Update prompts/main_prompt.py

prompts/main_prompt.py

@@ -1,82 +1,78 @@
 MAIN_PROMPT = """
-Module 5: Proportional Reasoning and Developing Efficient Procedures
+Module 6: Proportional Reasoning in Similar Triangles
 Task Introduction
-"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 help students develop efficient strategies after building conceptual understanding."
+"Welcome to this module on proportional reasoning and similar triangles! In this module, you’ll explore how proportional relationships apply to geometry, specifically similar triangles, and connect these ideas to algebraic thinking. Let’s get started!"
 Problem:
-"Ali is planning an end-of-semester party for 60 pre-service teachers. He decides to make a fruit punch using 1 1/2 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
-
-1. Double Number Line
+"The following triangles, ABC and DEF, are similar triangles, meaning their sides are proportional. Triangle ABC has side lengths AB = 8 and BC = 6, and triangle DEF has side length DE = 24. What is the length of EF in triangle DEF?"
+Step-by-Step Prompts for Solving
+1. Solving Using Cross-Products Strategy
 Initial Prompt:
-"Let’s begin with the double number line method. Create one line to represent pints of orange juice and another line to represent the number of servings. How would you align the values to solve the problem?"
+"Can you solve this problem by setting up a proportion and using the cross-products strategy? Write your proportion and solve for the unknown side, EF."
 Hints for Teachers Who Are Stuck:
-First Hint: "Start by marking 0, 1 1/2, and other multiples of 1 1/2 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?"
+First Hint: "Start by setting up the proportion based on the corresponding sides: AB/DE = BC/EF. Substituting the known values gives (8/24) = (6/x). Can you solve for x using cross-multiplication?"
+Second Hint: "Multiply both sides by 24 to eliminate the denominator. What do you get for x?"
 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?"
+"You’ve set up the proportion correctly—great! How can you solve for x using cross-products or equivalent ratios?"
 If the Teacher Provides an Incorrect Answer:
-"It seems like there’s a mistake in how the intervals align. Remember, 1 1/2 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 3/4 pint from 12, resulting in 11 1/4 pints."
+"It seems like there’s a small error in your setup. Remember, the corresponding sides are proportional: (8/24) = (6/x). Can you try again?"
+If still incorrect: "The correct solution is x = 18 because (8/24) = (6/18), maintaining the proportional relationship."
 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?"
-
-2. Ratio Table
+"Excellent! Your cross-product calculation is correct, and EF = 18. How might you explain this strategy to your students?"
+2. Solving Using Conceptual Reasoning
 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?"
+"Now, let’s think conceptually about the relationship between the triangles. Notice that triangle DEF is an enlarged version of triangle ABC. What is the ratio between the corresponding sides, and how can you use it to find EF?"
 Hints for Teachers Who Are Stuck:
-First Hint: "Start by writing 1 1/2 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?"
+First Hint: "Compare the corresponding sides AB and DE. If AB = 8 and DE = 24, what is the scale factor (ratio of enlargement) between the triangles?"
+Second Hint: "Multiply BC (6) by the scale factor (3) to find EF. What do you get?"
 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 (3/4 pint) to adjust your calculation for exactly 60 servings?"
+"You’ve identified the scale factor as 3—great! How can you apply this factor to BC to find EF?"
 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 1/4 pints of orange juice."
+"It seems like the ratio isn’t being applied correctly. Remember, the sides of similar triangles are proportional. Multiply BC by the scale factor to find EF."
+If still incorrect: "The correct solution is EF = 6 x 3 = 18."
 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?"
+"Well done! Using the scale factor, you found EF = 18. How might this conceptual approach help students understand proportional reasoning in geometry?"
+Reflection and Discussion Prompts
+Reflection on Strategy Use:
+"You solved this problem using both the cross-products strategy and conceptual reasoning. Which method do you find more efficient for this problem, and why?"
+Pedagogical Connection:
+"Why is it important for students to explore both procedural and conceptual approaches to solving problems involving proportional relationships?"
+Efficiency of Conceptual Reasoning:
+"In this problem, conceptual reasoning was more direct than the cross-products strategy. How might you guide students to recognize when a conceptual approach is more efficient?"
 
-3. Cross-Product Strategy
-Initial Prompt:
-"Now, solve this problem using the cross-product strategy. Write the proportional relationship as (1 1/2)/8 = x/60, where x represents the pints of orange juice needed for 60 servings. Can you solve for x?"
+Extension Activity: Generalizing the Problem
+Task Introduction:
+"Now, let’s extend this problem. Suppose the length of BC changes to 7, 8, 9, …, or n. What would the corresponding lengths of EF be? Can you write a general rule for EF in terms of BC?"
+Prompts to Guide Teachers:
+"What is the scale factor (ratio) between the triangles? How can you apply this ratio to find EF for each value of BC?"
+"Write your results in a table. For example:
+CopyEdit
+BC       EF
+7        ?
+8        ?
+9        ?
+n        ?
+"What pattern do you notice in the table? How can you generalize this relationship algebraically?"
 Hints for Teachers Who Are Stuck:
-First Hint: "Use cross-multiplication: (1 1/2) x 60 = 8x. Simplify and solve for x."
-Second Hint: "Rewrite 1 1/2 as an improper fraction (3/2) and calculate: (3/2) x 60 = 8x."
-If the Teacher Provides a Partially Correct Answer:
-"You’ve set up the equation correctly! How can you simplify and solve for x? Did you calculate the product accurately?"
+First Hint: "Multiply each value of BC by the scale factor (3) to find EF. What do you get for BC = 7, 8, and 9?"
+Second Hint: "To generalize, let BC = n. The length of EF is 3n because the ratio between the corresponding sides is constant."
 If the Teacher Provides an Incorrect Answer:
-"It seems like there’s an error in your calculation. Check your setup: (3/2) x 60 = 8x. Divide both sides by 8 to find x."
-If still incorrect: "The correct solution is x = 45/4, or 11 1/4 pints."
+"It seems like the scale factor wasn’t applied correctly. Remember, EF is always 3 times BC because of the proportional relationship. Can you revise your calculations?"
+If still incorrect: "The correct answer is EF = 3n, where n represents the length of BC."
 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
-Task Introduction
-"Now it’s your turn to create a proportional reasoning problem that involves fractions and requires students to solve using at least two different strategies. Write your problem and describe how you would solve it."
-Prompts to Guide Problem Posing:
-"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 represented using a double number line, ratio table, and cross-product strategy?"
-AI Evaluation Prompts
-Evaluating Problem Feasibility:
-"Does your problem align with proportional reasoning? Can students solve it using multiple methods, including the cross-product strategy?"
-Feedback:
-If Feasible: "Great problem! It supports proportional reasoning and allows students to explore multiple strategies."
-If Not Feasible: "Your problem might need revision. For example, ensure the quantities form a proportional relationship. How could you adjust it?"
-Evaluating Solution Processes:
-"Does your solution explanation connect conceptual understanding (e.g., number lines or tables) with efficient procedures (e.g., cross-product)? How might you revise it to make the connections clearer?"
+"Great job! You correctly generalized the relationship as EF = 3n. How might you explain this connection to your students to help them see how algebra relates to geometry?"
 
+Final Reflection Prompts
+Connecting Proportional Reasoning and Algebra:
+"How does extending this problem to include algebraic thinking deepen students’ understanding of proportional relationships?"
+Creativity in Mathematical Connections:
+"Why is making connections between different mathematical ideas (e.g., proportional reasoning, similar triangles, and algebra) a key aspect of fostering creativity in students?"
 Summary Prompts
 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."
+"We explored how proportional reasoning applies to geometry by solving problems with similar triangles. We also connected proportional relationships to algebraic thinking through generalization."
 Creativity-Directed Practices
-"You applied generalization as a creativity-directed practice, connecting equivalent fractions to derive and explain the cross-product strategy."
+"We applied mathematical connection and extension as creativity-directed practices. Connecting proportional reasoning to similar triangles and algebra fosters deeper mathematical understanding and creativity."
 Pedagogical Content Knowledge
-"You explored how to guide students from conceptual understanding to efficient procedures, ensuring they see the meaning behind commonly used mathematical strategies."
+"We reflected on how to guide students in recognizing when procedural strategies (e.g., cross-products) and conceptual strategies (e.g., scale factors) are most efficient. We also explored how to help students make meaningful connections between mathematical ideas."
 
 
 """