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MAIN_PROMPT = """
### **Module 4: Proportional Thinking with Percentages**
"Welcome to this module on proportional reasoning with percentages!
Your task is to **solve a problem using different representations** and connect the proportional relationship to the meaning of the problem."
πŸ“Œ **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.
πŸ’‘ **How much do they invest together?**
πŸ’‘ **Solve using a Bar Model, Double Number Line, or Equations.**
βœ… **Remember:**
- "Explain your thought process after solving each part."
- "Try your best before I give hints!"
πŸš€ **Let’s begin! Which method would you like to use first?**
"""
def next_step(step):
if step == 1:
return """πŸš€ **Step 1: Solve Using a Bar Model**
"How can we use a **bar model** to solve this problem?"
πŸ’‘ **OK! Let's hear your ideas first.**
- "What does the full bar represent?"
- "How might we divide the bar to show 60%?"
- "How can this help us find the total investment?"
πŸ”Ή **Share your thinking before I provide any hints!**
"""
elif step == 2:
return """πŸ”Ή **Hint 1:**
"Try drawing a **bar to represent the total investment**.
- Since 60% = **$1,500**, divide the bar into **10 equal sections** (each representing 10%).
- Shade in **6 sections** to represent Orrin’s 60%.
Does this setup make sense to you?"
"""
elif step == 3:
return """πŸ”Ή **Hint 2:**
"Now, let’s determine the value of one part.
- Since 6 sections represent **$1,500**, we divide:
\\[
\\text{Value of 1 part} = \\frac{1500}{6}
\\]
What do you get?"
"""
elif step == 4:
return """πŸ”Ή **Hint 3:**
"Now that we know the value of **one part**, we can find the total investment by multiplying by 10:
\\[
\\text{Total Investment} = \\text{Value of 1 part} \\times 10
\\]
Can you calculate and explain your answer?"
"""
elif step == 5:
return """βœ… **Solution:**
"Nice work! You found that **1 part = $250**.
Now, multiplying by **10**:
\\[
\\text{Total Investment} = 250 \\times 10 = 2500
\\]
So, the total investment by Orrin and Damen together is **$2,500.**"
πŸ’‘ **Reflection:**
- "How does this visual help in understanding the problem?"
- "Would this be useful for students struggling with percentages?"
πŸš€ "Now, let's solve this problem using a **double number line!**"
"""
elif step == 6:
return """πŸš€ **Step 2: Solve Using a Double Number Line**
"How can a **double number line** help solve this problem?"
πŸ’‘ **OK! Let's hear your ideas first.**
- "What should the two number lines represent?"
- "What key points should we label on the number lines?"
- "How can we use this to find the total investment?"
πŸ”Ή **Try before I give hints!**
"""
elif step == 7:
return """πŸ”Ή **Hint 1:**
"Start by labeling the number lines:
- One represents **percentages**: **0%, 60%, and 100%**.
- The other represents **dollars**: **$0, $1,500, and the total investment**.
What values go in between?"
"""
elif step == 8:
return """πŸ”Ή **Hint 2:**
"Now, divide $1,500 by 6 to find 10%:
\\[
\\text{Value of 10\\%} = \\frac{1500}{6} = 250
\\]
Align this with **10% on the number line.**
Now, what is the value at 100%?"
"""
elif step == 9:
return """βœ… **Solution:**
"Now that we’ve aligned the values:
- 10% = **$250**
- 100% = **$2500**
So, the total investment is **$2,500!**
πŸ’‘ **Reflection:**
- "How does this method compare to the bar model?"
- "Would this approach help students struggling with percentages?"
πŸš€ "Now, let's try solving with an **equation!**"
"""
elif step == 10:
return """πŸš€ **Step 3: Solve Using an Equation**
"How can we set up an **equation** to represent this problem?"
πŸ’‘ **OK! Let's hear your ideas first.**
- "What proportional relationship can we write?"
- "How can we express 60% mathematically?"
- "What unknown are we solving for?"
πŸ”Ή **Try setting up the equation before I provide hints!**
"""
elif step == 11:
return """πŸ”Ή **Hint 1:**
"Write the relationship as a proportion:
\\[
\\frac{60}{100} = \\frac{1500}{x}
\\]
How can we solve for \\(x\\)?"
"""
elif step == 12:
return """πŸ”Ή **Hint 2:**
"Use **cross-multiplication**:
\\[
60x = 1500 \\times 100
\\]
Now divide both sides by 60. What do you get?"
"""
elif step == 13:
return """βœ… **Solution:**
"Nice work! Solving the equation:
\\[
x = \\frac{1500 \\times 100}{60} = 2500
\\]
So, the total investment is **$2,500!**
πŸ’‘ **Reflection:**
- "Which method do you prefer: Bar Model, Double Number Line, or Equation?"
- "How can we help students connect all three approaches?"
πŸš€ "Now, let’s reflect on the **Common Core practices** we used."
"""
elif step == 14:
return """πŸ“Œ **Common Core Standards Discussion**
"Great job! Let’s reflect on how this connects to teaching strategies."
πŸ”Ή **Which Common Core Standards did we cover?**
- **CCSS.MATH.CONTENT.6.RP.A.3** (Solving real-world proportional reasoning problems)
- **CCSS.MATH.CONTENT.7.RP.A.2** (Recognizing proportional relationships)
- **CCSS.MATH.PRACTICE.MP1** (Making sense of problems & persevering)
- **CCSS.MATH.PRACTICE.MP4** (Modeling with mathematics)
πŸ’‘ "Which of these standards do you think applied most? Why?"
"""
elif step == 15:
return """πŸ“Œ **Creativity-Directed Practices Discussion**
"Throughout this module, we engaged in creativity-directed strategies, such as:
βœ… Using multiple solution methods
βœ… Encouraging deep reasoning
βœ… Connecting visual and numerical representations
πŸ’‘ "How do these strategies help students build deeper understanding?"
πŸš€ "Now, let’s create your own problem!"
"""
return "πŸŽ‰ **You've completed the module! Would you like to review anything again?**"