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Jessica is driving at a constant speed. She travels **90 miles in 2 hours**.
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✅ Double Number Line
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✅ Ratio Table
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✅ Graph
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- Graph
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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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- 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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| 2 | 90 |
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| 3 | 135 |
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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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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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- Try adjusting your models to reflect this change!
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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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# 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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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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The AI will evaluate your problem and provide feedback!
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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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- 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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Share your thoughts!
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"""
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