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MAIN_PROMPT = """
### **Module 4: Proportional Thinking with Percentages**
#### **Task Introduction**
"Welcome to this module on **proportional reasoning with percentages!**
Today, we will explore how to use **bar models, double number lines, and equations** to solve percentage problems.
π‘ **Your task is to solve the following problem using different representations.**
π‘ **I will prompt you to think critically before offering hints.**
π‘ **You will explain your reasoning step by step.**
π **Letβs begin!**"
---
### **π Solve the Following 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.
How much do Orrin and Damen invest together?"
π‘ **Before choosing a strategy, think about:**
- "What does **60% of the total investment** mean in this situation?"
- "What strategies might help visualize or solve this problem?"
πΉ **Try solving it first. Let me know your initial thoughts!**
---
"""
# β
**STEP 1: BAR MODEL REPRESENTATION**
def bar_model_step(step):
if step == 1:
return """π **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?"
π‘ **Before I give hints, think about:**
- "How can we represent the **total investment** as a bar?"
- "If 60% is **$1,500**, how many sections should the bar have?"
πΉ **Try setting it up before I provide hints!**
"""
elif step == 2:
return """πΉ **Hint 1:**
"Start by dividing the bar into **10 equal sections**, where each represents **10%** of the total.
Since 60% is **$1,500**, how much does **each 10% section** represent?"
"""
elif step == 3:
return """πΉ **Hint 2:**
"Divide **$1,500 by 6** to find **10%** of the total investment.
Then, multiply by **10** to find **100%**."
"""
elif step == 4:
return """β
**Solution:**
"$1,500 Γ· 6 = $250$ (for 10%)
$250 Γ 10 = $2,500$
So, the total investment is **$2,500.**"
π‘ "Does this make sense? How would you explain this to students?"
π "Now, let's solve this problem using a **double number line!**"
"""
# β
**STEP 2: DOUBLE NUMBER LINE REPRESENTATION**
def double_number_line_step(step):
if step == 1:
return """π **Step 2: Solve Using a Double Number Line**
"How might a **double number line** help in this situation?"
π‘ **Think about:**
- "If **60% = $1,500**, what are the missing values for **10%, 20%, and 100%**?"
- "How would you label and align the values?"
πΉ **Try setting up your number line before I provide hints!**
"""
elif step == 2:
return """πΉ **Hint 1:**
"Start by labeling the number lines:
- **Percentages:** 0%, 10%, 20%, 60%, 100%
- **Dollars:** $0, ???, ???, $1,500, ???"
"What values should go in the missing spots?"
"""
elif step == 3:
return """πΉ **Hint 2:**
"Divide **$1,500 by 6** to get **10%** of the total.
Align this value with the corresponding percentage."
"""
elif step == 4:
return """β
**Solution:**
"The correct number line alignment:
- **10% = $250**
- **20% = $500**
- **100% = $2,500**
π‘ "How does this compare to the bar model?"
π "Now, let's solve it using an **equation!**"
"""
# β
**STEP 3: EQUATION REPRESENTATION**
def equation_step(step):
if step == 1:
return """π **Step 3: Solve Using an Equation**
"Can you set up an **equation** to represent the proportional relationship?"
π‘ **Think about:**
- "How can we express **60% as a fraction**?"
- "What equation relates **$1,500 and x**?"
πΉ **Try setting up the equation before I provide hints!**
"""
elif step == 2:
return """πΉ **Hint 1:**
"Write the proportion as:
\\[
\\frac{60}{100} = \\frac{1,500}{x}
\\]
Now, solve for \\( x \\)."
"""
elif step == 3:
return """πΉ **Hint 2:**
"Use **cross-multiplication** to find \\( x \\)."
"""
elif step == 4:
return """β
**Solution:**
\\[
60x = 100(1,500)
\\]
\\[
x = \\frac{150,000}{60} = 2,500
\\]
π‘ "How does this method compare to the others?"
π "Now, letβs reflect on what weβve learned!"
"""
# β
**REFLECTION & PROBLEM-POSING**
REFLECTION_PROMPT = """
π **Common Core & Creativity-Directed Practices Discussion**
"Great job! Now, letβs connect this to key teaching strategies."
πΉ **Which Common Core Practices 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 applied most to our problem? Why?"
"""
CREATIVITY_DIRECTED_PRACTICES_PROMPT = """
πΉ **Which Creativity-Directed Practices did we use?**
- Encouraging **multiple solution methods**
- Using **real-world contexts**
- Thinking critically about **proportional relationships**
π‘ "Which of these strategies did you use? How do they help students?"
"""
PROBLEM_POSING_PROMPT = """
π **Problem-Posing Activity**
"Now, try writing your own **percentage-based proportional reasoning problem!**
Use different representations (bar models, number lines, equations) to solve it."
π‘ **Questions to Guide Your Problem:**
- "What real-world context will you use?" (e.g., discounts, investments, recipes)
- "What percentage and total values will you include?"
- "How will your problem allow students to connect concepts?"
π "Once you've written your problem, I'll help evaluate and refine it!"
"""
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