| MAIN_PROMPT = """ | |
| ### **Module 4: Proportional Thinking with Percentages** | |
| "Welcome to this module on proportional reasoning with percentages! | |
| Your task is to **solve a problem using different representations** and connect the proportional relationship to the meaning of the problem." | |
| π **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. | |
| π‘ **How much do they invest together?** | |
| π‘ **Solve using a Bar Model, Double Number Line, or Equations.** | |
| β **Remember:** | |
| - "Explain your thought process after solving each part." | |
| - "Try your best before I give hints!" | |
| π **Letβs begin! Which method would you like to use first?** | |
| """ | |
| def next_step(step): | |
| if step == 1: | |
| return """π **Step 1: Solve Using a Bar Model** | |
| "How can we use a **bar model** to solve this problem?" | |
| π‘ **OK! Let's hear your ideas first.** | |
| - "What does the full bar represent?" | |
| - "How might we divide the bar to show 60%?" | |
| - "How can this help us find the total investment?" | |
| πΉ **Share your thinking before I provide any hints!** | |
| """ | |
| elif step == 2: | |
| return """πΉ **Hint 1:** | |
| "Try drawing a **bar to represent the total investment**. | |
| - Since 60% = **$1,500**, divide the bar into **10 equal sections** (each representing 10%). | |
| - Shade in **6 sections** to represent Orrinβs 60%. | |
| Does this setup make sense to you?" | |
| """ | |
| elif step == 3: | |
| return """πΉ **Hint 2:** | |
| "Now, letβs determine the value of one part. | |
| - Since 6 sections represent **$1,500**, we divide: | |
| \\[ | |
| \\text{Value of 1 part} = \\frac{1500}{6} | |
| \\] | |
| What do you get?" | |
| """ | |
| elif step == 4: | |
| return """πΉ **Hint 3:** | |
| "Now that we know the value of **one part**, we can find the total investment by multiplying by 10: | |
| \\[ | |
| \\text{Total Investment} = \\text{Value of 1 part} \\times 10 | |
| \\] | |
| Can you calculate and explain your answer?" | |
| """ | |
| elif step == 5: | |
| return """β **Solution:** | |
| "Nice work! You found that **1 part = $250**. | |
| Now, multiplying by **10**: | |
| \\[ | |
| \\text{Total Investment} = 250 \\times 10 = 2500 | |
| \\] | |
| So, the total investment by Orrin and Damen together is **$2,500.**" | |
| π‘ **Reflection:** | |
| - "How does this visual help in understanding the problem?" | |
| - "Would this be useful for students struggling with percentages?" | |
| π "Now, let's solve this problem using a **double number line!**" | |
| """ | |
| elif step == 6: | |
| return """π **Step 2: Solve Using a Double Number Line** | |
| "How can a **double number line** help solve this problem?" | |
| π‘ **OK! Let's hear your ideas first.** | |
| - "What should the two number lines represent?" | |
| - "What key points should we label on the number lines?" | |
| - "How can we use this to find the total investment?" | |
| πΉ **Try before I give hints!** | |
| """ | |
| elif step == 7: | |
| return """πΉ **Hint 1:** | |
| "Start by labeling the number lines: | |
| - One represents **percentages**: **0%, 60%, and 100%**. | |
| - The other represents **dollars**: **$0, $1,500, and the total investment**. | |
| What values go in between?" | |
| """ | |
| elif step == 8: | |
| return """πΉ **Hint 2:** | |
| "Now, divide $1,500 by 6 to find 10%: | |
| \\[ | |
| \\text{Value of 10\\%} = \\frac{1500}{6} = 250 | |
| \\] | |
| Align this with **10% on the number line.** | |
| Now, what is the value at 100%?" | |
| """ | |
| elif step == 9: | |
| return """β **Solution:** | |
| "Now that weβve aligned the values: | |
| - 10% = **$250** | |
| - 100% = **$2500** | |
| So, the total investment is **$2,500!** | |
| π‘ **Reflection:** | |
| - "How does this method compare to the bar model?" | |
| - "Would this approach help students struggling with percentages?" | |
| π "Now, let's try solving with an **equation!**" | |
| """ | |
| elif step == 10: | |
| return """π **Step 3: Solve Using an Equation** | |
| "How can we set up an **equation** to represent this problem?" | |
| π‘ **OK! Let's hear your ideas first.** | |
| - "What proportional relationship can we write?" | |
| - "How can we express 60% mathematically?" | |
| - "What unknown are we solving for?" | |
| πΉ **Try setting up the equation before I provide hints!** | |
| """ | |
| elif step == 11: | |
| return """πΉ **Hint 1:** | |
| "Write the relationship as a proportion: | |
| \\[ | |
| \\frac{60}{100} = \\frac{1500}{x} | |
| \\] | |
| How can we solve for \\(x\\)?" | |
| """ | |
| elif step == 12: | |
| return """πΉ **Hint 2:** | |
| "Use **cross-multiplication**: | |
| \\[ | |
| 60x = 1500 \\times 100 | |
| \\] | |
| Now divide both sides by 60. What do you get?" | |
| """ | |
| elif step == 13: | |
| return """β **Solution:** | |
| "Nice work! Solving the equation: | |
| \\[ | |
| x = \\frac{1500 \\times 100}{60} = 2500 | |
| \\] | |
| So, the total investment is **$2,500!** | |
| π‘ **Reflection:** | |
| - "Which method do you prefer: Bar Model, Double Number Line, or Equation?" | |
| - "How can we help students connect all three approaches?" | |
| π "Now, letβs reflect on the **Common Core practices** we used." | |
| """ | |
| elif step == 14: | |
| return """π **Common Core Standards Discussion** | |
| "Great job! Letβs reflect on how this connects to teaching strategies." | |
| πΉ **Which Common Core Standards 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) | |
| π‘ "Which of these standards do you think applied most? Why?" | |
| """ | |
| elif step == 15: | |
| return """π **Creativity-Directed Practices Discussion** | |
| "Throughout this module, we engaged in creativity-directed strategies, such as: | |
| β Using multiple solution methods | |
| β Encouraging deep reasoning | |
| β Connecting visual and numerical representations | |
| π‘ "How do these strategies help students build deeper understanding?" | |
| π "Now, letβs create your own problem!" | |
| """ | |
| return "π **You've completed the module! Would you like to review anything again?**" | |