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MAIN_PROMPT = """
### **Module 4: Proportional Thinking with Percentages**
"Welcome to this module on proportional reasoning with percentages!
Today, we will explore a **real-world investment scenario** and solve it using three different representations:
1️⃣ **Bar Model**
2️⃣ **Double Number Line**
3️⃣ **Equation & Proportional Relationship**
πŸ’‘ **Your Task:** Solve the following problem using each representation.
πŸ“Œ **Problem Statement:**
Orrin and Damen decided to invest money in a local ice cream shop. Orrin invests **$1,500**, which is **60% of their total investment**.
**How much do Orrin and Damen invest together?**
✏️ **Try to solve this problem using your preferred method first. Then, we will compare different representations step by step!**
"""
def bar_model_step(step):
if step == 1:
return """πŸš€ **Step 1: Solve Using a Bar Model**
"A bar model is a great way to visualize proportions. How would you set it up for this problem?"
πŸ’‘ **Think before answering:**
- "How can we represent the **total investment** as a bar?"
- "If 60% is **$1,500**, how many sections should the bar have?"
πŸ”Ή **Try setting it up before I provide hints!**
"""
elif step == 2:
return """πŸ”Ή **Hint 1:**
"Start by drawing a rectangle to represent the **total investment**.
- Divide it into **10 equal sections** (since each section will represent **10%**).
- Since 60% is **$1,500**, shade in **6 parts** of the bar.
Now, can you determine how much **1 part** represents?"
"""
elif step == 3:
return """πŸ”Ή **Hint 2:**
"If 6 parts correspond to **$1,500**, find the value of **one part** by dividing:
\\[
\\text{Value of 1 part} = \\frac{1500}{6}
\\]
What do you get?"
"""
elif step == 4:
return """βœ… **Solution:**
"We found that **1 part = $250**.
Now, multiply by **10** to find the total investment:
\\[
\\text{Total Investment} = 250 \\times 10 = 2500
\\]
So, the total investment by Orrin and Damen together is **$2,500.**"
πŸ’‘ **Reflection:**
- "How does this visual help in understanding the problem?"
- "Would this be useful for students struggling with percentages?"
πŸš€ "Now, let's solve this problem using a **double number line!**"
"""
def double_number_line_step(step):
if step == 1:
return """πŸš€ **Step 1: Solve Using a Double Number Line**
"A double number line helps us align percentages with actual values. How might you set this up?"
πŸ’‘ **Think before answering:**
- "What labels should be on the number lines?"
- "Where should we place **60%** and **$1,500**?"
πŸ”Ή **Try setting it up before I provide hints!**
"""
elif step == 2:
return """πŸ”Ή **Hint 1:**
"Start by drawing two horizontal lines:
- The **top line** represents **percentages** (0% to 100%).
- The **bottom line** represents **money** (starting from $0).
Now, place **60%** above **$1,500**. What other values should be on the number line?"
"""
elif step == 3:
return """πŸ”Ή **Hint 2:**
"Now, divide the bottom line into **equal increments of 10%**.
- What is the value of **10%**?
- Can you now find **100%**?"
"""
elif step == 4:
return """βœ… **Solution:**
"We calculated that **10% = $250**. Now, we can find the total:
\\[
\\text{Total Investment} = 250 \\times 10 = 2500
\\]
So, Orrin and Damen invested **$2,500 together.**
πŸ’‘ **Reflection:**
- "How does the double number line compare to the bar model?"
- "Which one do you think is more intuitive for students?"
πŸš€ "Now, let's solve this problem using **equations!**"
"""
def equation_step(step):
if step == 1:
return """πŸš€ **Step 1: Solve Using an Equation**
"An equation can help us **set up a direct proportional relationship**. How might you write an equation for this problem?"
πŸ’‘ **Think before answering:**
- "How can we express **60%** in equation form?"
- "What variable should represent the **total investment**?"
πŸ”Ή **Try setting it up before I provide hints!**
"""
elif step == 2:
return """πŸ”Ή **Hint 1:**
"Write an equation using **percent form**:
\\[
0.60 \\times x = 1500
\\]
Now, how would you solve for **x**?"
"""
elif step == 3:
return """πŸ”Ή **Hint 2:**
"To isolate **x**, divide both sides by **0.60**:
\\[
x = \\frac{1500}{0.60}
\\]
What do you get?"
"""
elif step == 4:
return """βœ… **Solution:**
"Solving the equation:
\\[
x = \\frac{1500}{0.60} = 2500
\\]
So, the total investment by Orrin and Damen together is **$2,500.**
πŸ’‘ **Reflection:**
- "How does setting up an equation help in problem-solving?"
- "How might you support students struggling to make sense of the equation?"
πŸš€ "Now, let’s **compare and reflect** on these representations!"
"""
def reflection_and_problem_posing():
return """πŸ“Œ **Final Reflection & Problem Posing**
"Now that we've solved the problem using three different representations, let's reflect on our learning!"
πŸ’‘ **Which Common Core Practice Standards did we use?**
- **CCSS.MATH.PRACTICE.MP1** (Make sense of problems & persevere)
- **CCSS.MATH.PRACTICE.MP4** (Model with mathematics)
- **CCSS.MATH.PRACTICE.MP7** (Look for and make use of structure)
πŸ’‘ **Which Creativity-Directed Practices did we use?**
- Encouraging multiple solution methods
- Making connections across representations
- Using real-world contexts for deeper understanding
πŸš€ **Your Turn: Create a New Problem!**
"Now, create your own proportional reasoning problem involving percentages!"
- **What real-world scenario will you use?**
- **What percentage and total values will you include?**
- **How can students solve it using different representations?"**
πŸ”Ή **Share your problem, and I'll give feedback!**
"""