## Task: Representing Jessica’s Driving Distance 🚗
Jessica is driving at a constant speed. She travels **90 miles in 2 hours**.

### Your Goal:
Represent the relationship between **time and distance** using different mathematical models:
✅ Bar Model  
✅ Double Number Line  
✅ Ratio Table  
✅ Graph  

Let’s go through each representation step by step!

---

### Step 1: Identifying Current Representation  
Which representations have you already used to show the relationship between time and distance?  
- Bar Model  
- Double Number Line  
- Ratio Table  
- Graph  

If you haven’t used all of them, let’s go through each one step by step.

---

### Step 2: Bar Model Representation 📊  
Have you created a **bar model** to represent Jessica’s travel?  

**If not, follow these steps:**  
1️⃣ Draw a **long bar** to represent **2 hours of driving**, labeling it **90 miles**.  
2️⃣ Divide the bar into **two equal parts** to show **1 hour = 45 miles**.  
3️⃣ Extend the bar to **3 hours** by adding another **45-mile segment**.  
4️⃣ Divide **one 1-hour segment in half** to show **½ hour = 22.5 miles**.  

✅ Does your bar model correctly show **½, 1, 2, and 3 hours**?

---

### Step 3: Double Number Line Representation 📏  
Have you created a **double number line** for time and distance?  

**If not, follow these steps:**  
1️⃣ Draw **two parallel number lines**:  
   - The **top line** represents **time (hours)**.  
   - The **bottom line** represents **distance (miles)**.  
2️⃣ Mark these key points:  
   - **0 hours → 0 miles**  
   - **½ hour → 22.5 miles**  
   - **1 hour → 45 miles**  
   - **2 hours → 90 miles**  
   - **3 hours → 135 miles**  
3️⃣ Ensure the distances are evenly spaced.  

✅ Does your number line show a **proportional relationship**?

---

### Step 4: Ratio Table Representation 📋  
Have you created a **ratio table**?  

**If not, follow these steps:**  
1️⃣ Fill in the table below:  

| Time (hours) | Distance (miles) |  
|-------------|-----------------|  
| 0.5         | 22.5            |  
| 1           | 45              |  
| 2           | 90              |  
| 3           | 135             |  

2️⃣ Look for patterns.  
3️⃣ What would be the distance for **4 hours**?  

✅ Does your table clearly show a **proportional pattern**?

---

### Step 5: Graph Representation 📈  
Have you created a **graph** to represent this relationship?  

**If not, follow these steps:**  
1️⃣ Draw a **coordinate plane**:  
   - **x-axis → time (hours)**  
   - **y-axis → distance (miles)**  
2️⃣ Plot these points:  
   - (0, 0)  
   - (0.5, 22.5)  
   - (1, 45)  
   - (2, 90)  
   - (3, 135)  
3️⃣ Draw a straight line through these points.  
4️⃣ What does the **slope of the line** tell you about Jessica’s driving rate?  

✅ Does your graph correctly show a **linear relationship**?

---

### Step 6: Final Reflection 💭  
Great job! Now, take a moment to reflect:  
1️⃣ Which representation helped you understand the relationship best? Why?  
2️⃣ How do these representations show the **same proportional relationship** in different ways?  
3️⃣ Can you apply this method to another real-world proportional relationship?  

---

### New Challenge 🌟  
Imagine Jessica **increases her speed** by **10 miles per hour**.  
- How would this affect the bar model, number line, ratio table, and graph?  
- Try adjusting your models to reflect this change!  

---

### Summary of Objectives 🎯  
- You explored **four ways** to represent proportional relationships: **Bar Model, Double Number Line, Ratio Table, and Graph**.  
- You understood how **time and distance** relate at a **constant rate**.  
- You analyzed how different models show the **same mathematical pattern**.  

---

### Common Core Math Standards 🏆  
- **6.RP.A.1** - Understand the concept of a ratio.  
- **6.RP.A.3a** - Use ratio reasoning to solve real-world problems.  
- **7.RP.A.2** - Recognize proportional relationships.  

✅ **Congratulations! You’ve completed this module.** 🚀