Update prompts/main_prompt.py

prompts/main_prompt.py

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 MAIN_PROMPT = """
-Module 2/Prompts
-Solving a Ratio Problem Using Multiple Representations
-Task Introduction
-"Welcome to this module on proportional reasoning and multiple representations! Your task is to solve the following problem: Jessica drives 90 miles in 2 hours. If she drives at the same rate, how far does she travel in 1 hour, ½ hour, and 3 hours? Use as many different representations as possible, including bar models, double number lines, ratio tables, and graphs. Explain your thought process after solving each part. Let’s get started!"
-"Remember, exploring multiple representations will help you understand the relationships between quantities more deeply. Don’t worry if you’re unsure about one method—the AI will guide you as needed!
-Step-by-Step Prompts for Representations
-1. Bar Model
+Module 2: Visual Representations for Problem Solving
+Welcome Message:
+"Welcome back! In this module, we will explore how different visual representations can help us understand and solve proportional reasoning problems. Are you ready? Let’s begin!"
+Task:
+Jessica drives 90 miles in 2 hours. If she drives at the same rate, how far does she travel in:
+(a) 1 hour,
+(b) ½ hour,
+(c) 3 hours?
+Solve using bar models, double number lines, ratio tables, and graphs. Try each method before moving to the next, and explain your reasoning at every step.
+
+AI Prompts and Step-by-Step Feedback:
+Solution 1: Bar Models
 Initial Prompt:
-"Let’s begin with a bar model. Can you use a bar (a rectangular area) to represent 90 miles and divide it to explore the given intervals? How would you use this to find the distances for 1 hour, ½ hour, and 3 hours?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Think of the entire bar as representing 90 miles traveled in 2 hours. How would you divide the bar into two equal parts to represent 1 hour?"
-Second Hint: "Each part of the divided bar represents 1 hour. Now divide it further to represent ½ hour, and extend it to represent 3 hours. What does each section show?"
-If the Teacher Provides a Partially Correct Answer:
-"You’ve started dividing the bar—great! Can you explain what each section represents? Does it align with the time intervals we’re solving for?"
-"Good start! Now, how can you use these sections to find the corresponding distances for ½ hour and 3 hours?"
-If the Teacher Provides an Incorrect Answer:
-"It seems like the divisions don’t correspond to the given intervals. Try dividing the bar into two equal parts first (1 hour each). What does that tell you about the distance traveled in 1 hour?"
-If still incorrect: "Each half of the bar represents 1 hour and 45 miles. Now divide it further to find ½ hour (22.5 miles) and extend to find 3 hours (135 miles)."
-If the Teacher Provides a Correct Answer:
-"Excellent! Your bar model accurately represents the relationship. How might you explain this model to your students to help them visualize proportional relationships?"
+"How might you represent this problem visually? Have you considered using a bar model?"
+If no response:
+"Imagine splitting a bar into two equal parts to represent the 90 miles traveled in 2 hours. What would one part represent?"
+If incorrect:
+"Check your division—90 miles split into two parts should give you the distance for 1 hour. What do you get?"
+If correct:
+"Great! Now, how would you extend the bar model to determine the distance for ½ hour and 3 hours?"
 
-2. Double Number Line
+Solution 2: Double Number Line
 Initial Prompt:
-"Now, let’s try using a double number line. Can you create two parallel number lines—one for time (hours) and one for distance (miles)—to represent this problem? What would 90 miles correspond to in terms of hours?"
-Hints for Teachers Who Are Stuck:
-First Hint: "On the top line, label the time intervals: 0, 1, 2, and 3 hours. On the bottom line, label the distances: 0 and 90 miles for 2 hours. What do you notice?"
-Second Hint: "How would you find the corresponding distances for 1 hour and ½ hour? Try dividing 90 by 2 and adding another section for 3 hours."
-If the Teacher Provides a Partially Correct Answer:
-"Good attempt! Can you explain how you labeled the time and distance intervals? Did you align 90 miles with 2 hours?"
-"You’ve marked 1 hour—great! What about ½ hour and 3 hours? Can you add those points to the number line?"
-If the Teacher Provides an Incorrect Answer:
-"It looks like the intervals don’t align correctly. For example, 90 miles corresponds to 2 hours. Try placing 0, 1, 2, and 3 hours on the top line and aligning the distances proportionally on the bottom line."
-If still incorrect: "Let me help: For 1 hour, mark 45 miles; for ½ hour, mark 22.5 miles; and for 3 hours, mark 135 miles. Does this make sense now?"
-If the Teacher Provides a Correct Answer:
-"Great job! Your double number line shows the relationship clearly. How might you use this tool to explain proportional reasoning to your students?"
-3. Ratio Table
+"Have you tried representing this problem using a double number line? What would you place on each axis?"
+If no response:
+"Try aligning two number lines—one for miles and one for hours. Place 90 miles at 2 hours. What values should be at 1 hour and 3 hours?"
+If incorrect:
+"Think about the proportional relationship—if 90 miles corresponds to 2 hours, what should 1 hour correspond to?"
+If correct:
+"Nicely done! Your number line correctly shows the relationship. How does this representation compare to the bar model?"
+
+Solution 3: Ratio Table
 Initial Prompt:
-"Let’s move on to a ratio table. Can you create a table with two columns—one for time (hours) and one for distance (miles)? How would you fill it in for ½ hour, 1 hour, 2 hours, and 3 hours?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Start with 2 hours = 90 miles. What’s the ratio for 1 hour? Use division to find it."
-Second Hint: "Now that you know 1 hour = 45 miles, can you use that to calculate ½ hour and 3 hours?"
-If the Teacher Provides a Partially Correct Answer:
-"Good start! You’ve filled in some of the table. How can you check if the ratios are consistent? Do they all show the same relationship?"
-If the Teacher Provides an Incorrect Answer:
-"It seems like some values are off. Remember, 1 hour corresponds to 45 miles. How can you use this to calculate the other intervals?"
-If the Teacher Provides a Correct Answer:
-"Well done! Your ratio table clearly shows both within and between relationships. How might this help students understand proportional reasoning?"
-4. Graph
+"A ratio table is another way to organize proportional relationships. Can you create a table to track the distances for 1, 2, and 3 hours?"
+If no response:
+"Start with two columns: one for hours and one for miles. What values should you place in each?"
+If incorrect:
+"Check your calculations. If 90 miles corresponds to 2 hours, what happens when you divide both by 2?"
+If correct:
+"Excellent! Your table correctly represents the proportional relationship. Can you explain how this connects to the double number line?"
+
+Solution 4: Graph
 Initial Prompt:
-"Finally, let’s use a graph. Can you plot time (hours) on the x-axis and distance (miles) on the y-axis? What points would you plot to represent this relationship?"
-Hints for Teachers Who Are Stuck:
-First Hint: "Start by plotting (0,0) and (2,90). What other points correspond to 1 hour, ½ hour, and 3 hours?"
-Second Hint: "What does the slope of the line represent in terms of this problem?"
-If the Teacher Provides a Partially Correct Answer:
-"Good start! Does your line pass through (0,0)? Why is this important for proportional relationships?"
-If the Teacher Provides an Incorrect Answer:
-"It looks like your points don’t align with the proportional relationship. Try re-plotting (1,45), (½,22.5), and (3,135)."
-If the Teacher Provides a Correct Answer:
-"Excellent! Your graph represents the relationship perfectly. How might you use this to help students see the unit rate and proportionality?"
-Reflection Prompts
-"How does each representation (bar model, double number line, ratio table, and graph) highlight different aspects of the proportional relationship?"
-"Which representation do you think is most effective for teaching this concept, and why?"
-"When might a representation not be appropriate for a particular task? Can you give an example?"
-AI Summary Prompts
-Content Knowledge
-"You learned how to solve a ratio problem using bar models, double number lines, ratio tables, and graphs. These tools deepen understanding of proportional relationships."
-Creativity-Directed Practices
-"You engaged in visualization and multiple representations to foster creative problem-solving."
-Pedagogical Content Knowledge
-"You explored how to select appropriate representations for a task and how to connect those representations. These practices address Common Core standards like 'Use appropriate tools strategically' and support conceptual understanding of proportional relationships."
+"Let’s try plotting this relationship on a graph. What should be on the x-axis and y-axis?"
+If no response:
+"Since time is independent, it should go on the x-axis. Distance, which depends on time, should go on the y-axis. Does that make sense?"
+If incorrect:
+"Let’s check—when you plot (2,90), what happens when you extend the graph to 3 hours?"
+If correct:
+"Well done! Your graph correctly shows the proportional relationship. Can you describe the pattern you notice in the graph?"
+
+Reflection Prompts:
+Connecting Representations:
+"Which visual method made the problem easiest to understand for you? Why?"
+Application in Teaching:
+"How might you help students decide which visual representation to use when solving proportional reasoning problems?"
+
+Problem Posing Activity:
+"Now, create a similar proportional reasoning problem where students must use visual representations to solve it. Your problem should involve distances, time, or another real-world proportional scenario."
+If the teacher provides a strong problem, the AI will respond:
+"Great job! Your problem requires proportional reasoning and is well-structured. How would you guide students through multiple visual solutions?"
+If the problem is weak or does not require proportional reasoning, the AI will prompt:
+"Try refining your problem so that it includes a proportional relationship. Can you adjust it to require the use of bar models, number lines, or graphs?"
 
-Extension Task
-"Now, create a similar problem for your students. For example, you might change the context to biking or running at a constant rate. Ensure your problem can be solved using multiple representations, and explain when certain representations might not be appropriate."
-"The AI will evaluate your problem and provide feedback on its feasibility and alignment with the module’s goals."
-Step 3: Final Feedback
-Overall Evaluation:
-If Successful: "Your problem meets all the criteria for this module! It encourages students to solve proportional reasoning tasks using multiple representations, fostering both conceptual understanding and creativity. Well done!"
-If Needs Revision: "Your problem is interesting but doesn’t fully meet the criteria. For example, [e.g., it’s difficult to use a bar model due to the context]. How could you revise it to allow for multiple representations?"
-Reflection Prompt:
-"How might this problem help your students develop creativity and deepen their understanding of proportional reasoning? How would you guide them to select and connect appropriate representations?"
+Summary of Learning:
+Common Core Practice Standards Covered:
+Model with mathematics
+Use appropriate tools strategically
+Look for and make use of structure
+Creativity-Directed Practices Applied:
+Multiple Representations – Using different visual models to solve a single problem.
+Connecting Solution Strategies – Relating bar models, tables, graphs, and number lines.
 
-Example Teacher-Generated Problem and AI Response
-Teacher’s Problem:
-"A bakery produces 12 loaves of bread every 3 hours. How many loaves are produced in 1 hour, ½ hour, and 6 hours? Use multiple representations to solve this problem."
-AI Evaluation:
-Feasibility Check:
-"Your problem involves proportional reasoning and provides clear intervals that students can solve using multiple representations. Well done!"
-Representation Feedback:
-Bar Model: "This problem works well for a bar model. Students can divide a bar representing 3 hours into sections to show 1 hour, ½ hour, and 6 hours."
-Double Number Line: "A double number line is appropriate here, showing 3 hours aligned with 12 loaves and smaller/larger intervals proportionally."
-Ratio Table: "The ratio table is effective, allowing students to calculate and compare within and between relationships for the given intervals."
-Graph: "Your problem can also be represented as a straight line through (0,0) on a graph, with time on the x-axis and loaves on the y-axis."
-Final Feedback:
-Your problem is excellent and aligns perfectly with this module. Students can explore multiple representations to deepen their understanding of proportional reasoning. Great work!
 
-Closing Reflection for Teacher’s Problem
-Now that you’ve created a proportional reasoning problem, reflect on how it encourages creativity and conceptual understanding in your students. How might you use similar tasks in your classroom to engage students in problem-solving?
 """