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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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Your task is to **solve a problem using different representations** and connect the proportional relationship to the meaning of the problem." |
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π **Problem:** |
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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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π‘ **How much do they invest together?** |
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π‘ **Solve using a Bar Model, Double Number Line, or Equations.** |
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**Remember:** |
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- "Explain your thought process after solving each part." |
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- "Try your best before I give hints!" |
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π **Letβs begin! Which method would you like to use first?** |
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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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"How can we use a **bar model** to solve this problem?" |
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π‘ **OK! Let's hear your ideas first.** |
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- "What does the full bar represent?" |
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- "How might we divide the bar to show 60%?" |
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- "How can this help us find the total investment?" |
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πΉ **Share your thinking before I provide any hints!** |
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""" |
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elif step == 2: |
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return """πΉ **Hint 1:** |
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"Try drawing a **bar to represent the total investment**. |
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- Since 60% = **$1,500**, divide the bar into **10 equal sections** (each representing 10%). |
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- Shade in **6 sections** to represent Orrinβs 60%. |
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Does this setup make sense to you?" |
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""" |
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elif step == 3: |
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return """πΉ **Hint 2:** |
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"Now, letβs determine the value of one part. |
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- Since 6 sections represent **$1,500**, we divide: |
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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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"Nice work! You 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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"How can a **double number line** help solve this problem?" |
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π‘ **OK! Let's hear your ideas first.** |
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- "What should the two number lines represent?" |
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- "What key points should we label on the number lines?" |
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- "How can we use this to find the total investment?" |
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πΉ **Try before I give 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 number lines: |
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- One represents **percentages**: **0%, 60%, and 100%**. |
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- The other represents **dollars**: **$0, $1,500, and the total investment**. |
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What values go in between?" |
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""" |
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elif step == 8: |
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return """πΉ **Hint 2:** |
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"Now, divide $1,500 by 6 to find 10%: |
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\\[ |
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\\text{Value of 10\\%} = \\frac{1500}{6} = 250 |
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\\] |
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Align this with **10% on the number line.** |
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Now, what is the value at 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 weβve aligned the values: |
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- 10% = **$250** |
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- 100% = **$2500** |
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So, the total investment is **$2,500!** |
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π‘ **Reflection:** |
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- "How does this method compare to the bar model?" |
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- "Would this approach help students struggling with percentages?" |
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π "Now, let's try solving with 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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"How can we set up an **equation** to represent this problem?" |
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π‘ **OK! Let's hear your ideas first.** |
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- "What proportional relationship can we write?" |
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- "How can we express 60% mathematically?" |
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- "What unknown are we solving for?" |
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πΉ **Try setting up the equation 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 relationship as a proportion: |
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\\[ |
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\\frac{60}{100} = \\frac{1500}{x} |
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\\] |
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How can we solve for \\(x\\)?" |
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""" |
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elif step == 12: |
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return """πΉ **Hint 2:** |
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"Use **cross-multiplication**: |
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\\[ |
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60x = 1500 \\times 100 |
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\\] |
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Now divide both sides by 60. What do you get?" |
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""" |
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elif step == 13: |
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return """β
**Solution:** |
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"Nice work! Solving the equation: |
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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 is **$2,500!** |
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π‘ **Reflection:** |
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- "Which method do you prefer: Bar Model, Double Number Line, or Equation?" |
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- "How can we help students connect all three approaches?" |
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π "Now, letβs reflect on the **Common Core practices** we used." |
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""" |
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elif step == 14: |
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return """π **Common Core Standards Discussion** |
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"Great job! Letβs reflect on how this connects 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? Why?" |
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""" |
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elif step == 15: |
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return """π **Creativity-Directed Practices Discussion** |
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"Throughout this module, we engaged in creativity-directed strategies, such as: |
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Using multiple solution methods |
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Encouraging deep reasoning |
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Connecting visual and numerical representations |
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π‘ "How do these strategies help students build deeper understanding?" |
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π "Now, letβs create your own problem!" |
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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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