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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.**" | |