MAIN_PROMPT = """ ### **Module 4: Proportional Thinking with Percentages** #### **Task Introduction** "Welcome to this module on **proportional reasoning with percentages!** Today, we will explore how to use **bar models, double number lines, and equations** to solve percentage problems. πŸ’‘ **Your task is to solve the following problem using different representations.** πŸ’‘ **I will guide you step by step, prompting you to think critically.** πŸ’‘ **You will explain your reasoning before I provide hints.** πŸš€ **Let’s get started!**" --- ### **πŸš€ Solve the Following Problem** πŸ“Œ **Problem:** "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?" πŸ’‘ "Try solving it using a **bar model, double number line, or an equation.** Which representation do you prefer?" --- """ # βœ… **STEP 1: BAR MODEL REPRESENTATION** def bar_model_step(step): if step == 1: return """πŸš€ **Step 1: Solve Using a Bar Model** "Can you use a **bar model** to represent this problem? Think of a rectangular bar divided into parts to represent percentages. How can you use this model to find the total investment?" πŸ’‘ **Before I give hints, consider these questions:** - "If **60% = $1,500**, what does **10%** represent?" - "How many equal parts should you divide the bar into?" πŸ”Ή **Try solving it before I provide hints! Type your answer below.** """ elif step == 2: return """πŸ”Ή **Hint 1:** "Start by drawing a bar representing **100% of the total investment**. Divide it into **10 equal parts**, where each part represents **10%**. Since **60% = $1,500**, how much does **each part** represent?" """ elif step == 3: return """πŸ”Ή **Hint 2:** "Divide **$1,500 by 6** to find **10%** of the total investment. Then, multiply by **10** to find **100%**." """ elif step == 4: return """βœ… **Solution:** "$1,500 Γ· 6 = $250$ (for 10%) $250 Γ— 10 = $2,500$ So, the total investment is **$2,500.**" πŸ’‘ "Does this make sense? How would you explain this to students?" πŸš€ "Now, let's solve this problem using a **double number line!**" """ # βœ… **STEP 2: DOUBLE NUMBER LINE REPRESENTATION** def double_number_line_step(step): if step == 1: return """πŸš€ **Step 2: Solve Using a Double Number Line** "Can you use a **double number line** to solve this problem? One line represents **percentages**, and the other represents **dollars**. How would you align the intervals?" πŸ’‘ **Before I give hints, consider these:** - "If **60% = $1,500**, what are the missing values for 10%, 20%, and 100%?" - "How do you align the values on the number line?" πŸ”Ή **Try solving before I provide hints!** """ elif step == 2: return """πŸ”Ή **Hint 1:** "Start by labeling the number lines: - **Percentages:** 0%, 10%, 20%, 60%, 100% - **Dollars:** $0, ???, ???, $1,500, ???" "What values should go in the missing spots?" """ elif step == 3: return """πŸ”Ή **Hint 2:** "Divide **$1,500 by 6** to get **10%** of the total. Align this value with the corresponding percentage." """ elif step == 4: return """βœ… **Solution:** "The correct number line alignment: - **10% = $250** - **20% = $500** - **100% = $2,500** πŸ’‘ "How did this representation help you understand the proportional relationship?" πŸš€ "Now, let's solve it using an **equation!**" """ # βœ… **STEP 3: EQUATION REPRESENTATION** def equation_step(step): if step == 1: return """πŸš€ **Step 3: Solve Using an Equation** "Can you set up an **equation** to represent the proportional relationship? How would you write the relationship between **60%** and **$1,500**?" πŸ’‘ **Try setting up an equation before I provide hints!** """ elif step == 2: return """πŸ”Ή **Hint 1:** "Write the proportion as: \\[ \\frac{60}{100} = \\frac{1,500}{x} \\] Now, solve for \\( x \\)." """ elif step == 3: return """πŸ”Ή **Hint 2:** "Use **cross-multiplication** to find \\( x \\)." """ elif step == 4: return """βœ… **Solution:** \\[ 60x = 100(1,500) \\] \\[ x = \\frac{150,000}{60} = 2,500 \\] πŸ’‘ "How does setting up an equation compare to the other methods?" πŸš€ "Now, let’s reflect on what we’ve learned!" """ # βœ… **REFLECTION & PROBLEM-POSING** REFLECTION_PROMPT = """ πŸ“Œ **Common Core & Creativity-Directed Practices Discussion** "Great work! Now, let’s connect this to key teaching strategies." πŸ”Ή **Which Common Core Practices 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) πŸ’‘ "Which of these standards applied most to our problem? Why?" """ CREATIVITY_DIRECTED_PRACTICES_PROMPT = """ πŸ”Ή **Which Creativity-Directed Practices did we use?** - Encouraging **multiple solution methods** - Using **real-world contexts** - Thinking critically about **proportional relationships** πŸ’‘ "Which of these strategies did you use? How do they help students?" """ PROBLEM_POSING_PROMPT = """ πŸ“Œ **Problem-Posing Activity** "Now, try writing your own **percentage-based proportional reasoning problem!** Use different representations (bar models, number lines, equations) to solve it." πŸ’‘ **Questions to Guide Your Problem:** - "What real-world context will you use?" (e.g., discounts, investments, recipes) - "What percentage and total values will you include?" - "How will your problem allow students to connect concepts?" πŸš€ "Once you've written your problem, I'll help evaluate and refine it!" """