| MAIN_PROMPT = """ | |
| Module 7: Understanding Non-Proportional Relationships | |
| Task Introduction | |
| "Welcome to this module on understanding non-proportional relationships! In this module, you’ll explore why certain relationships are not proportional, identify key characteristics, and connect these ideas to algebraic thinking. Let’s dive into some problems to analyze!" | |
| Problems: | |
| Problem 1: Ali drives at an average rate of 25 miles per hour for 3 hours to get to his house from work. How long will it take him if he is able to average 50 miles per hour? | |
| Problem 2: Tugce’s cell phone service charges her $22.50 per month for phone service, plus $0.35 for each text she sends or receives. Last month, she sent or received 30 texts, and her bill was $33. How much will she pay if she sends or receives 60 texts this month? | |
| Problem 3: Ali and Deniz both go for a run. When they run, both run at the same rate. Today, they started at different times. Ali had run 3 miles when Deniz had run 2 miles. How many miles had Deniz run when Ali had run 6 miles? | |
| Step-by-Step Prompts for Analysis | |
| 1. Problem 1: Inverse Proportionality | |
| Initial Prompt: | |
| "Let’s start with Problem 1. Is the relationship between speed and time proportional? Why or why not?" | |
| Hints for Teachers: | |
| - "Think about the relationship between speed and time. If Ali increases his speed, what happens to the time taken?" | |
| - "Consider whether the ratio of miles to hours remains constant." | |
| 2. Problem 2: Non-Proportional Linear Relationship | |
| Initial Prompt: | |
| "Is the relationship between the number of texts and the total bill proportional? Why or why not?" | |
| Hints for Teachers: | |
| - "Think about the initial cost of $22.50. Does this fixed amount affect whether the relationship is proportional?" | |
| - "Consider if doubling the number of texts would double the total bill." | |
| 3. Problem 3: Additive Relationship | |
| Initial Prompt: | |
| "Now, let’s look at Problem 3. Is the relationship between the miles Ali and Deniz run proportional? Why or why not?" | |
| Hints for Teachers: | |
| - "Think about whether the difference in miles remains constant as they run." | |
| - "If Ali always has a one-mile lead, does that suggest a proportional relationship or a consistent additive difference?" | |
| Reflection and Discussion: | |
| - "What are the key characteristics that distinguish proportional relationships from non-proportional ones?" | |
| - "How can graphing these relationships help students understand proportionality?" | |
| - "Why is it important to expose students to both proportional and non-proportional relationships?" | |
| Problem Posing Activity: | |
| - "Now it’s your turn to create three non-proportional problems similar to the ones we explored. Write each problem and explain why the relationship is not proportional." | |
| Summary: | |
| - "We explored non-proportional relationships, distinguishing them from proportional ones by analyzing characteristics like inverse relationships, fixed costs, and additive differences." | |
| - "We applied mathematical generalization and extension, thinking creatively about different relationships." | |
| - "We discussed how to guide students in understanding proportionality by exploring non-examples." | |
| """ | |