How Can I Design A Desmos-based Activity For 8th-grade Students To Explore The Concept Of Exponential Growth, Using A Real-world Scenario Such As Population Growth Or Compound Interest, While Also Incorporating Collaborative Features To Facilitate Peer-to-peer Feedback And Discourse In A One-to-one Chromebook Classroom?

Desmos-Based Exponential Growth Activity for 8th Graders

Objective: Students will explore exponential growth using Desmos, applying it to real-world scenarios and engaging in collaborative learning through peer feedback and discourse.

Materials:

• Chromebooks with Desmos access
• Projector and screen
• Whiteboard and markers
• Optional: Printed graph paper, calculators

Time Needed: Approximately 75 minutes

1. Introduction to Exponential Growth (10 minutes)

a. Whole-Class Discussion:

• Initiate a discussion on exponential growth, using examples like bacteria growth or population increase.
• Define exponential growth and its formula: ${ y = a \cdot b^x }$, where ${ a }$ is the initial amount and ${ b }$ is the growth factor.

b. Desmos Demonstration:

• Introduce Desmos, demonstrating how to graph an exponential function (e.g., ${ y = 2 \cdot 3^x }$).
• Explain the roles of ${ a }$ and ${ b }$, emphasizing growth vs. decay.

2. Exploration with Desmos (20 minutes)

a. Interactive Activity:

• Create a Desmos activity where students adjust ${ a }$ and ${ b }$ to observe graph changes.
• Include challenges, such as predicting graph changes when altering parameters.

b. Guided Challenges:

• Pose questions like, "How does doubling ${ a }$ affect the graph?" to encourage exploration.

3. Real-World Application (20 minutes)

a. Population Growth Scenario:

• Present a problem, e.g., modeling population growth with an initial population of 1000 and a 2% annual growth rate.
• Students create equations and graphs in Desmos, answering questions like future population or time to reach a specific number.

b. Different Scenarios:

• Assign varied initial populations or growth rates to groups, encouraging comparative analysis.

4. Collaborative Learning and Feedback (15 minutes)

a. Group Work:

• Students work in pairs or small groups, sharing their Desmos graphs and findings.
• Encourage discussion on model accuracy and real-world applications.

b. Peer Feedback:

• Use a feedback form for students to evaluate each other's models, focusing on fit and suggestions for improvement.

5. Reflection and Sharing (10 minutes)

a. Group Presentations:

• Groups present their findings, discussing challenges and insights.

b. Whole-Class Discussion:

• Facilitate a discussion on the implications of exponential growth, addressing questions and misconceptions.

c. Individual Reflection:

• Students reflect on their learning, writing about applications and lingering questions.

6. Assessment and Differentiation

a. Formative Assessment:

• Observe participation and understanding during activities.
• Review reflections and feedback for comprehension.

b. Differentiation:

• Provide structured prompts for struggling students and more complex scenarios for advanced learners.

Conclusion: This activity integrates interactive learning, collaboration, and real-world application, fostering a deep understanding of exponential growth. The use of Desmos enhances engagement, while peer feedback and reflection reinforce learning.