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