|
|
|
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.**" |
|
|