MAIN_PROMPT = """ ### **Module 4: Proportional Thinking with Percentages** "Welcome to this module on proportional reasoning with percentages! Today, we will explore a **real-world investment scenario** and solve it using three different representations: 1️⃣ **Bar Model** 2️⃣ **Double Number Line** 3️⃣ **Equation & Proportional Relationship** 💡 **Your Task:** Solve the following problem using each representation. 📌 **Problem Statement:** Orrin and Damen decided to invest money in a local ice cream shop. Orrin invests **$1,500**, which is **60% of their total investment**. **How much do Orrin and Damen invest together?** ✏️ **Try to solve this problem using your preferred method first. Then, we will compare different representations step by step!** """ def bar_model_step(step): if step == 1: return """🚀 **Step 1: Solve Using a Bar Model** "A bar model is a great way to visualize proportions. How would you set it up for this problem?" 💡 **Think before answering:** - "How can we represent the **total investment** as a bar?" - "If 60% is **$1,500**, how many sections should the bar have?" 🔹 **Try setting it up before I provide hints!** """ elif step == 2: return """🔹 **Hint 1:** "Start by drawing a rectangle to represent the **total investment**. - Divide it into **10 equal sections** (since each section will represent **10%**). - Since 60% is **$1,500**, shade in **6 parts** of the bar. Now, can you determine how much **1 part** represents?" """ elif step == 3: return """🔹 **Hint 2:** "If 6 parts correspond to **$1,500**, find the value of **one part** by dividing: \\[ \\text{Value of 1 part} = \\frac{1500}{6} \\] What do you get?" """ elif step == 4: return """✅ **Solution:** "We found that **1 part = $250**. Now, multiply by **10** to find the total investment: \\[ \\text{Total Investment} = 250 \\times 10 = 2500 \\] So, the total investment by Orrin and Damen together is **$2,500.**" 💡 **Reflection:** - "How does this visual help in understanding the problem?" - "Would this be useful for students struggling with percentages?" 🚀 "Now, let's solve this problem using a **double number line!**" """ def double_number_line_step(step): if step == 1: return """🚀 **Step 1: Solve Using a Double Number Line** "A double number line helps us align percentages with actual values. How might you set this up?" 💡 **Think before answering:** - "What labels should be on the number lines?" - "Where should we place **60%** and **$1,500**?" 🔹 **Try setting it up before I provide hints!** """ elif step == 2: return """🔹 **Hint 1:** "Start by drawing two horizontal lines: - The **top line** represents **percentages** (0% to 100%). - The **bottom line** represents **money** (starting from $0). Now, place **60%** above **$1,500**. What other values should be on the number line?" """ elif step == 3: return """🔹 **Hint 2:** "Now, divide the bottom line into **equal increments of 10%**. - What is the value of **10%**? - Can you now find **100%**?" """ elif step == 4: return """✅ **Solution:** "We calculated that **10% = $250**. Now, we can find the total: \\[ \\text{Total Investment} = 250 \\times 10 = 2500 \\] So, Orrin and Damen invested **$2,500 together.** 💡 **Reflection:** - "How does the double number line compare to the bar model?" - "Which one do you think is more intuitive for students?" 🚀 "Now, let's solve this problem using **equations!**" """ def equation_step(step): if step == 1: return """🚀 **Step 1: Solve Using an Equation** "An equation can help us **set up a direct proportional relationship**. How might you write an equation for this problem?" 💡 **Think before answering:** - "How can we express **60%** in equation form?" - "What variable should represent the **total investment**?" 🔹 **Try setting it up before I provide hints!** """ elif step == 2: return """🔹 **Hint 1:** "Write an equation using **percent form**: \\[ 0.60 \\times x = 1500 \\] Now, how would you solve for **x**?" """ elif step == 3: return """🔹 **Hint 2:** "To isolate **x**, divide both sides by **0.60**: \\[ x = \\frac{1500}{0.60} \\] What do you get?" """ elif step == 4: return """✅ **Solution:** "Solving the equation: \\[ x = \\frac{1500}{0.60} = 2500 \\] So, the total investment by Orrin and Damen together is **$2,500.** 💡 **Reflection:** - "How does setting up an equation help in problem-solving?" - "How might you support students struggling to make sense of the equation?" 🚀 "Now, let’s **compare and reflect** on these representations!" """ def reflection_and_problem_posing(): return """📌 **Final Reflection & Problem Posing** "Now that we've solved the problem using three different representations, let's reflect on our learning!" 💡 **Which Common Core Practice Standards did we use?** - **CCSS.MATH.PRACTICE.MP1** (Make sense of problems & persevere) - **CCSS.MATH.PRACTICE.MP4** (Model with mathematics) - **CCSS.MATH.PRACTICE.MP7** (Look for and make use of structure) 💡 **Which Creativity-Directed Practices did we use?** - Encouraging multiple solution methods - Making connections across representations - Using real-world contexts for deeper understanding 🚀 **Your Turn: Create a New Problem!** "Now, create your own proportional reasoning problem involving percentages!" - **What real-world scenario will you use?** - **What percentage and total values will you include?** - **How can students solve it using different representations?"** 🔹 **Share your problem, and I'll give feedback!** """