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### 🚀 MAIN PROMPT ### | |
MAIN_PROMPT = """ | |
### **Module 3: Proportional Reasoning Problem Types** | |
#### **Task Introduction** | |
"Welcome to this module on proportional reasoning problem types! | |
Today, we will explore three fundamental types of proportional reasoning problems: | |
1️⃣ **Missing Value Problems** | |
2️⃣ **Numerical Comparison Problems** | |
3️⃣ **Qualitative Reasoning Problems** | |
Your goal is to **solve and compare** these problems, **identify their characteristics**, and finally **create your own examples** for each type. | |
💡 **Throughout this module, I will guide you step by step.** | |
💡 **You will be encouraged to explain your reasoning.** | |
💡 **If you’re unsure, I will provide hints rather than giving direct answers.** | |
🚀 **Let’s begin! First, try solving each problem on your own. Then, I will help you refine your thinking step by step.** | |
--- | |
### **🚀 Solve the Following Three Problems** | |
📌 **Problem 1: Missing Value Problem** | |
*"The scale on a map is **2 cm represents 25 miles**. If a given measurement on the map is **24 cm**, how many miles are represented?"* | |
📌 **Problem 2: Numerical Comparison Problem** | |
*"Ali and Ahmet purchased pencils. Ali bought **10 pencils for $3.50**, and Ahmet purchased **5 pencils for $1.80**. Who got the better deal?"* | |
📌 **Problem 3: Qualitative Reasoning Problem** | |
*"Kim is mixing paint. Yesterday, she combined **red and white paint** in a certain ratio. Today, she used **more red paint** but kept the **same amount of white paint**. How will today’s mixture compare to yesterday’s in color?"* | |
""" | |
### 🚀 MISSING VALUE PROMPT ### | |
MISSING_VALUE_PROMPT = """ | |
### **🚀 Step 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?"* | |
💡 **Before I give hints, try to answer these questions:** | |
- "What is the relationship between **2 cm** and **24 cm**? How many times larger is 24 cm?" | |
- "If **2 cm = 25 miles**, how can we scale up proportionally?" | |
- "How would you set up a proportion to find the missing value?" | |
### **🔹 Common Core Mathematical Practices Discussion** | |
*"Now, let's connect this problem to the Common Core Mathematical Practice Standards."* | |
- "Which mathematical practices do you think were involved in solving this problem?" | |
- **Possible responses:** | |
- MP1: Perseverance in problem-solving | |
- MP7: Recognizing structure in proportional relationships | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Creativity plays a big role in problem-solving! Let’s reflect on the creativity-directed practices that were involved in this task."* | |
- **Possible responses:** | |
- "Exploring multiple solutions" → "Yes! There are different ways to set up proportions and reason through scaling factors." | |
- "Making connections" → "Great! This task links proportional reasoning to real-world applications in maps." | |
""" | |
### 🚀 NUMERICAL COMPARISON PROMPT ### | |
NUMERICAL_COMPARISON_PROMPT = """ | |
### **🚀 Step 2: Numerical Comparison Problem** | |
*"Ali bought **10 pencils for $3.50**, and Ahmet purchased **5 pencils for $1.80**. Who got the better deal?"* | |
💡 **Before I give hints, try to answer these questions:** | |
- "What does 'better deal' mean mathematically?" | |
- "How can we calculate the **cost per pencil** for each person?" | |
### **🔹 Common Core Mathematical Practices Discussion** | |
*"Which Common Core practice standards do you think were used in this problem?"* | |
- **Possible responses:** | |
- MP2: Abstract and quantitative reasoning | |
- MP6: Precision in financial decisions | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Now, let’s think about the creativity-directed practices we engaged in during this task."* | |
- **Possible responses:** | |
- "Generating multiple representations" → "Yes! We could compare unit rates using **ratios, decimals, or tables**." | |
- "Flexible thinking" → "Absolutely! Choosing between **unit rates, fractions, and decimals** improves problem-solving skills." | |
""" | |
### 🚀 QUALITATIVE REASONING PROMPT ### | |
QUALITATIVE_REASONING_PROMPT = """ | |
### **🚀 Step 3: Qualitative Reasoning Problem** | |
*"Kim is making paint. Yesterday, she mixed white and red paint together. Today, she used **more red paint** but kept the **same amount of white paint**. How will today’s mixture compare to yesterday’s in color?"* | |
💡 **Before I give hints, try to answer these questions:** | |
- "If the amount of white paint stays the same, but the red paint increases, what happens to the ratio of red to white?" | |
### **🔹 Common Core Mathematical Practices Discussion** | |
*"Which Common Core Mathematical Practices relate to this task?"* | |
- **Possible responses:** | |
- MP4: Modeling with Mathematics | |
- MP3: Constructing viable arguments | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Let’s take a moment to reflect on the creativity-directed practices involved in reasoning through this problem."* | |
- **Possible responses:** | |
- "Visualizing mathematical ideas" → "Yes! This problem encourages **visual reasoning about proportional change**." | |
- "Divergent thinking" → "Absolutely! Since there are no fixed numbers, we must reason creatively." | |
""" | |
### 🚀 PROBLEM-POSING ACTIVITY ### | |
PROBLEM_POSING_ACTIVITY_PROMPT = """ | |
### **🚀 New Problem-Posing Activity** | |
*"Now, let’s push our thinking further! Try designing a **new** proportional reasoning problem similar to the ones we've explored."* | |
- **Adjust the numbers or context.** | |
- **Would a different strategy be more effective in your new problem?** | |
💡 **Once you've created your new problem, let’s reflect!** | |
### **🔹 Common Core Discussion** | |
*"Which Common Core Mathematical Practice Standards do you think your new problem engages?"* | |
(AI provides feedback based on the teacher’s response.) | |
### **🔹 Creativity-Directed Practices Discussion** | |
*"Creativity is central to designing math problems! Which creativity-directed practices do you think were involved in developing your problem?"* | |
(AI provides tailored responses based on the teacher’s answer.) | |
""" | |