Spaces:
Sleeping
Sleeping
File size: 6,088 Bytes
704c1ec 583b035 477fd16 f0b6b27 0ca1e65 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 3dd625a 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 3dd625a 704c1ec 4bfb23b 704c1ec 3dd625a 704c1ec 4bfb23b 704c1ec 4bfb23b 727a35a 4bfb23b 704c1ec 3dd625a 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 4bfb23b 704c1ec 4bfb23b 2f0985e 4bfb23b 704c1ec 4bfb23b 9134722 2897d48 704c1ec 2897d48 704c1ec 2897d48 704c1ec 4bfb23b 2897d48 9134722 2897d48 704c1ec 2897d48 f0b6b27 12acada 2897d48 704c1ec 2897d48 704c1ec 583b035 f0b6b27 2897d48 a828bd5 4bfb23b 2897d48 a828bd5 2897d48 4bfb23b 3dd625a |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 |
### 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! Before I summarize, letβs think:
π‘ **Which Common Core Standards do you think we covered?**
- Did we solve real-world proportional reasoning problems?
- Did we recognize and represent proportional relationships?
- Were we modeling with mathematics?"
πΉ **Take a moment to reflect before I provide a summary!**
"""
elif step == 11:
return """π **Common Core Standards Covered**
β
**CCSS.MATH.CONTENT.6.RP.A.3** (Solving real-world proportional reasoning problems)
β
**CCSS.MATH.CONTENT.7.RP.A.2** (Recognizing proportional relationships)
β
**CCSS.MATH.PRACTICE.MP1** (Making sense of problems & persevering)
β
**CCSS.MATH.PRACTICE.MP4** (Modeling with mathematics)
π‘ "How do these standards apply to the problems we solved?"
"""
elif step == 12:
return """π **Creativity-Directed Practices Discussion**
"Now, letβs reflect on **creativity in problem-solving!**
π‘ **Which Creativity-Directed Practices do you think we used?**
- Did we try multiple solution methods?
- Did we use real-world contexts?
- Were we encouraged to think critically about proportional relationships?"
πΉ **Pause and think before I summarize!**
"""
elif step == 13:
return """π **Creativity-Directed Practices Used**
β
Encouraging multiple solution methods
β
Using real-world contexts
β
Thinking critically about proportional relationships
π‘ "Which of these strategies do you think helped deepen understanding?"
"""
elif step == 14:
return """π **Reflection & Problem Posing Activity**
"Now, letβs create your own proportional reasoning problem!"
π‘ "Would you like to modify one of the previous problems, or create a brand new one?"
"""
elif step == 15:
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 == 16:
return """π **Final Encouragement**
"Great job today! Would you like to explore additional examples or discuss how to use these strategies in the classroom?"
"""
return "π **End of module! Thanks for participating.**"
|