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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."
π **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.
π‘ **How much do they invest together?**
β
**Choose a method to solve:**
1οΈβ£ **Bar Model**
2οΈβ£ **Double Number Line**
3οΈβ£ **Equations**
π‘ **Explain your thought process before I provide any hints!**
π **Letβs begin! Which method would you like to use first?**
"""
def next_step(step):
if step == 1:
return """π **Step 1: Choose Your Method**
"Which method would you like to use to solve this problem?"
π‘ **Select one method:**
- **Bar Model**
- **Double Number Line**
- **Equation**
πΉ **Once you choose a method, explain your approach first.**
πΉ **Try your best before I provide guidance!**
"""
elif step == 2:
return """π **Step 2: Solve Using a Bar Model**
"Great choice! Let's use a bar model to visualize the problem."
π‘ **How do you think a bar model can help?**
- "How will you divide the bar to represent percentages?"
- "What should each section represent?"
- "How will you calculate the total investment?"
πΉ **Explain your reasoning before I provide hints!**
"""
elif step == 3:
return """πΉ **Hint 1:**
"Try drawing a **bar representing 100% of the total investment**.
- Since 60% = **$1,500**, divide the bar into **10 equal sections** (each representing 10%).
- Shade in **6 sections** to represent Orrinβs 60%.
Does this setup make sense?"
"""
elif step == 4:
return """πΉ **Hint 2:**
"Now, find the value of **1 part** by dividing **$1,500 by 6**:
\\[
\\text{Value of 1 part} = \\frac{1500}{6} = 250
\\]
What is the total investment?"
"""
elif step == 5:
return """β
**Solution:**
"Great job! Since **1 part = $250**, multiplying by **10** gives:
\\[
\\text{Total Investment} = 250 \\times 10 = 2500
\\]
So, the total investment by Orrin and Damen together is **$2,500.**"
π‘ **Reflection:**
- "How did the bar model help in understanding this problem?"
π "Would you like to try another method, such as a **double number line**?"
"""
elif step == 6:
return """π **Step 3: Solve Using a Double Number Line**
"Now, let's try solving this using a **double number line**."
π‘ **Before I provide hints, explain your approach:**
- "How will you set up the two number lines?"
- "What key points should be labeled?"
- "How can you use it to find the total investment?"
πΉ **Think about it and explain before I provide guidance!**
"""
elif step == 7:
return """πΉ **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 """πΉ **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 """β
**Solution:**
"Now that weβve aligned the values:
- 10% = **$250**
- 100% = **$2500**
So, the total investment is **$2,500!**
π‘ **Reflection:**
- "How does this method compare to the bar model?"
π "Would you like to try solving with an **equation**?"
"""
elif step == 10:
return """π **Step 4: Solve Using an Equation**
"Now, let's try setting up an **equation** to represent the problem."
π‘ **Before I provide hints, explain your approach:**
- "How can we express 60% mathematically?"
- "What unknown are we solving for?"
πΉ **Try setting up the equation before I provide hints!**
"""
elif step == 11:
return """πΉ **Hint 1:**
"Write the relationship as a proportion:
\\[
\\frac{60}{100} = \\frac{1500}{x}
\\]
How can we solve for \\(x\\)?"
"""
elif step == 12:
return """πΉ **Hint 2:**
"Use **cross-multiplication**:
\\[
60x = 1500 \\times 100
\\]
Now divide both sides by 60. What do you get?"
"""
elif step == 13:
return """β
**Solution:**
"Great job! Solving the equation:
\\[
x = \\frac{1500 \\times 100}{60} = 2500
\\]
So, the total investment is **$2,500!**
π‘ **Reflection:**
- "Which method do you prefer: Bar Model, Double Number Line, or Equation?"
π "Now, letβs reflect on the **Common Core practices** we used."
"""
elif step == 14:
return """π **Common Core Standards Discussion**
"Great job! Letβs reflect on how this connects to teaching strategies."
πΉ **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)
π‘ "Which of these standards do you think applied most? Why?"
"""
elif step == 15:
return """π **Creativity-Directed Practices Discussion**
"Throughout this module, we engaged in creativity-directed strategies, such as:
β
Using multiple solution methods
β
Encouraging deep reasoning
β
Connecting visual and numerical representations
π‘ "How do these strategies help students build deeper understanding?"
π "Now, letβs create your own problem!"
"""
return "π **You've completed the module! Would you like to review anything again?**"
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