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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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Today, we will explore a **real-world investment scenario** and solve it using three different representations: |
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1οΈβ£ **Bar Model** |
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2οΈβ£ **Double Number Line** |
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3οΈβ£ **Equation & Proportional Relationship** |
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π‘ **Your Task:** Solve the following problem using each representation. |
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π **Problem Statement:** |
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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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**How much do Orrin and Damen invest together?** |
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βοΈ **Try to solve this problem using your preferred method first. Then, we will compare different representations step by step!** |
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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‘ **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 will represent **10%**). |
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- Since 60% is **$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 """β
**Solution:** |
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"We found that **1 part = $250**. |
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Now, multiply by **10** to find the total investment: |
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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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def double_number_line_step(step): |
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if step == 1: |
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return """π **Step 1: Solve Using a Double Number Line** |
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"A double number line helps us align percentages with actual values. How might you set this up?" |
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π‘ **Think before answering:** |
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- "What labels should be on the number lines?" |
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- "Where should we place **60%** and **$1,500**?" |
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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 two horizontal lines: |
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- The **top line** represents **percentages** (0% to 100%). |
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- The **bottom line** represents **money** (starting from $0). |
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Now, place **60%** above **$1,500**. What other values should be on the number line?" |
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""" |
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elif step == 3: |
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return """πΉ **Hint 2:** |
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"Now, divide the bottom line into **equal increments of 10%**. |
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- What is the value of **10%**? |
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- Can you now find **100%**?" |
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""" |
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elif step == 4: |
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return """β
**Solution:** |
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"We calculated that **10% = $250**. Now, we can find the total: |
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\\[ |
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\\text{Total Investment} = 250 \\times 10 = 2500 |
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\\] |
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So, Orrin and Damen invested **$2,500 together.** |
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π‘ **Reflection:** |
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- "How does the double number line compare to the bar model?" |
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- "Which one do you think is more intuitive for students?" |
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π "Now, let's solve this problem using **equations!**" |
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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 1: Solve Using an Equation** |
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"An equation can help us **set up a direct proportional relationship**. How might you write an equation for this problem?" |
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π‘ **Think before answering:** |
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- "How can we express **60%** in equation form?" |
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- "What variable should represent 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 == 2: |
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return """πΉ **Hint 1:** |
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"Write an equation using **percent form**: |
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\\[ |
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0.60 \\times x = 1500 |
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\\] |
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Now, how would you 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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"To isolate **x**, divide both sides by **0.60**: |
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\\[ |
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x = \\frac{1500}{0.60} |
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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 """β
**Solution:** |
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"Solving the equation: |
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\\[ |
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x = \\frac{1500}{0.60} = 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 setting up an equation help in problem-solving?" |
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- "How might you support students struggling to make sense of the equation?" |
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π "Now, letβs **compare and reflect** on these representations!" |
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""" |
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def reflection_and_problem_posing(): |
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return """π **Final Reflection & Problem Posing** |
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"Now that we've solved the problem using three different representations, let's reflect on our learning!" |
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π‘ **Which Common Core Practice Standards did we use?** |
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- **CCSS.MATH.PRACTICE.MP1** (Make sense of problems & persevere) |
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- **CCSS.MATH.PRACTICE.MP4** (Model with mathematics) |
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- **CCSS.MATH.PRACTICE.MP7** (Look for and make use of structure) |
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π‘ **Which Creativity-Directed Practices did we use?** |
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- Encouraging multiple solution methods |
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- Making connections across representations |
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- Using real-world contexts for deeper understanding |
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π **Your Turn: Create a New Problem!** |
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"Now, create your own proportional reasoning problem involving percentages!" |
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- **What real-world scenario will you use?** |
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- **What percentage and total values will you include?** |
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- **How can students solve it using different representations?"** |
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πΉ **Share your problem, and I'll give feedback!** |
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""" |
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