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MAIN_PROMPT = """ |
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### **Module 4: Proportional Thinking with Percentages** |
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"Welcome to this module on proportional reasoning with percentages! |
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In this module, you will explore different representations of proportional thinking: |
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1οΈβ£ **Bar Models** |
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2οΈβ£ **Double Number Lines** |
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3οΈβ£ **Equations & Proportional Relationships** |
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π‘ **You will solve the given problem using different strategies and explain your reasoning.** |
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π‘ **The AI will guide you through hints if neededβtry solving before asking for help!** |
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π **Letβs begin!** |
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""" |
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def next_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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"Orrin invests **$1,500**, which is **60%** of their total investment. |
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How can you use a bar model to solve this problem?" |
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π‘ **Think before answering:** |
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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 drawing a rectangle to represent the **total investment**. |
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- Divide it into **10 equal sections** (since each section represents **10%** of the total). |
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- Since **60% corresponds to $1,500**, shade in **6 parts** of the bar. |
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Now, can you determine how much **1 part** represents?" |
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""" |
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elif step == 3: |
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return """πΉ **Hint 2:** |
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"If 6 parts correspond to **$1,500**, find the value of **one part** by dividing: |
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\\[ |
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\\text{Value of 1 part} = \\frac{1500}{6} |
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\\] |
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What do you get?" |
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""" |
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elif step == 4: |
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return """πΉ **Hint 3:** |
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"Now that we know the value of **one part**, we can find the total investment by multiplying by 10: |
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\\[ |
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\\text{Total Investment} = \\text{Value of 1 part} \\times 10 |
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\\] |
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Can you calculate and explain your answer?" |
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""" |
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elif step == 5: |
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return """β
**Solution:** |
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"We found that **1 part = $250**. |
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Now, multiplying by **10**: |
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\\[ |
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\\text{Total Investment} = 250 \\times 10 = 2500 |
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\\] |
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So, the total investment by Orrin and Damen together is **$2,500.**" |
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π‘ **Reflection:** |
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- "How does this visual help in understanding the problem?" |
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- "Would this be useful for students struggling with percentages?" |
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π "Now, let's solve this problem using a **double number line!**" |
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""" |
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elif step == 6: |
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return """π **Step 2: Solve Using a Double Number Line** |
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"A double number line is another great way to visualize this problem. |
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How would you set up a **double number line** to solve this?" |
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π‘ **Think before answering:** |
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- "What labels would you use for the two number lines?" |
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- "How can you align percentages with dollar values?" |
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πΉ **Try setting it up before I provide hints!** |
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""" |
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elif step == 7: |
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return """πΉ **Hint 1:** |
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"Start by labeling the two number lines: |
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- The **top line** represents **percentages** (0%, 10%, 20%, β¦, 100%). |
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- The **bottom line** represents **dollars** ($0, $?, $?, β¦, Total Investment). |
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- Since **60% = $1,500**, mark this point on both lines. |
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Can you determine what **10%** would be?" |
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""" |
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elif step == 8: |
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return """πΉ **Hint 2:** |
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"To find **10%**, divide **$1,500 by 6**: |
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\\[ |
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\\text{10% Value} = \\frac{1500}{6} = 250 |
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\\] |
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Now, use this to determine **100%**!" |
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""" |
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elif step == 9: |
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return """β
**Solution:** |
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"Now that we know **10% = $250**, we can multiply by 10: |
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\\[ |
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\\text{Total Investment} = 250 \\times 10 = 2500 |
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\\] |
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So, the total investment by Orrin and Damen together is **$2,500.**" |
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π‘ **Reflection:** |
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- "How does the double number line help in understanding the proportional relationship?" |
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π "Now, let's solve this using **an equation!**" |
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""" |
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elif step == 10: |
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return """π **Step 3: Solve Using an Equation** |
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"An equation allows us to solve proportions algebraically. |
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How can you set up an equation for this problem?" |
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π‘ **Think before answering:** |
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- "How can we represent 60% in fractional form?" |
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- "How can we write a proportion to find the total investment?" |
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πΉ **Try setting it up before I provide hints!** |
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""" |
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elif step == 11: |
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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{1500}{x} |
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\\] |
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Now, can you **cross-multiply** and solve for **x**?" |
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""" |
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elif step == 12: |
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return """β
**Solution:** |
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"Using cross-multiplication: |
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\\[ |
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60x = 1500 \\times 100 |
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\\] |
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\\[ |
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x = \\frac{1500 \\times 100}{60} = 2500 |
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\\] |
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So, the total investment by Orrin and Damen together is **$2,500.**" |
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π‘ **Reflection:** |
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- "How does solving with an equation compare to visual methods?" |
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π "Now, let's reflect on teaching strategies!" |
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""" |
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elif step == 13: |
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return """π **Common Core & Creativity-Directed Practices Discussion** |
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"Great job! Now, letβs reflect on how these problems connect to teaching strategies." |
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πΉ **Which Common Core Standards 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 do you think applied most to the problems we solved? Why?** |
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""" |
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elif step == 14: |
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return """π **Creativity-Directed Practices Discussion** |
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"Throughout these problems, we engaged in creativity-directed strategies, such as: |
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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 while solving the problems?** |
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π‘ **How do you think encouraging creativity helps students develop deeper understanding?** |
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""" |
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elif step == 15: |
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return """π **Problem-Posing Activity** |
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"Now, letβs take it one step further! Try creating your own proportional reasoning problem." |
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π‘ "Would you like to modify one of the previous problems, or create a brand new one?" |
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""" |
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return "π **You've completed the module! Would you like to review anything again?**" |
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