Warm Up: Seedling Scramble

Objective: Activate prior knowledge of proportional relationships and prepare for linear equations.

Instructions: Read the scenarios below and determine if they represent a proportional relationship. Explain your reasoning in 1-2 sentences.

1. Scenario A: You are planting tomato seedlings. Each seedling you plant costs $3.

   • Is this a proportional relationship? Why or why not?
     
     
     
     
     
     
     
     
     
     
     

2. Scenario B: A sunflower grows 2 inches every week.

   • Is this a proportional relationship? Why or why not?
     
     
     
     
     
     
     
     
     
     
     

3. Scenario C: You start with 5 seeds, and then you find 3 more in your pocket.

   • Is this a proportional relationship? Why or why not?
     
     
     
     
     
     
     
     
     
     
     

Think about it: What makes a relationship

Discussion: Growing Together

Objective: Facilitate a discussion to deepen understanding of proportional relationships and linear equations in real-world contexts.

Instructions: Let's talk about the connections we're making! Be ready to share your thoughts and listen respectfully to your classmates.

1. Connecting the Dots: How does thinking about the cost of seeds or the growth of a plant help you understand what a "proportional relationship" means?
   
   
   
   
   
   

2. Lines and Life: We saw how a straight line can represent consistent growth or cost. Can you think of another example in everyday life where a straight line on a graph could show a relationship that changes consistently? (e.g., speed of a car, amount of water in a tank)
   
   
   
   
   
   

3. Predicting the Future (of Your Garden): If you know the linear equation for how much a specific vegetable yields per plant, how could that equation help you plan your garden for next year? What information would you need?
   
   
   
   
   
   

4. Challenges in the Garden: What might happen in a real garden that would make the relationship not perfectly linear? (e.g., unexpected weather, pests). How does this show that math models are often simplifications of the real world?
   
   
   
   
   
   

Activity: Plotting Our Harvest

Objective: Create a real-world linear equation from a gardening scenario, represent it graphically, and explain the proportional relationship.

Instructions: It's time to design your own mini-garden math problem! Follow the steps below.

Part 1: Your Garden Scenario (5 minutes)

1. Choose Your Focus: Will your scenario be about seed costs or vegetable yields? Circle one:

   • Seed Costs
   • Vegetable Yields

2. Describe Your Scenario: Create a short, creative description of your gardening situation. What kind of seeds are you buying? What vegetable are you growing? What is the constant rate in your scenario?
   (Example: "I want to grow carrots. Each packet of carrot seeds costs $1.50.")

   
   
   
   
   
   
   
   
   
   
   
   
   

Part 2: Build Your Equation (10 minutes)

3. Define Your Variables:

   • What does your independent variable (the one you control) represent? (e.g., number of seed packets, number of plants)
     • Variable Name: __________
   • What does your dependent variable (the one that changes because of the first variable) represent? (e.g., total cost, total yield)
     • Variable Name: __________

4. Identify the Constant Rate: What is the number that stays the same in your relationship?

   • Constant Rate: __________

5. Write Your Linear Equation: Use your variables and constant rate to write a linear equation in the form y = mx (or similar).

   • Equation:
     
     
     

Part 3: Graph Your Garden (10 minutes)

6. Create a Table of Values: Use your equation to find at least 3 points for your graph.

   Independent Variable	Dependent Variable

7. Plot Your Points: On a piece of graph paper (or in your notebook), draw an x-axis and a y-axis. Label them with your variable names. Plot your points and draw a line through them.

   • (Teacher will provide graph paper if needed.)

Part 4: Reflect (5 minutes)

8. Explain Proportionality: How does your graph visually show that your scenario is a proportional relationship? (Hint: Think about where the line starts!)
   
   
   
   
   
   
   
   
   
   
   
   

Cool Down: Reflect & Grow

Objective: Students will reflect on their learning and connect the lesson to their understanding of real-world math.

Instructions: Take a few minutes to think about what you learned today and how it connects to the world around you. Please answer in 1-2 sentences.

1. One Big Idea: What is one new thing you learned or one idea that became clearer to you today about linear equations or proportional relationships?
   
   
   

2. Real-World Connection: How might understanding linear equations be useful to someone in a real-life situation, not just in gardening? (Think outside the classroom!)
   
   
   

3. Feeling Green? On a scale of 1 to 5, how confident do you feel about explaining what a linear equation is and how it relates to proportional relationships? (1 = Not confident, 5 = Very confident)
   
   Circle one: 1   2   3   4   5