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MAIN_PROMPT = """
### **Module 4: Proportional Thinking with Percentages**
"Welcome to this module on proportional reasoning with percentages!
In this module, you will explore different representations of proportional thinking:
1οΈβ£ **Bar Models**
2οΈβ£ **Double Number Lines**
3οΈβ£ **Equations & Proportional Relationships**
π‘ **You will solve the given problem using different strategies and explain your reasoning.**
π‘ **The AI will guide you through hints if neededβtry solving before asking for help!**
π **Letβs begin!**
"""
def next_step(step):
if step == 1:
return """π **Step 1: Solve Using a Bar Model**
"Orrin invests **$1,500**, which is **60%** of their total investment.
How can you use a bar model to solve this problem?"
π‘ **Think before answering:**
- "How can we represent the **total investment** as a bar?"
- "If 60% is **$1,500**, how many sections should the bar have?"
πΉ **Try setting it up before I provide hints!**
"""
elif step == 2:
return """πΉ **Hint 1:**
"Start by drawing a rectangle to represent the **total investment**.
- Divide it into **10 equal sections** (since each section represents **10%** of the total).
- Since **60% corresponds to $1,500**, shade in **6 parts** of the bar.
Now, can you determine how much **1 part** represents?"
"""
elif step == 3:
return """πΉ **Hint 2:**
"If 6 parts correspond to **$1,500**, find the value of **one part** by dividing:
\\[
\\text{Value of 1 part} = \\frac{1500}{6}
\\]
What do you get?"
"""
elif step == 4:
return """πΉ **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 """β
**Solution:**
"We 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.**"
π‘ **Reflection:**
- "How does this visual help in understanding the problem?"
- "Would this be useful for students struggling with percentages?"
π "Now, let's solve this problem using a **double number line!**"
"""
elif step == 6:
return """π **Step 2: Solve Using a Double Number Line**
"A double number line is another great way to visualize this problem.
How would you set up a **double number line** to solve this?"
π‘ **Think before answering:**
- "What labels would you use for the two number lines?"
- "How can you align percentages with dollar values?"
πΉ **Try setting it up before I provide hints!**
"""
elif step == 7:
return """πΉ **Hint 1:**
"Start by labeling the two number lines:
- The **top line** represents **percentages** (0%, 10%, 20%, β¦, 100%).
- The **bottom line** represents **dollars** ($0, $?, $?, β¦, Total Investment).
- Since **60% = $1,500**, mark this point on both lines.
Can you determine what **10%** would be?"
"""
elif step == 8:
return """πΉ **Hint 2:**
"To find **10%**, divide **$1,500 by 6**:
\\[
\\text{10% Value} = \\frac{1500}{6} = 250
\\]
Now, use this to determine **100%**!"
"""
elif step == 9:
return """β
**Solution:**
"Now that we know **10% = $250**, we can multiply by 10:
\\[
\\text{Total Investment} = 250 \\times 10 = 2500
\\]
So, the total investment by Orrin and Damen together is **$2,500.**"
π‘ **Reflection:**
- "How does the double number line help in understanding the proportional relationship?"
π "Now, let's solve this using **an equation!**"
"""
elif step == 10:
return """π **Step 3: Solve Using an Equation**
"An equation allows us to solve proportions algebraically.
How can you set up an equation for this problem?"
π‘ **Think before answering:**
- "How can we represent 60% in fractional form?"
- "How can we write a proportion to find the total investment?"
πΉ **Try setting it up before I provide hints!**
"""
elif step == 11:
return """πΉ **Hint 1:**
"Write the proportion as:
\\[
\\frac{60}{100} = \\frac{1500}{x}
\\]
Now, can you **cross-multiply** and solve for **x**?"
"""
elif step == 12:
return """β
**Solution:**
"Using cross-multiplication:
\\[
60x = 1500 \\times 100
\\]
\\[
x = \\frac{1500 \\times 100}{60} = 2500
\\]
So, the total investment by Orrin and Damen together is **$2,500.**"
π‘ **Reflection:**
- "How does solving with an equation compare to visual methods?"
π "Now, let's reflect on teaching strategies!"
"""
elif step == 13:
return """π **Common Core & Creativity-Directed Practices Discussion**
"Great job! Now, letβs reflect on how these problems connect 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 to the problems we solved? Why?**
"""
elif step == 14:
return """π **Creativity-Directed Practices Discussion**
"Throughout these problems, we engaged in creativity-directed strategies, such as:
β
Encouraging multiple solution methods
β
Using real-world contexts
β
Thinking critically about proportional relationships
π‘ **Which of these strategies did you use while solving the problems?**
π‘ **How do you think encouraging creativity helps students develop deeper understanding?**
"""
elif step == 15:
return """π **Problem-Posing Activity**
"Now, letβs take it one step further! Try creating your own proportional reasoning problem."
π‘ "Would you like to modify one of the previous problems, or create a brand new one?"
"""
return "π **You've completed the module! Would you like to review anything again?**"
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