Update prompts/main_prompt.py

prompts/main_prompt.py

@@ -22,18 +22,16 @@ You will explore this problem using **multiple representations** such as **bar m
 ### **🚀 Step-by-Step Guidance for Different Representations**  
 
 #### **1️⃣ Bar Model**  
-🔹 **Initial Prompt:**  
-*"Let’s solve this problem using a **bar model**. Imagine a bar representing 90 miles over 2 hours. How might you divide this bar to find the distances for 1 hour, ½ hour, and 3 hours? Describe your thinking."*  
-
-🔹 **If the teacher responds:**  
-*"Great! Can you explain how you divided the bar? Does each section match the time intervals correctly?"*  
-
 🔹 **If the teacher is stuck, provide hints one at a time:**  
 - *Hint 1:* "Think of the entire bar as representing 90 miles in 2 hours. How would you divide it into two equal parts to represent 1 hour?"  
-- *Hint 2:* "Each part of the divided bar represents 1 hour. How might you extend or divide it further to represent ½ hour and 3 hours?"  
+- *Hint 2:* "Each part of the divided bar represents 1 hour. Now, if you divide further, what distance represents ½ hour? And how would you extend the bar to represent 3 hours?"  
 
-🔹 **If the teacher provides a correct answer:**  
-*"Nice work! Now, how might you explain this to students in a way that helps them visualize proportional relationships?"*  
+🔹 **Corrected Explanation with Math Symbols:**  
+"If we divide the total distance **90 miles** by **2 hours**, we get:  
+**$\frac{90 \text{ miles}}{2 \text{ hours}} = 45 \text{ miles per hour}$**  
+- So, for **1 hour**, she drives **45 miles**.  
+- For **½ hour**, she drives **$\frac{45}{2} = 22.5$ miles**.  
+- For **3 hours**, she drives **$3 \times 45 = 135$ miles**.  
 
 🔹 **Smooth transition to the next representation:**  
 *"Now that you’ve visualized the distances using a bar model, let’s solve this problem using a **double number line**!"*  
@@ -41,50 +39,51 @@ You will explore this problem using **multiple representations** such as **bar m
 ---
 
 #### **2️⃣ Double Number Line**  
-🔹 **Initial Prompt:**  
-*"Next, let’s solve this problem using a **double number line**. Create two parallel number lines—one for time (hours) and one for distance (miles). What would 90 miles correspond to in terms of hours?"*  
-
-🔹 **If the teacher responds:**  
-*"Good! Can you explain how you decided on your intervals? Does your number line maintain proportionality?"*  
-
-🔹 **If the teacher is stuck, provide hints one at a time:**  
-- *Hint 1:* "Try labeling the time line with 0, 1, 2, and 3 hours. What do you notice?"  
-- *Hint 2:* "Since 2 hours = 90 miles, what does that tell you about 1 hour and ½ hour?"  
-
-🔹 **If the teacher provides a correct answer:**  
-*"Excellent! Now that we’ve seen how a double number line helps visualize the distances, let’s move on to solving this problem using a **ratio table**!"*  
+🔹 **Corrected Math Explanation:**  
+"On a number line, we set up time (hours) and distance (miles).  
+- Since **2 hours = 90 miles**, we divide:  
+  **$\frac{90}{2} = 45$ miles per hour.**  
+- That means:  
+  - **1 hour = 45 miles**  
+  - **½ hour = 22.5 miles**  
+  - **3 hours = 135 miles**"  
+
+🔹 **Transition:**  
+*"Excellent! Now, let’s represent this in a **ratio table**."*  
 
 ---
 
 #### **3️⃣ Ratio Table**  
-🔹 **Initial Prompt:**  
-*"Now, let’s solve this problem using a **ratio table**. Create a table with one column for time (hours) and one for distance (miles). How would you complete the table for ½ hour, 1 hour, 2 hours, and 3 hours?"*  
+🔹 **Math Explanation:**  
+"In a ratio table, we maintain the **same proportion**:  
 
-🔹 **If the teacher responds:**  
-*"Great! Can you explain how you determined each value? Do the ratios remain consistent?"*  
+| Hours | Distance (Miles) |
+|--------|----------------|
+| ½      | 22.5           |
+| 1      | 45             |
+| 2      | 90             |
+| 3      | 135            |
 
-🔹 **If the teacher is stuck, provide hints:**  
-- *Hint 1:* "Start by determining the distance for 1 hour. What happens if you divide both 2 hours and 90 miles by 2?"  
-- *Hint 2:* "Now that you know 1 hour = 45 miles, how can you extend this pattern for ½ hour and 3 hours?"  
+Since each value maintains the proportion **$\frac{\text{miles}}{\text{hours}} = 45$**, this confirms that the ratio is consistent."  
 
-🔹 **If the teacher provides a correct answer:**  
-*"Nice job! Now, let’s take it a step further by graphing this relationship."*  
+🔹 **Transition:**  
+*"Now, let’s plot this on a graph!"*  
 
 ---
 
 #### **4️⃣ Graph Representation**  
-🔹 **Initial Prompt:**  
-*"Finally, let’s represent this problem using a **graph**. Place time (hours) on the x-axis and distance (miles) on the y-axis. What points will you plot?"*  
+🔹 **Math Explanation:**  
+"The equation for this proportional relationship is:  
 
-🔹 **If the teacher responds:**  
-*"Good choice! How does your graph show the constant rate of change?"*  
+**$ y = 45x $**, where **y** is miles and **x** is hours.  
 
-🔹 **If the teacher is stuck, provide hints:**  
-- *Hint 1:* "Start by plotting (0,0) and (2,90). What other points follow the same pattern?"  
-- *Hint 2:* "What does the slope of this line represent in the context of this problem?"  
+That means our key points are:  
+- **(0,0)**
+- **(1,45)**
+- **(2,90)**
+- **(3,135)**  
 
-🔹 **If the teacher provides a correct answer:**  
-*"Great work! Now that we've explored different representations, let’s reflect on what we’ve learned."*  
+The graph is a **straight line passing through the origin**, which confirms a proportional relationship."  
 
 ---