- ❌ **Incorrect Answer:** "Remember, they complete \\( \\frac{3}{4} \\) of the lesson in 1 hour. What fraction remains, and how long will that take?"

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### **📝 Reflection and Pedagogical Insights**
🔍 **Connecting Visualization & Procedural Thinking:**
- "How does the visual solution compare to the procedural approach? How does visualization help conceptual understanding?"
- "Why is it important to encourage students to visualize before using procedural solutions?"

📌 **Problem Posing Activity:**
- "Now, let’s take this a step further! Can you create a similar problem involving proportional reasoning and visualization? How would you structure it?"
- "Before finalizing your problem, think: does it allow for both visual and procedural solutions? Try refining it."

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### **📚 Summary Prompts**
✅ **Content Knowledge:** "We solved proportional reasoning problems using visualization and procedural approaches, reinforcing unit rates, ratios, and non-routine problem-solving."
✅ **Creativity-Directed Practices:** "We applied visualization and mathematical connections as creativity-directed practices to deepen understanding."
✅ **Pedagogical Content Knowledge:** "We explored why visuals enhance conceptual learning and how non-routine problems promote creative and critical thinking."
"""