# Module starts with the task TASK_PROMPT = """ Welcome to Module 2: Solving a Ratio Problem Using Multiple Representations! ### Task: Jessica drives 90 miles in 2 hours. If she drives at the same rate, how far does she travel in: - 1 hour? - ½ hour? - 3 hours? To solve this, try using different representations: - Bar models - Double number lines - Ratio tables - Graphs Remember: Don't just find the answer—explain why! I'll guide you step by step—let’s start with the bar model. """ # Step 1: Bar Model Representation BAR_MODEL_PROMPT = """ Step 1: Bar Model Representation Imagine a bar representing 90 miles—the distance Jessica travels in 2 hours. How might you divide this bar to explore the distances for 1 hour, ½ hour, and 3 hours? Hints if needed: 1. Think of the entire bar as representing 90 miles in 2 hours. How would you divide it into two equal parts to find 1 hour? 2. Now, extend or divide it further—what happens for ½ hour and 3 hours? If correct: Great! Can you explain why this model helps students visualize proportional relationships? If incorrect: Try dividing the bar into two equal sections. What does each section represent? """ # Step 2: Double Number Line DOUBLE_NUMBER_LINE_PROMPT = """ Step 2: Double Number Line Representation Now, let’s use a double number line. Create two parallel lines: one for time (hours) and one for distance (miles). Start by marking: - 0 and 2 hours on the top line - 0 and 90 miles on the bottom line What comes next? Hints if needed: 1. Try labeling the time line (0, 1, 2, 3). How does that help with placing distances below? 2. Since 2 hours = 90 miles, what does that tell you about 1 hour and ½ hour? If correct: Nice work! How does this help students understand proportional relationships? If incorrect: Check your spacing—does your number line keep a constant rate? """ # Step 3: Ratio Table RATIO_TABLE_PROMPT = """ Step 3: Ratio Table Representation Next, let’s create a ratio table. Make a table with: - Column 1: Time (hours) - Column 2: Distance (miles) You already know 2 hours = 90 miles. How would you complete the table for ½ hour, 1 hour, and 3 hours? Hints if needed: 1. Since 2 hours = 90 miles, how can you divide this to find 1 hour? 2. Once you know 1 hour = 45 miles, can you calculate for ½ hour and 3 hours? If correct: Well done! How might this help students compare proportional relationships? If incorrect: Something’s a little off. Try using unit rate: 90 ÷ 2 = ? """ # Step 4: Graph Representation GRAPH_PROMPT = """ Step 4: Graph Representation Now, let’s graph this problem! Plot: - Time (hours) on the x-axis - Distance (miles) on the y-axis You already know two key points: - (0,0) and (2,90) What other points will you add? Hints if needed: 1. Start by marking (0,0) and (2,90). 2. How can you use these to find (1,45), (½,22.5), and (3,135)? If correct: Fantastic! How does this graph reinforce the idea of constant rate and proportionality? If incorrect: Does your line pass through (0,0)? Why is that important? """ # Reflection Prompt REFLECTION_PROMPT = """ Reflection Time! Now that you've explored multiple representations, think about these questions: - How does each method highlight proportional reasoning differently? - Which representation do you prefer, and why? - Can you think of a situation where one of these representations wouldn’t be the best choice? Take a moment to reflect! """ # Summary Prompt SUMMARY_PROMPT = """ Summary of Module 2 In this module, you: - Solved a proportional reasoning problem using multiple representations - Explored how different models highlight proportional relationships - Reflected on teaching strategies aligned with Common Core practices Final Task: Try creating a similar proportional reasoning problem! Example: A runner covers a certain distance in a given time. Make sure your problem can be solved using: - Bar models - Double number lines - Ratio tables - Graphs The AI will evaluate your problem and provide feedback! """ # Final Reflection Prompt FINAL_REFLECTION_PROMPT = """ Final Reflection - How does designing and solving problems using multiple representations enhance students’ mathematical creativity? - How would you guide students to explain their reasoning, even if they get the correct answer? Share your thoughts! """