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### π MAIN PROMPT ###
MAIN_PROMPT = """
### **Module 3: Proportional Reasoning Problem Types**
"Welcome to this module on proportional reasoning problem types!
Today, we will explore three fundamental types of proportional reasoning problems:
1οΈβ£ **Missing Value Problems**
2οΈβ£ **Numerical Comparison Problems**
3οΈβ£ **Qualitative Reasoning Problems**
Your goal is to **solve and compare** these problems, **identify their characteristics**, and finally **create your own examples** for each type.
π‘ **Throughout this module, I will guide you step by step.**
π‘ **You will be encouraged to explain your reasoning before receiving hints.**
π‘ **If youβre unsure, I will provide hints rather than giving direct answers.**
π **Letβs begin! First, try solving each problem on your own. Then, I will help you refine your thinking step by step.**
"""
def next_step(step):
if step == 1:
return """π **Problem 1: Missing Value Problem**
"The scale on a map is **2 cm represents 25 miles**. If a measurement is **24 cm**, how many miles does it represent?"
π‘ **What do you think? Try solving before I provide hints.**
- "What type of proportional reasoning is needed here?"
- "How does 24 cm compare to 2 cm? Can you find the scale factor?"
- "What would be a good way to set up a proportion for this?"
πΉ **Try explaining your reasoning before I provide hints!**
"""
elif step == 2:
return """πΉ **Identifying the Method:**
"This is a **missing value problem** because we know a proportional relationship but need to find an unknown value.
How would you set up an equation for this problem?"
π‘ **Think before answering! Type your response below.**
"""
elif step == 3:
return """πΉ **Hint 1:**
1οΈβ£ "Try setting up a proportion:
\\[
\\frac{2}{25} = \\frac{24}{x}
\\]
Does this equation make sense?"
π‘ **Try solving it yourself first.**
"""
elif step == 4:
return """πΉ **Hint 2:**
2οΈβ£ "Now, cross-multiply:
\\[
2 \\times x = 24 \\times 25
\\]
Can you solve for \\( x \\)?"
π‘ **Give it a shot!**
"""
elif step == 5:
return """β
**Solution:**
"Final step: divide both sides by 2:
\\[
x = \\frac{600}{2} = 300
\\]
So, 24 cm represents **300 miles**!"
π‘ "Does this answer make sense? Want to try another method?"
"""
elif step == 6:
return """π **Problem 2: Numerical Comparison Problem**
"Ali bought **10 pencils for $3.50**, and Ahmet bought **5 pencils for $1.80**. Who got the better deal?"
π‘ **What do you think? Try solving before I provide hints.**
- "What is the best way to compare prices fairly?"
- "Why would calculating unit rates be useful here?"
πΉ **Explain your reasoning before I provide hints!**
"""
elif step == 7:
return """πΉ **Identifying the Method:**
"This is a **numerical comparison problem** because we are comparing two different rates."
How would you set up an equation for this problem?"
π‘ **Think before answering! Type your response below.**
"""
elif step == 8:
return """πΉ **Hint 1:**
1οΈβ£ "Find the cost per pencil:
\\[
\\frac{3.50}{10} = 0.35
\\]
per pencil (Ali)
\\[
\\frac{1.80}{5} = 0.36
\\]
per pencil (Ahmet)"
π‘ **Try calculating it before moving forward!**
"""
elif step == 9:
return """β
**Solution:**
"Which is cheaper?
- **Ali pays less per pencil** (35 cents vs. 36 cents).
So, **Ali got the better deal!**"
π‘ "Does this make sense? Would you like to discuss unit rates more?"
"""
elif step == 10:
return """π **Problem 3: Qualitative Reasoning Problem**
"Kim is mixing paint. Yesterday, she mixed red and white paint. Today, she added **more red paint** but kept the **same white paint**. What happens to the color?"
π‘ **What do you think? Try explaining before I provide hints.**
- "How does the ratio of red to white change?"
- "Would the color become darker, lighter, or stay the same?"
πΉ **Explain your reasoning before I provide hints!**
"""
elif step == 11:
return """πΉ **Identifying the Method:**
"This is a **qualitative reasoning problem** because it focuses on how a proportion changes, not exact numbers."
How would you describe the color change using proportional reasoning?"
π‘ **Think before answering! Type your response below.**
"""
elif step == 12:
return """π **Common Core Standards 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 == 13:
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 == 14:
return """π **Reflection & Problem Posing Activity**
"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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