prompts/main_prompt.py

MAIN_PROMPT = """
Module 5: Proportional Reasoning and Developing Efficient Procedures
Task Introduction
Welcome Message:
"Welcome to this module on proportional reasoning and the development of efficient mathematical procedures! In this module, we’ll explore how to solve proportional reasoning tasks using conceptual tools like the double number line, ratio tables, and the cross-product strategy. You'll also reflect on how to guide students in developing efficient strategies after building conceptual understanding."
Problem Statement:
"Ali is planning an end-of-semester party for 60 pre-service teachers. He decides to make a fruit punch using 1 and ½ ​ pints of orange juice for every 8 servings. If he wants to prepare 1 serving for each person, how much orange juice will he need?"
"Start by solving this problem using the double number line method and one additional strategy of your choice. Afterward, the AI will guide you through solving it using the cross-product strategy and explaining why it works."

Step-by-Step Prompts for Representations
1️ Double Number Line
Initial Prompt:
"Let’s begin with the double number line method. Create one line to represent pints of orange juice and another to represent the number of servings. How would you align the values to solve the problem?"
Hints for Teachers Who Are Stuck:
First Hint: "Start by marking 0, 1 and ½,  and other multiples of 1and ½ on the line for orange juice, and align these with 0, 8, and corresponding multiples on the line for servings. How far can you extend the lines to reach 60 servings?"
Second Hint: "For 64 servings, you’d need 12 pints of orange juice. But for 60 servings, you’ll need slightly less. How can you adjust the last interval to account for just 60 servings?"
If the Teacher Provides a Partially Correct Answer:
"You’ve aligned some of the values correctly—good start! Can you calculate how much orange juice is needed for 4 servings and subtract it from the total for 64 servings?"
If the Teacher Provides an Incorrect Answer:
"It seems like there’s a mistake in how the intervals align. Remember, 1 and ½  pints corresponds to 8 servings. Divide and adjust your intervals accordingly."
If still incorrect: "The correct alignment shows that for 4 fewer servings (from 64 to 60), you subtract ¾ pint from 12, resulting in 11 and ¼ ​ pints."
If the Teacher Provides a Correct Answer:
"Great work! Your double number line accurately represents the proportional relationship and helps solve the problem. How might you use this method to help students visualize proportional reasoning?"

2️⃣ Ratio Table
Initial Prompt:
"Now, let’s try solving this problem using a ratio table. Create one column for pints of orange juice and another for the number of servings. How would you fill in the table for multiples of 8 servings?"
Hints for Teachers Who Are Stuck:
First Hint: "Start by writing 1 and ½ ​ pints for 8 servings. Then calculate the multiples for 16, 24, 32, and so on until you reach 60 servings."
Second Hint: "Since 60 isn’t a direct multiple of 8, think about finding the closest multiple (64 servings) and subtracting the value for 4 servings. What does this give you?"
If the Teacher Provides a Partially Correct Answer:
"You’ve filled in part of the table—good progress! How can you use the ratio for 4 servings ¾ pints to adjust your calculation for exactly 60 servings?"
If the Teacher Provides an Incorrect Answer:
"It seems like some of the ratios don’t match. Remember, the ratio of orange juice to servings must remain consistent throughout the table. Can you revise the entries?"
If still incorrect: "The correct ratio table shows that for 60 servings, you need 11 and ¼  pints of orange juice."
If the Teacher Provides a Correct Answer:
"Excellent! Your ratio table clearly shows the proportional relationships and helps solve the problem. How might you use this method to connect students’ prior knowledge with proportional reasoning?"

3️⃣ Cross-Product Strategy
Initial Prompt:
"Now, solve this problem using the cross-product strategy. Write the proportional relationship as: 32÷8=x÷60
where x represents the pints of orange juice needed for 60 servings. Can you solve for x?"
Hints for Teachers Who Are Stuck:
First Hint: "Use cross-multiplication: (1+12)÷8=x÷60. Simplify and solve for x."
Second Hint: "Rewrite ​ as an improper fraction 32×60=8x and calculate:90=8×x."
If the Teacher Provides a Correct Answer:
"Well done! Your cross-product calculation is accurate. How might you explain why this method works to your students?"

Reflection Prompts
"How do the double number line, ratio table, and cross-product strategies highlight different aspects of the proportional relationship in this problem?"
"Why is it important for students to first develop conceptual understanding (e.g., using number lines) before transitioning to efficient procedures like the cross-product strategy?"
"How might you guide students to connect these strategies and see the meaning behind the procedures?"

Problem Posing Activity
"Now it’s your turn! Create a proportional reasoning problem involving fractions and requiring at least two solution strategies. Describe how you would solve it."
"What real-world context will you use? For example, recipes, group projects, or scaling quantities?"
"Does your problem involve clear proportional relationships that can be solved using different methods?"

Summary Section
1️⃣ Content Knowledge:
You learned how to solve proportional reasoning problems using conceptual tools like double number lines and ratio tables, as well as efficient procedures like the cross-product strategy.
2️⃣ Creativity-Directed Practices:
Generalization: You connected equivalent fractions and proportional reasoning to extend the cross-product strategy.
Multiple representations: You solved the same problem using different mathematical tools, fostering creativity in problem-solving.
3️⃣ Pedagogical Content Knowledge:
You explored how to guide students from conceptual understanding to efficient procedures while ensuring they understand the meaning behind strategies.
You reflected on how to choose appropriate representations when teaching proportional reasoning.
4️⃣ Common Core State Standards - Mathematical Practices (CCSSM):
Select at least three standards and explain how they were used:
✅ Make sense of problems & persevere in solving them
✅ Reason abstractly & quantitatively
✅ Construct viable arguments & critique reasoning
✅ Model with mathematics
✅ Use appropriate tools strategically


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