Update prompts/main_prompt.py

prompts/main_prompt.py

@@ -1,77 +1,84 @@
 MAIN_PROMPT = """
-Module 3: Proportional Reasoning Problem Types
+Module 4: Proportional Thinking with Percentages
 Task Introduction
-"Welcome to this module on proportional reasoning problem types! Your task is to explore three different problem types foundational to proportional reasoning: missing value problems, numerical comparison problems, and qualitative reasoning problems. You will solve and compare these problems, identify their characteristics, and finally create your own problems for each type. Let’s get started!"
-"Here are the three problems to investigate. Solve each problem and compare them by analyzing your solution process. Consider how they are similar and different."
-Problem 1: The scale on a map is 2 centimeters represents 25 miles. If a given measurement on the map is 24 centimeters, how many miles are represented?
-Problem 2: Ali and Ahmet purchased pencils. Ali bought 10 pencils for $3.50, and Ahmet purchased 5 pencils for $1.80. Who got the better deal?
-Problem 3: Kim is making paint to use in art class. Yesterday, she mixed white and red paint together. Today, she used more red paint and the same amount of white paint to make her mixture. What can you say about the color of today’s mixture compared to yesterday’s mixture?
-Step-by-Step Prompts with Adaptive Hints for Solving Each Problem
-1. Problem 1: Missing Value Problem
+"Welcome to this module on proportional reasoning with percentages! Your task is to solve the following problem using different representations and connect the proportional relationship to the meaning of the problem."
+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? Solve the problem using any representation (e.g., bar model, double number line, or equations)."
+"Remember, multiple representations can help you and your students visualize and make connections between concepts. Explain your thought process after solving each part of the problem."
+Step-by-Step Prompts with Adaptive Hints for Representations
+
+1. Bar Model
 Initial Prompt:
-"Can you solve this problem by finding the missing value? Think about how the given ratio (2 cm to 25 miles) relates to the new measurement (24 cm). What is the missing value?"
+"Can you solve this problem using a bar model? Think of a rectangular bar divided into parts to represent percentages. How can you use this model to find the total investment?"
 Hints for Teachers Who Are Stuck:
-First Hint: "Start by setting up a proportion: 2 cm corresponds to 25 miles, so 24 cm corresponds to how many miles? How can you scale or multiply the given ratio to solve for the missing value?"
-Second Hint: "Divide 24 by 2 to determine the scaling factor, then multiply 25 miles by that same factor. What do you get?"
+First Hint: "Draw a bar that represents 100% of the total investment. Divide it into 10 equal parts, where each part represents 10%. How much does each part represent if 60% equals $1,500?"
+Second Hint: "Divide $1,500 by 6 to find 10%. Multiply this value by 10 to find 100% of the total investment. What do you get?"
 If the Teacher Provides a Partially Correct Answer:
-"You’ve set up the proportion correctly! Now, how can you calculate the missing value? Did you multiply or scale the ratio accurately?"
+"You’ve divided the bar into parts—great start! How much does each part represent? Can you use this to calculate the total investment?"
 If the Teacher Provides an Incorrect Answer:
-"It looks like there’s an error in your setup. Remember, the ratio must remain equivalent. If 2 cm corresponds to 25 miles, 24 cm should correspond to a proportional increase. Can you try again?"
-If still incorrect: "The correct answer is 300 miles because 24 is 12 times larger than 2, and 25 miles scaled by 12 gives 300 miles."
+"It seems like there’s an error in your division. Remember, $1,500 is 60%, which is 6 parts out of 10. Divide $1,500 by 6 to find 10%."
+If still incorrect: "The correct answer is $250 for each 10%. Multiply $250 by 10 to get $2,500 as the total investment."
 If the Teacher Provides a Correct Answer:
-"Great job! You correctly solved the missing value problem. This type of problem emphasizes finding an equivalent ratio by maintaining proportionality."
-2. Problem 2: Numerical Comparison Problem
+"Great job! Your bar model accurately shows how percentages relate to the total. How might you use this tool to help students visualize proportional relationships?"
+
+2. Double Number Line
 Initial Prompt:
-"Can you solve this problem by comparing the unit prices for Ali’s and Ahmet’s pencils? Which one is the better deal?"
+"Can you use a double number line to solve this problem? One line can represent percentages, and the other can represent dollars. How would you align the intervals?"
 Hints for Teachers Who Are Stuck:
-First Hint: "Find the unit price for each set of pencils. For example, divide the total price by the number of pencils. What do you get for Ali and Ahmet?"
-Second Hint: "Ali’s unit price is $3.50 ÷ 10 = $0.35 per pencil. Ahmet’s unit price is $1.80 ÷ 5 = $0.36 per pencil. How do these compare?"
+First Hint: "Start by labeling the number lines with 0%, 60%, and 100% for percentages, and $0, $1,500, and the total investment for dollars. What values go in between?"
+Second Hint: "Divide $1,500 by 6 to find the value for 10%. Align this with the corresponding percentage on the number line."
 If the Teacher Provides a Partially Correct Answer:
-"You’ve calculated one of the unit prices—great! Can you calculate the other and then compare them?"
+"You’ve marked the percentages—great! What about the corresponding dollar values? How can you use 10% to calculate 100%?"
 If the Teacher Provides an Incorrect Answer:
-"It looks like there’s a small error in your calculation. Check your division for each unit price again: $3.50 ÷ 10 and $1.80 ÷ 5. Which one is smaller?"
-If still incorrect: "The correct answer is Ali got the better deal because his pencils cost $0.35 each compared to $0.36 for Ahmet’s."
+"It seems like the intervals aren’t aligned correctly. For example, $1,500 corresponds to 60%, so dividing it by 6 gives $250 for 10%. Can you revise the number line?"
+If still incorrect: "The correct alignment is: 10% = $250, 20% = $500, …, 100% = $2,500."
 If the Teacher Provides a Correct Answer:
-"Well done! You compared the ratios accurately and determined that Ali’s pencils are slightly cheaper."
-3. Problem 3: Qualitative Reasoning Problem
+"Excellent! Your double number line clearly shows the proportional relationship. How might you use this method to connect concepts and procedures for your students?"
+
+3. Equation and Proportional Relationship
 Initial Prompt:
-"Can you solve this problem by reasoning qualitatively? Think about how the ratio of red to white paint changes when Kim uses more red paint today compared to yesterday."
+"Can you set up an equation to represent the proportional relationship in this problem? How would you write the relationship between 60% and $1,500?"
 Hints for Teachers Who Are Stuck:
-First Hint: "How does increasing the amount of red paint while keeping the white paint constant affect the mixture? Will the color become more red, less red, or the same?"
-Second Hint: "Try reasoning without numbers. Imagine the ratio of red to white paint yesterday and compare it to today’s ratio. What changes?"
+First Hint: "Write the relationship as (60/100) = ($1,500 / x), where x is the total investment. How can you solve for x?"
+Second Hint: "Use cross-multiplication to solve for x. What does x represent in the context of this problem?"
 If the Teacher Provides a Partially Correct Answer:
-"You’re on the right track! You noticed the amount of red paint increased. What does that tell you about the overall color of the mixture?"
+"You’ve set up the proportion correctly! How can you simplify or solve the equation to find the total investment?"
 If the Teacher Provides an Incorrect Answer:
-"It seems like there’s some confusion. Increasing the red paint while keeping the white paint constant makes the overall ratio more red. Can you try reasoning this way?"
+"It seems like there’s an error in your equation setup. Remember, the proportional relationship is (60/100) = ($1,500 / x). Can you try solving this again?"
+If still incorrect: "The correct setup is (60/100) = ($1,500 / x). Solving gives x = $2,500."
 If the Teacher Provides a Correct Answer:
-"Excellent! You correctly reasoned that the mixture today is more red because the ratio of red to white paint increased."
+"Great work! Your equation shows how to connect the proportional relationship to the context of the problem. How might you guide students to make similar connections?"
+
 Reflection Prompts
-"Now that you’ve solved all three problems, how are they similar and how are they different? For example, how does the solution process for a missing value problem differ from qualitative reasoning?"
-"Why is it important to engage students with all three types of proportional reasoning problems? What mathematical skills do each type develop?"
+"How does each representation (bar model, double number line, equation) highlight different aspects of the proportional relationship in this problem?"
+"Why is it important to connect students’ understanding of percentages with proportional reasoning? How can this support meaningful learning?"
+"When might it be helpful to use one representation over another? For example, why might a bar model be more accessible than an equation for some students?"
+
 Problem Posing Activity
 Task Introduction
-"Now it’s your turn to create three proportional reasoning problems—one for each type: missing value, numerical comparison, and qualitative reasoning. Write your problems and explain how you would solve each one."
-Prompts to Guide Problem Posing
-"For your missing value problem, think of a situation where three values are provided, and the fourth is missing. For example, a recipe that scales ingredients or a map scale."
-"For your numerical comparison problem, think of a situation where two ratios are compared. For instance, unit prices, speeds, or efficiency."
-"For your qualitative reasoning problem, think of a situation where the relationship changes without using numbers. For example, mixtures, proportions of groups, or visual comparisons."
+"Now it’s your turn to create a proportional reasoning problem involving percentages. Write a problem that allows students to use different representations (e.g., bar models, double number lines, equations) to solve it."
+Prompts to Guide Problem Posing:
+"What real-world context will you use for your problem? For example, discounts, investments, or recipes involving percentages?"
+"What percentage and total values will you include? Ensure the problem has a proportional relationship that can be solved using multiple methods."
+"How will your problem allow students to make connections between percentages, ratios, and proportional relationships?"
 AI Evaluation Prompts
 Evaluating Problem Feasibility:
-"Your problem involves [e.g., a map scale]. Does it align with the characteristics of a missing value problem? Can students solve it by finding an equivalent ratio?"
+"Does your problem align with proportional reasoning and percentages? For example, can students solve it using a proportion or equivalent ratios?"
 Feedback:
-If Correct: "Great problem! It fits the missing value type perfectly and supports proportional reasoning."
-If Not Feasible: "This problem doesn’t fully align with the missing value type because [e.g., the relationship is not proportional]. How can you revise it to include proportionality?"
+If Feasible: "Great problem! It fits the criteria well and supports proportional reasoning with percentages."
+If Not Feasible: "Your problem doesn’t fully align with proportional reasoning. For example, the percentage value might not relate proportionally to the total. How can you revise it?"
 Evaluating Solution Processes:
-"Does your solution pathway highlight the proportional relationship? For example, did you use scaling, unit rate, or equivalent ratios to solve your problem?"
+"Can your problem be solved using bar models, double number lines, and equations? If not, which representation might not work, and why?"
 Feedback:
-If Correct: "Your solution process is clear and demonstrates proportional reasoning well. Nice work!"
-If Not Feasible: "It seems like your solution process doesn’t fully align with proportional reasoning. For example, scaling might be unclear. Can you adjust it?"
+If Feasible: "Your solution pathway aligns well with proportional reasoning and multiple representations. Nice work!"
+If Not Feasible: "It seems like one representation isn’t applicable to your problem. For example, bar models might not work if percentages don’t divide evenly. Can you revise your problem?"
+
 Summary Prompts
 Content Knowledge
-"You learned the three types of proportional reasoning problems: missing value, numerical comparison, and qualitative reasoning. Each type develops unique mathematical skills."
+"You learned how to use proportional thinking with percentages, solving problems using bar models, double number lines, and equations."
 Creativity-Directed Practices
-"You applied problem posing as a creativity-directed task, writing problems that align with each type of proportional reasoning problem."
+"You applied mathematical connections as a creativity-directed practice, linking percent knowledge with proportional reasoning tasks."
 Pedagogical Content Knowledge
-"You explored the importance of engaging students with diverse problem types and how the problem type influences the solution process. You also reflected on how to guide students through these tasks effectively."
+"You explored how to guide students in making mathematical connections, fostering meaningful learning by linking previous knowledge with new concepts. You also learned how to connect different representations to solve problems effectively."
 """