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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.
πŸ’‘ **Your task is to solve the following problem using different representations.**
πŸ’‘ **I will guide you step by step, prompting you to think critically.**
πŸ’‘ **You will explain your reasoning before I provide hints.**
πŸš€ **Let’s get started!**"
---
### **πŸš€ Solve the Following Problem**
πŸ“Œ **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?"
πŸ’‘ "Try solving it using a **bar model, double number line, or an equation.** Which representation do you prefer?"
---
"""
# βœ… **STEP 1: BAR MODEL REPRESENTATION**
def bar_model_step(step):
if step == 1:
return """πŸš€ **Step 1: Solve Using a Bar Model**
"Can you use a **bar model** to represent this problem?
Think of a rectangular bar divided into parts to represent percentages. How can you use this model to find the total investment?"
πŸ’‘ **Before I give hints, consider these questions:**
- "If **60% = $1,500**, what does **10%** represent?"
- "How many equal parts should you divide the bar into?"
πŸ”Ή **Try solving it before I provide hints! Type your answer below.**
"""
elif step == 2:
return """πŸ”Ή **Hint 1:**
"Start by drawing a bar representing **100% of the total investment**.
Divide it into **10 equal parts**, where each part represents **10%**.
Since **60% = $1,500**, how much does **each part** represent?"
"""
elif step == 3:
return """πŸ”Ή **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 """βœ… **Solution:**
"$1,500 Γ· 6 = $250$ (for 10%)
$250 Γ— 10 = $2,500$
So, the total investment is **$2,500.**"
πŸ’‘ "Does this make sense? How would you explain this to students?"
πŸš€ "Now, let's solve this problem using a **double number line!**"
"""
# βœ… **STEP 2: DOUBLE NUMBER LINE REPRESENTATION**
def double_number_line_step(step):
if step == 1:
return """πŸš€ **Step 2: Solve Using a Double Number Line**
"Can you use a **double number line** to solve this problem?
One line represents **percentages**, and the other represents **dollars**. How would you align the intervals?"
πŸ’‘ **Before I give hints, consider these:**
- "If **60% = $1,500**, what are the missing values for 10%, 20%, and 100%?"
- "How do you align the values on the number line?"
πŸ”Ή **Try solving before I provide hints!**
"""
elif step == 2:
return """πŸ”Ή **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 """πŸ”Ή **Hint 2:**
"Divide **$1,500 by 6** to get **10%** of the total.
Align this value with the corresponding percentage."
"""
elif step == 4:
return """βœ… **Solution:**
"The correct number line alignment:
- **10% = $250**
- **20% = $500**
- **100% = $2,500**
πŸ’‘ "How did this representation help you understand the proportional relationship?"
πŸš€ "Now, let's solve it using an **equation!**"
"""
# βœ… **STEP 3: EQUATION REPRESENTATION**
def equation_step(step):
if step == 1:
return """πŸš€ **Step 3: Solve Using an Equation**
"Can you set up an **equation** to represent the proportional relationship?
How would you write the relationship between **60%** and **$1,500**?"
πŸ’‘ **Try setting up an equation before I provide hints!**
"""
elif step == 2:
return """πŸ”Ή **Hint 1:**
"Write the proportion as:
\\[
\\frac{60}{100} = \\frac{1,500}{x}
\\]
Now, solve for \\( x \\)."
"""
elif step == 3:
return """πŸ”Ή **Hint 2:**
"Use **cross-multiplication** to find \\( x \\)."
"""
elif step == 4:
return """βœ… **Solution:**
\\[
60x = 100(1,500)
\\]
\\[
x = \\frac{150,000}{60} = 2,500
\\]
πŸ’‘ "How does setting up an equation compare to the other methods?"
πŸš€ "Now, let’s reflect on what we’ve learned!"
"""
# βœ… **REFLECTION & PROBLEM-POSING**
REFLECTION_PROMPT = """
πŸ“Œ **Common Core & Creativity-Directed Practices Discussion**
"Great work! Now, let’s connect this to key teaching strategies."
πŸ”Ή **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)
πŸ’‘ "Which of these standards applied most to our problem? Why?"
"""
CREATIVITY_DIRECTED_PRACTICES_PROMPT = """
πŸ”Ή **Which Creativity-Directed Practices did we use?**
- Encouraging **multiple solution methods**
- Using **real-world contexts**
- Thinking critically about **proportional relationships**
πŸ’‘ "Which of these strategies did you use? How do they help students?"
"""
PROBLEM_POSING_PROMPT = """
πŸ“Œ **Problem-Posing Activity**
"Now, try writing your own **percentage-based proportional reasoning problem!**
Use different representations (bar models, number lines, equations) to solve it."
πŸ’‘ **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?"
πŸš€ "Once you've written your problem, I'll help evaluate and refine it!"
"""