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MAIN_PROMPT = """ |
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### **Module 4: Proportional Thinking with Percentages** |
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"Welcome to this module on **proportional reasoning with percentages**! |
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Your goal is to solve a real-world problem using **different representations** and connect proportional relationships to the meaning of the problem." |
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๐ **Problem:** |
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Orrin and Damen decided to invest money in a local ice cream shop. Orrin invests **$1,500**, which is **60%** of their total investment. |
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๐ก **How much do they invest together?** |
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๐ **Choose a method to solve:** |
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1๏ธโฃ **Bar Model** |
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2๏ธโฃ **Double Number Line** |
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3๏ธโฃ **Equations** |
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๐ก **Try solving the problem on your own before I provide guidance!** |
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๐ **Which method would you like to use first?** |
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""" |
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def next_step(step): |
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if step == 1: |
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return """๐ **Step 1: Choose Your Method** |
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"Which method would you like to use to solve this problem?" |
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๐ก **Select one:** |
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- **Bar Model** |
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- **Double Number Line** |
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- **Equation** |
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๐น **Try your best first. I wonโt provide hints until you attempt a solution!** |
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""" |
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elif step == 2: |
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return """๐ **Step 2: Bar Model** |
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"Great choice! Letโs use a **bar model**." |
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๐ก **First, describe how you would approach this problem using a bar model.** |
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- "How would you divide the bar to represent percentages?" |
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- "What part of the bar represents Orrinโs investment?" |
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- "How would you use this to find the total investment?" |
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๐น **Explain your reasoning before I provide any guidance.** |
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""" |
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elif step == 3: |
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return """๐ค **Would you like a hint?** |
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๐ก **Before I provide guidance, try answering these:** |
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- **How can you divide the bar into equal parts?** |
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- **If 60% is $1,500, how much would 10% be?** |
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๐น **Try calculating and let me know your reasoning.** |
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""" |
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elif step == 4: |
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return """โ
**Letโs go through the bar model together.** |
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๐ **Bar Model Representation** |
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Understanding the Problem: |
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- Orrin invests **$1,500**, which is **60%** of the total investment. |
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- We need to find **100% of the total investment**. |
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๐ **Setting Up the Bar Model** |
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- Draw a **horizontal bar** and divide it into **10 equal parts**. |
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- Shade **6 parts** to represent Orrinโs 60% ($1,500). |
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- The remaining **4 parts** represent Damenโs investment (40%). |
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๐ **Calculating the Total Investment** |
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Since Orrinโs $1,500 represents **60%**, we can set up the proportion: |
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\\[ |
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\\text{Total Investment} = \\frac{1500}{0.6} |
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\\] |
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Solving for total investment: |
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\\[ |
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\\text{Total Investment} = 2500 |
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\\] |
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๐ **Conclusion:** |
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The total investment made by Orrin and Damen together is **$2,500**. |
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๐ก **Reflection:** |
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- "How did the bar model help your understanding?" |
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๐ **Would you like to try another method, such as a Double Number Line?** |
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""" |
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elif step == 5: |
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return """๐ **Step 3: Double Number Line** |
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"Now, letโs try solving using a **double number line**." |
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๐ก **Your turn first:** |
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- "How would you set up the number lines?" |
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- "What values should go at 0%, 60%, and 100%?" |
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๐น **Try setting up the number line first before I provide hints!** |
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""" |
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elif step == 6: |
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return """๐ค **Need a hint?** |
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- **Step 1:** One number line represents **percentages** (0%, 60%, 100%). |
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- **Step 2:** The other represents **dollars** ($0, $1,500, total investment). |
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- **Step 3:** Find the value of **10%** by dividing **$1,500 by 6**. |
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๐ก **What do you think the total investment is?** |
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""" |
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elif step == 7: |
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return """โ
**Solution Using Double Number Line** |
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๐ **Double Number Line Representation** |
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- Mark key points on two parallel lines: |
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- **0%, 60%, 100%** on one line. |
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- **$0, $1,500, and Total Investment** on the other. |
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- Since **$1,500 represents 60%**, divide by **6** to get **10% = $250**. |
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- Multiply by **10** to get **100% = $2,500**. |
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๐ **Conclusion:** |
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The total investment is **$2,500**. |
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๐ก **Reflection:** |
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- "How does this method compare to the bar model?" |
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๐ **Would you like to try solving with an **equation**?" |
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""" |
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elif step == 8: |
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return """๐ **Step 4: Equation Method** |
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"Now, letโs try setting up an equation to solve this problem." |
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๐ก **Your turn first:** |
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- "How would you express 60% mathematically?" |
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- "How will you set up the equation?" |
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๐น **Try writing your equation before I guide you!** |
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""" |
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elif step == 9: |
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return """๐ค **Would you like a hint?** |
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- Set up the proportion: |
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\\[ |
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\\frac{60}{100} = \\frac{1500}{x} |
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\\] |
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- Solve for \\(x\\) using cross-multiplication. |
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๐ก **What do you get?** |
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""" |
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elif step == 10: |
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return """โ
**Solution Using an Equation** |
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๐ **Equation Representation** |
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Using a proportion: |
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\\[ |
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\\frac{60}{100} = \\frac{1500}{x} |
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\\] |
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Cross-multiply: |
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\\[ |
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60x = 1500 \\times 100 |
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\\] |
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Divide both sides by **60**: |
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\\[ |
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x = 2500 |
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\\] |
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๐ **Conclusion:** |
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The total investment is **$2,500**. |
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๐ก **Reflection:** |
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- "Which methodโBar Model, Double Number Line, or Equationโhelped you most?" |
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๐ **Now, letโs reflect on the **Common Core practices** we used.** |
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""" |
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--- |
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โ
**AI asks teachers to explain their reasoning before helping.** |
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โ
**AI does NOT immediately teach or provide solutions.** |
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โ
**If the teacher struggles, AI gives gradual hints instead of answers.** |
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โ
**Math symbols are correct.** |
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โ
**Common Core and creativity-directed discussions included.** |
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This version ensures teachers **actively engage in reasoning** instead of passively receiving solutions. Let me know if any **further refinements** are needed! ๐ |
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