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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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Today, we will explore how to use **bar models, double number lines, and equations** to solve percentage problems. |
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π‘ **Your task is to solve the following problem using different representations.** |
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π‘ **I will prompt you to think critically before offering hints.** |
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π‘ **You will explain your reasoning step by step.** |
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π **Letβs begin!**" |
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--- |
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### **π Solve the Following Problem** |
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π **Problem:** |
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"Orrin and Damen decided to invest money in a local ice cream shop. |
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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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π‘ **Before choosing a strategy, think about:** |
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- "What does **60% of the total investment** mean in this situation?" |
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- "What strategies might help visualize or solve this problem?" |
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πΉ **Try solving it first. Let me know your initial thoughts!** |
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--- |
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""" |
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def bar_model_step(step): |
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if step == 1: |
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return """π **Step 1: Solve Using a Bar Model** |
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"A bar model is a great way to visualize proportions. How would you set it up for this problem?" |
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π‘ **Before I give hints, think about:** |
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- "How can we represent the **total investment** as a bar?" |
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- "If 60% is **$1,500**, how many sections should the bar have?" |
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πΉ **Try setting it up before I provide hints!** |
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""" |
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elif step == 2: |
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return """πΉ **Hint 1:** |
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"Start by dividing the bar into **10 equal sections**, where each represents **10%** of the total. |
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Since 60% is **$1,500**, how much does **each 10% section** represent?" |
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""" |
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elif step == 3: |
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return """πΉ **Hint 2:** |
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"Divide **$1,500 by 6** to find **10%** of the total investment. |
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Then, multiply by **10** to find **100%**." |
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""" |
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elif step == 4: |
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return """β
**Solution:** |
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"$1,500 Γ· 6 = $250$ (for 10%) |
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$250 Γ 10 = $2,500$ |
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So, the total investment is **$2,500.**" |
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π‘ "Does this make sense? How would you explain this to students?" |
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π "Now, let's solve this problem using a **double number line!**" |
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""" |
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def double_number_line_step(step): |
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if step == 1: |
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return """π **Step 2: Solve Using a Double Number Line** |
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"How might a **double number line** help in this situation?" |
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π‘ **Think about:** |
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- "If **60% = $1,500**, what are the missing values for **10%, 20%, and 100%**?" |
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- "How would you label and align the values?" |
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πΉ **Try setting up your number line before I provide hints!** |
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""" |
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elif step == 2: |
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return """πΉ **Hint 1:** |
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"Start by labeling the number lines: |
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- **Percentages:** 0%, 10%, 20%, 60%, 100% |
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- **Dollars:** $0, ???, ???, $1,500, ???" |
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"What values should go in the missing spots?" |
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""" |
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elif step == 3: |
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return """πΉ **Hint 2:** |
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"Divide **$1,500 by 6** to get **10%** of the total. |
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Align this value with the corresponding percentage." |
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""" |
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elif step == 4: |
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return """β
**Solution:** |
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"The correct number line alignment: |
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- **10% = $250** |
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- **20% = $500** |
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- **100% = $2,500** |
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π‘ "How does this compare to the bar model?" |
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π "Now, let's solve it using an **equation!**" |
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""" |
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def equation_step(step): |
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if step == 1: |
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return """π **Step 3: Solve Using an Equation** |
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"Can you set up an **equation** to represent the proportional relationship?" |
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π‘ **Think about:** |
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- "How can we express **60% as a fraction**?" |
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- "What equation relates **$1,500 and x**?" |
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πΉ **Try setting up the equation before I provide hints!** |
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""" |
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elif step == 2: |
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return """πΉ **Hint 1:** |
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"Write the proportion as: |
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\\[ |
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\\frac{60}{100} = \\frac{1,500}{x} |
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\\] |
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Now, solve for \\( x \\)." |
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""" |
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elif step == 3: |
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return """πΉ **Hint 2:** |
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"Use **cross-multiplication** to find \\( x \\)." |
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""" |
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elif step == 4: |
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return """β
**Solution:** |
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\\[ |
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60x = 100(1,500) |
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\\] |
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\\[ |
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x = \\frac{150,000}{60} = 2,500 |
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\\] |
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π‘ "How does this method compare to the others?" |
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π "Now, letβs reflect on what weβve learned!" |
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""" |
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REFLECTION_PROMPT = """ |
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π **Common Core & Creativity-Directed Practices Discussion** |
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"Great job! Now, letβs connect this to key teaching strategies." |
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πΉ **Which Common Core Practices did we cover?** |
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- **CCSS.MATH.CONTENT.6.RP.A.3** (Solving real-world proportional reasoning problems) |
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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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π‘ "Which of these standards applied most to our problem? Why?" |
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""" |
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CREATIVITY_DIRECTED_PRACTICES_PROMPT = """ |
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πΉ **Which Creativity-Directed Practices did we use?** |
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- Encouraging **multiple solution methods** |
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- Using **real-world contexts** |
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- Thinking critically about **proportional relationships** |
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π‘ "Which of these strategies did you use? How do they help students?" |
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""" |
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PROBLEM_POSING_PROMPT = """ |
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π **Problem-Posing Activity** |
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"Now, try writing your own **percentage-based proportional reasoning problem!** |
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Use different representations (bar models, number lines, equations) to solve it." |
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π‘ **Questions to Guide Your Problem:** |
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- "What real-world context will you use?" (e.g., discounts, investments, recipes) |
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- "What percentage and total values will you include?" |
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- "How will your problem allow students to connect concepts?" |
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π "Once you've written your problem, I'll help evaluate and refine it!" |
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""" |
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