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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‘ **Think before answering:**
- "How does 24 cm compare to 2 cm? Can you find the scale factor?"
- "If **2 cm = 25 miles**, how can we use this to scale up?"
πΉ **Try solving it before I provide hints! Type your answer below.**
"""
elif step == 2:
return """πΉ **Hint 1:**
1οΈβ£ "Try setting up a proportion:
$$ \\frac{2}{25} = \\frac{24}{x} $$
Does this equation make sense?"
π‘ **Try answering before moving forward.**
"""
elif step == 3:
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 == 4:
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 == 5:
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‘ **Try solving it before I provide hints!**
"""
elif step == 6:
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 == 7:
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 == 8:
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‘ **Think before answering:**
- "How does the ratio of red to white change?"
- "Would the color become darker, lighter, or stay the same?"
πΉ **Try explaining before I provide hints!**
"""
elif step == 9:
return """πΉ **Hint 1:**
1οΈβ£ "Yesterday: **Ratio of red:white** was **R:W**."
2οΈβ£ "Today: More red, same white β **Higher red-to-white ratio**."
3οΈβ£ "Higher red β **Darker shade!**"
π‘ "Does this explanation match your thinking?"
π **Now, let's connect what we did to teaching strategies. Ready?"**
"""
elif step == 10:
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 == 11:
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 == 12:
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?"
"""
elif step == 13:
return """π **Final Reflection**
"Before we wrap up, letβs reflect!"
- "Which problem type was the most challenging? Why?"
- "Which strategies helped you solve these problems efficiently?"
- "What insights did you gain about proportional reasoning?"
"""
elif step == 14:
return """π― **Final Encouragement**
"Great job today! Would you like to explore additional examples or discuss how to integrate these strategies into your classroom?"
"""
elif step == 20:
return """π **You've completed the module! Would you like to review anything again?**"""
return "π **End of module! Thanks for participating.**"
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