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- ## Task: Representing Jessica’s Driving Distance 🚗
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- Jessica is driving at a constant speed. She travels **90 miles in 2 hours**.
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- ### Your Goal:
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- Represent the relationship between **time and distance** using different mathematical models:
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- Bar Model
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- ✅ Double Number Line
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- ✅ Ratio Table
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- ✅ Graph
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- Let’s go through each representation step by step!
 
 
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- ---
 
 
 
 
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- ### Step 1: Identifying Current Representation
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- Which representations have you already used to show the relationship between time and distance?
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- - Bar Model
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- - Double Number Line
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- - Ratio Table
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- - Graph
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- If you haven’t used all of them, let’s go through each one step by step.
 
 
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- ---
 
 
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- ### Step 2: Bar Model Representation 📊
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- Have you created a **bar model** to represent Jessica’s travel?
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- **If not, follow these steps:**
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- 1️⃣ Draw a **long bar** to represent **2 hours of driving**, labeling it **90 miles**.
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- 2️⃣ Divide the bar into **two equal parts** to show **1 hour = 45 miles**.
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- 3️⃣ Extend the bar to **3 hours** by adding another **45-mile segment**.
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- 4️⃣ Divide **one 1-hour segment in half** to show **½ hour = 22.5 miles**.
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- Does your bar model correctly show **½, 1, 2, and 3 hours**?
 
 
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- ---
 
 
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- ### Step 3: Double Number Line Representation 📏
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- Have you created a **double number line** for time and distance?
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- **If not, follow these steps:**
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- 1️⃣ Draw **two parallel number lines**:
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- - The **top line** represents **time (hours)**.
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- - The **bottom line** represents **distance (miles)**.
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- 2️⃣ Mark these key points:
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- - **0 hours → 0 miles**
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- - **½ hour → 22.5 miles**
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- - **1 hour → 45 miles**
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- - **2 hours → 90 miles**
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- - **3 hours → 135 miles**
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- 3️⃣ Ensure the distances are evenly spaced.
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- Does your number line show a **proportional relationship**?
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- ---
 
 
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- ### Step 4: Ratio Table Representation 📋
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- Have you created a **ratio table**?
 
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- **If not, follow these steps:**
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- 1️⃣ Fill in the table below:
 
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- | Time (hours) | Distance (miles) |
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- |-------------|-----------------|
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- | 0.5 | 22.5 |
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- | 1 | 45 |
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- | 2 | 90 |
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- | 3 | 135 |
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- 2️⃣ Look for patterns.
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- 3️⃣ What would be the distance for **4 hours**?
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- Does your table clearly show a **proportional pattern**?
 
 
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- ---
 
 
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- ### Step 5: Graph Representation 📈
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- Have you created a **graph** to represent this relationship?
 
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- **If not, follow these steps:**
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- 1️⃣ Draw a **coordinate plane**:
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- - **x-axis → time (hours)**
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- - **y-axis → distance (miles)**
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- 2️⃣ Plot these points:
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- - (0, 0)
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- - (0.5, 22.5)
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- - (1, 45)
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- - (2, 90)
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- - (3, 135)
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- 3️⃣ Draw a straight line through these points.
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- 4️⃣ What does the **slope of the line** tell you about Jessica’s driving rate?
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- Does your graph correctly show a **linear relationship**?
 
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- ---
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- ### Step 6: Final Reflection 💭
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- Great job! Now, take a moment to reflect:
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- 1️⃣ Which representation helped you understand the relationship best? Why?
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- 2️⃣ How do these representations show the **same proportional relationship** in different ways?
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- 3️⃣ Can you apply this method to another real-world proportional relationship?
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- ---
 
 
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- ### New Challenge 🌟
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- Imagine Jessica **increases her speed** by **10 miles per hour**.
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- - How would this affect the bar model, number line, ratio table, and graph?
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- - Try adjusting your models to reflect this change!
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- ---
 
 
 
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- ### Summary of Objectives 🎯
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- - You explored **four ways** to represent proportional relationships: **Bar Model, Double Number Line, Ratio Table, and Graph**.
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- - You understood how **time and distance** relate at a **constant rate**.
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- - You analyzed how different models show the **same mathematical pattern**.
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- ---
 
 
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- ### Common Core Math Standards 🏆
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- - **6.RP.A.1** - Understand the concept of a ratio.
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- - **6.RP.A.3a** - Use ratio reasoning to solve real-world problems.
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- - **7.RP.A.2** - Recognize proportional relationships.
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- **Congratulations! You’ve completed this module.** 🚀
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ # prompts/main_prompt.py
 
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+ __all__ = ["TASK_PROMPT", "BAR_MODEL_PROMPT", "DOUBLE_NUMBER_LINE_PROMPT",
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+ "RATIO_TABLE_PROMPT", "GRAPH_PROMPT", "REFLECTION_PROMPT",
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+ "SUMMARY_PROMPT", "FINAL_REFLECTION_PROMPT"]
 
 
 
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+ # Module starts with the task
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+ TASK_PROMPT = """
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+ Welcome to Module 2: Solving a Ratio Problem Using Multiple Representations!
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+ Task:
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+ Jessica drives 90 miles in 2 hours. If she drives at the same rate, how far does she travel in:
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+ - 1 hour?
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+ - ½ hour?
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+ - 3 hours?
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+ To solve this, try using different representations:
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+ - Bar models
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+ - Double number lines
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+ - Ratio tables
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+ - Graphs
 
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+ Remember: Don't just find the answer—explain why!
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+ I'll guide you step by step—let’s start with the bar model.
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+ """
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+ # Bar Model Prompt
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+ BAR_MODEL_PROMPT = """
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+ Step 1: Bar Model Representation
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+ Imagine a bar representing 90 miles—the distance Jessica travels in 2 hours.
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+ How might you divide this bar to explore the distances for 1 hour, ½ hour, and 3 hours?
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+ Hints if needed:
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+ 1. Think of the entire bar as representing 90 miles in 2 hours. How would you divide it into two equal parts to find 1 hour?
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+ 2. Now, extend or divide it further—what happens for ½ hour and 3 hours?
 
 
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+ If correct: Great! Can you explain why this model helps students visualize proportional relationships?
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+ If incorrect: Try dividing the bar into two equal sections. What does each section represent?
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+ """
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+ # Double Number Line Prompt
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+ DOUBLE_NUMBER_LINE_PROMPT = """
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+ Step 2: Double Number Line Representation
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+ Now, let’s use a double number line.
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+ Create two parallel lines: one for time (hours) and one for distance (miles).
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+ Start by marking:
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+ - 0 and 2 hours on the top line
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+ - 0 and 90 miles on the bottom line
 
 
 
 
 
 
 
 
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+ What comes next?
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+ Hints if needed:
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+ 1. Try labeling the time line (0, 1, 2, 3). How does that help with placing distances below?
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+ 2. Since 2 hours = 90 miles, what does that tell you about 1 hour and ½ hour?
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+ If correct: Nice work! How does this help students understand proportional relationships?
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+ If incorrect: Check your spacing—does your number line keep a constant rate?
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+ """
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+ # Ratio Table Prompt
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+ RATIO_TABLE_PROMPT = """
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+ Step 3: Ratio Table Representation
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+ Next, let’s create a ratio table.
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+ Make a table with:
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+ - Column 1: Time (hours)
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+ - Column 2: Distance (miles)
 
 
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+ You already know 2 hours = 90 miles.
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+ How would you complete the table for ½ hour, 1 hour, and 3 hours?
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+ Hints if needed:
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+ 1. Since 2 hours = 90 miles, how can you divide this to find 1 hour?
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+ 2. Once you know 1 hour = 45 miles, can you calculate for ½ hour and 3 hours?
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+ If correct: Well done! How might this help students compare proportional relationships?
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+ If incorrect: Something’s a little off. Try using unit rate: 90 ÷ 2 = ?
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+ """
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+ # Graph Prompt
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+ GRAPH_PROMPT = """
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+ Step 4: Graph Representation
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+ Now, let’s graph this problem!
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+ Plot:
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+ - Time (hours) on the x-axis
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+ - Distance (miles) on the y-axis
 
 
 
 
 
 
 
 
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+ You already know two key points:
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+ - (0,0) and (2,90)
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+ What other points will you add?
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+ Hints if needed:
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+ 1. Start by marking (0,0) and (2,90).
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+ 2. How can you use these to find (1,45), (½,22.5), and (3,135)?
 
 
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+ If correct: Fantastic! How does this graph reinforce the idea of constant rate and proportionality?
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+ If incorrect: Does your line pass through (0,0)? Why is that important?
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+ """
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+ # Reflection Prompt
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+ REFLECTION_PROMPT = """
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+ Reflection Time!
 
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+ Now that you've explored multiple representations, think about these questions:
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+ - How does each method highlight proportional reasoning differently?
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+ - Which representation do you prefer, and why?
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+ - Can you think of a situation where one of these representations wouldn’t be the best choice?
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+ Take a moment to reflect!
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+ """
 
 
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+ # Summary Prompt
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+ SUMMARY_PROMPT = """
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+ Summary of Module 2
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+ In this module, you:
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+ - Solved a proportional reasoning problem using multiple representations
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+ - Explored how different models highlight proportional relationships
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+ - Reflected on teaching strategies aligned with Common Core practices
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+ Final Task: Try creating a similar proportional reasoning problem!
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+ Example: A runner covers a certain distance in a given time.
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+
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+ Make sure your problem can be solved using:
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+ - Bar models
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+ - Double number lines
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+ - Ratio tables
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+ - Graphs
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+
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+ The AI will evaluate your problem and provide feedback!
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+ """
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+
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+ # Final Reflection Prompt
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+ FINAL_REFLECTION_PROMPT = """
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+ Final Reflection
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+
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+ - How does designing and solving problems using multiple representations enhance students’ mathematical creativity?
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+ - How would you guide students to explain their reasoning, even if they get the correct answer?
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+
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+ Share your thoughts!
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+ """