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# Module 2: Solving a Ratio Problem Using Multiple Representations | |
INTRO_PROMPT = """ | |
👋 Welcome to **Module 2** on **proportional reasoning and multiple representations**! | |
Today, you’ll explore a real-world problem using different mathematical tools. | |
🚗 **Jessica drives 90 miles in 2 hours. If she drives at the same rate, how far does she travel in 1 hour, ½ hour, and 3 hours?** | |
You'll use: | |
✅ **Bar models** | |
✅ **Double number lines** | |
✅ **Ratio tables** | |
✅ **Graphs** | |
🔍 **Remember:** The goal is not just to get the right answer, but to explore **why** the relationships work the way they do. | |
💬 I’ll guide you step by step—feel free to ask for hints along the way! | |
Let's start with the **bar model**! | |
""" | |
BAR_MODEL_PROMPT = """ | |
📊 **Step 1: Bar Model Representation** | |
Imagine a **bar** representing 90 miles—the distance Jessica travels in **2 hours**. | |
🧩 How might you divide this bar to explore the distances for **1 hour, ½ hour, and 3 hours**? | |
💭 *Please explain how each section of your bar relates to these time intervals!* | |
**💡 Need a hint?** | |
1️⃣ *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?* | |
2️⃣ *Now, extend or divide it further—what happens for **½ hour and 3 hours**?* | |
✅ If correct: *Great! Can you explain why this model helps students visualize proportional relationships?* | |
❌ If incorrect: *Try dividing the bar into two equal sections. What does each section represent?* | |
""" | |
DOUBLE_NUMBER_LINE_PROMPT = """ | |
📏 **Step 2: Double Number Line Representation** | |
Now, let’s use a **double number line**! | |
📌 **Create two parallel lines**: one for **time (hours)** and one for **distance (miles)**. | |
Start by marking: | |
⏳ **0 and 2 hours** on the top line | |
🚗 **0 and 90 miles** on the bottom line | |
What comes next? | |
**💡 Need a hint?** | |
1️⃣ Try labeling the time line **(0, 1, 2, 3)**. How does that help with placing distances below? | |
2️⃣ Since **2 hours = 90 miles**, what does that tell you about **1 hour and ½ hour**? | |
✅ If correct: *Nice work! How does this help students understand proportional relationships?* | |
❌ If incorrect: *Check your spacing—does your number line keep a constant rate?* | |
""" | |
RATIO_TABLE_PROMPT = """ | |
📋 **Step 3: Ratio Table Representation** | |
Next, let’s create a **ratio table**! | |
📝 Make a table with: | |
📌 **Column 1:** Time (hours) | |
📌 **Column 2:** Distance (miles) | |
You already know **2 hours = 90 miles**. | |
🤔 How would you complete the table for **½ hour, 1 hour, and 3 hours**? | |
**💡 Need a hint?** | |
1️⃣ Since **2 hours = 90 miles**, how can you divide this to find **1 hour**? | |
2️⃣ Once you know **1 hour = 45 miles**, can you calculate for **½ hour and 3 hours**? | |
✅ If correct: *Well done! How might this help students compare proportional relationships?* | |
❌ If incorrect: *Something’s a little off. Try using unit rate: 90 ÷ 2 = ?* | |
""" | |
GRAPH_PROMPT = """ | |
📉 **Step 4: Graph Representation** | |
Now, let’s **graph this problem**! | |
🛠 **Plot:** | |
📌 **Time (hours) on the x-axis** | |
📌 **Distance (miles) on the y-axis** | |
You already know two key points: | |
🔹 **(0,0) and (2,90)** | |
🤔 What other points will you add? | |
**💡 Need a hint?** | |
1️⃣ Start by marking **(0,0) and (2,90)**. | |
2️⃣ How can you use these to find **(1,45), (½,22.5), and (3,135)?** | |
✅ If correct: *Fantastic! How does this graph reinforce the idea of constant rate and proportionality?* | |
❌ If incorrect: *Does your line pass through (0,0)? Why is that important?* | |
""" | |
REFLECTION_PROMPT = """ | |
🔄 **Reflection Time!** | |
Now that you've explored **multiple representations**, think about these questions: | |
💡 How does each method highlight **proportional reasoning differently**? | |
💬 Which representation do you prefer, and why? | |
🚀 Can you think of a situation where one of these representations **wouldn’t** be the best choice? | |
Take a moment to reflect! 😊 | |
""" | |
SUMMARY_PROMPT = """ | |
🎯 **Summary of Module 2** | |
📌 **In this module, you:** | |
✅ Solved a proportional reasoning problem using **multiple representations** | |
✅ Explored how different models highlight proportional relationships | |
✅ Reflected on teaching strategies aligned with **Common Core practices** | |
To **wrap up**, try creating a **similar proportional reasoning problem**! | |
Example: A **runner covers a certain distance in a given time**. | |
💡 Make sure your problem can be solved using: | |
✅ **Bar models** | |
✅ **Double number lines** | |
✅ **Ratio tables** | |
✅ **Graphs** | |
📢 *The AI will evaluate your problem and provide feedback!* | |
""" | |
FINAL_REFLECTION_PROMPT = """ | |
🚀 **Final Reflection** | |
- How does designing and solving problems using **multiple representations** enhance students’ mathematical creativity? | |
- How would you guide students to explain their **reasoning**, even if they get the correct answer? | |
📌 Share your thoughts! | |
""" | |