|
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 guide you step by step, prompting you to think critically.** |
|
π‘ **You will explain your reasoning before I provide hints.** |
|
π **Letβs get started!**" |
|
|
|
--- |
|
### **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‘ "Try solving it using a **bar model, double number line, or an equation.** Which representation do you prefer?" |
|
--- |
|
""" |
|
|
|
|
|
def bar_model_step(step): |
|
if step == 1: |
|
return """π **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?" |
|
|
|
π‘ **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?" |
|
|
|
πΉ **Try solving it before I provide hints! Type your answer below.** |
|
""" |
|
elif step == 2: |
|
return """πΉ **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 """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!**" |
|
""" |
|
|
|
|
|
def double_number_line_step(step): |
|
if step == 1: |
|
return """π **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?" |
|
|
|
π‘ **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?" |
|
|
|
πΉ **Try solving 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 did this representation help you understand the proportional relationship?" |
|
π "Now, let's solve it using an **equation!**" |
|
""" |
|
|
|
|
|
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? |
|
How would you write the relationship between **60%** and **$1,500**?" |
|
|
|
π‘ **Try setting up an 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 setting up an equation compare to the other methods?" |
|
π "Now, letβs reflect on what weβve learned!" |
|
""" |
|
|
|
|
|
REFLECTION_PROMPT = """ |
|
π **Common Core & Creativity-Directed Practices Discussion** |
|
"Great work! 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!" |
|
""" |