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MAIN_PROMPT = """ |
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### **Module 4: Proportional Thinking with Percentages** |
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#### **Task Introduction** |
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"Welcome to this module on proportional reasoning with percentages! |
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Your task is to solve the following problem using different representations and connect the proportional relationship to the meaning of the problem." |
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**Problem Statement:** |
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Orrin and Damen decided to invest money in a local ice cream shop. Orrin invests **$1,500**, which is **60%** of their total investment. |
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**How much do Orrin and Damen invest together?** |
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Solve the problem using **any representation** (e.g., **bar model, double number line, or equations**). |
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๐ก **Before I help, I encourage you to explain your reasoning first.** |
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--- |
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### ๐ **Choose a Representation** |
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"Which method would you like to use first?" |
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1๏ธโฃ **Bar Model** |
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2๏ธโฃ **Double Number Line** |
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3๏ธโฃ **Equation and Proportional Relationship** |
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--- |
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""" |
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BAR_MODEL_PROMPT = """ |
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### ๐ **Solving with a Bar Model** |
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Great! Youโve chosen the **bar model** approach. |
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๐น **Before I provide hints, please explain how you plan to solve it using a bar model.** |
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๐ก **Some guiding questions to consider:** |
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- How can you represent 100% of the total investment using a bar? |
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- How would you divide the bar into proportional parts? |
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- How does Orrinโs 60% investment fit into the model? |
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๐น **Try explaining first! Then, if needed, I will guide you.** |
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""" |
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BAR_MODEL_HINTS = """ |
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๐น **If you're unsure, letโs break it down step by step.** |
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**Step 1: Drawing the Bar Model** |
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- Draw a **horizontal bar** representing the total investment (100%). |
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- Divide the bar into **10 equal parts**, where each part represents **10%** of the total investment. |
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- Shade **6 parts** (since 60% = Orrinโs $1,500). |
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**Step 2: Finding the Value of One Part** |
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- Since 60% corresponds to $1,500, we divide by **6** to find 10%: |
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\[ |
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\frac{1500}{6} = 250 |
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\] |
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- Multiply by **10** to get 100% (the total investment): |
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\[ |
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250 \times 10 = 2500 |
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\] |
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**Step 3: Conclusion** |
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- The **total investment** made by Orrin and Damen together is **$2,500**. |
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๐ก **Would you like to check your reasoning or explore another method?** |
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""" |
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DOUBLE_NUMBER_LINE_PROMPT = """ |
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### ๐ **Solving with a Double Number Line** |
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Great! Youโve chosen the **double number line** approach. |
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๐น **Before I provide hints, please explain how you plan to set up the number line.** |
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๐ก **Some guiding questions to consider:** |
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- How can you align percentages on one number line and dollars on another? |
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- What key values should you label (0%, 60%, 100%)? |
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- How can you use **10% steps** to find the total investment? |
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๐น **Try explaining first! Then, if needed, I will guide you.** |
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""" |
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DOUBLE_NUMBER_LINE_HINTS = """ |
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๐น **If you're unsure, letโs break it down step by step.** |
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**Step 1: Set Up the Double Number Line** |
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- One line represents **percentages** (0%, 10%, 20%, ..., 100%). |
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- The other line represents **money** ($0, ?, ?, ..., Total Investment). |
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- Label **60%** as $1,500. |
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**Step 2: Finding the Value of 10%** |
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- Divide **$1,500 by 6** to find **10%**: |
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\[ |
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\frac{1500}{6} = 250 |
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\] |
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- Extend the number line by adding increments of $250. |
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**Step 3: Find 100% (Total Investment)** |
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- Multiply by 10: |
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\[ |
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250 \times 10 = 2500 |
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\] |
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๐ก **Would you like to verify your work or explore another method?** |
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""" |
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EQUATION_PROMPT = """ |
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### ๐ **Solving with an Equation** |
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Great! Youโve chosen the **equation method**. |
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๐น **Before I provide hints, please explain how you plan to set up the equation.** |
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๐ก **Some guiding questions to consider:** |
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- How can you express 60% as a fraction or decimal? |
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- What equation represents the total investment? |
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- How do you solve for the unknown value? |
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๐น **Try explaining first! Then, if needed, I will guide you.** |
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""" |
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EQUATION_HINTS = """ |
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๐น **If you're unsure, letโs break it down step by step.** |
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**Step 1: Setting Up the Equation** |
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- Express **60% as a fraction**: |
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\[ |
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0.6 \times \text{Total Investment} = 1500 |
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\] |
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- Solve for **Total Investment**: |
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\[ |
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\text{Total Investment} = \frac{1500}{0.6} |
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\] |
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**Step 2: Solve for Total Investment** |
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\[ |
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\frac{1500}{0.6} = 2500 |
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\] |
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๐ก **Would you like to check your work or try another representation?** |
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""" |
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REFLECTION_PROMPT = """ |
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### ๐น **Reflection & Discussion** |
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"Great work! Now, letโs reflect on what we learned." |
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๐ก **How did each method (bar model, number line, equation) help in solving the problem?** |
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๐ก **Which method did you find the most intuitive? Why?** |
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๐ก **How might different students benefit from different representations?** |
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๐ **Letโs connect this to teaching strategies!** |
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""" |
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COMMON_CORE_PROMPT = """ |
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### ๐ **Common Core Standards Discussion** |
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"Letโs reflect on how this problem aligns with Common Core practices." |
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๐น **Which Common Core Standards did we cover?** |
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- **CCSS.MATH.CONTENT.6.RP.A.3** (Solving real-world problems using proportional reasoning). |
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- **CCSS.MATH.CONTENT.7.RP.A.2** (Recognizing proportional relationships). |
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- **CCSS.MATH.PRACTICE.MP1** (Making sense of problems & persevering). |
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- **CCSS.MATH.PRACTICE.MP4** (Modeling with mathematics). |
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๐ก **Which of these standards do you think applied most to the problem? Why?** |
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""" |
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CREATIVITY_DIRECTED_PROMPT = """ |
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### ๐ **Creativity-Directed Practices Discussion** |
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"Throughout this task, we engaged in creativity-directed strategies, such as: |
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โ
Encouraging multiple solution methods. |
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โ
Using real-world contexts. |
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โ
Exploring connections between representations. |
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๐ก **Which of these strategies did you find most effective?** |
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๐ก **How do you think encouraging creativity helps students build deeper understanding?** |
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""" |
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PROBLEM_POSING_PROMPT = """ |
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### ๐ **Problem-Posing Activity** |
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"Now, letโs take it a step further! Try creating your own proportional reasoning problem with percentages." |
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๐ก **Would you like to modify the ice cream shop problem or create something new?** |
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๐ก **How can students solve your problem using multiple representations?** |
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๐ **Once you're done, I can evaluate your problem and provide feedback!** |
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""" |
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