Zombie Apocalypse: Modeling Exponential Outbreaks in Pre-Calculus
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.In a hypothetical zombie apocalypse, how can we use exponential and logarithmic functions to model, analyze, and predict the spread of infection, and what factors must be considered to make informed decisions and potentially develop effective countermeasures?Essential Questions
Supporting questions that break down major concepts.- How can exponential functions model the rapid spread of a zombie virus?
- How do logarithmic functions help us analyze and predict the rate of zombie infection?
- What factors influence the rate of zombie outbreak?
- How can we use mathematical models to make informed decisions during a zombie apocalypse?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Understand and apply exponential functions to model the spread of a zombie outbreak.
- Understand and apply logarithmic functions to model the spread of a zombie outbreak.
- Analyze and interpret the parameters within exponential and logarithmic models in the context of the outbreak.
- Make predictions about the spread of the zombie outbreak based on the model.
- Evaluate the limitations and assumptions of the model.
- Communicate the findings and predictions of the model effectively.
Entry Events
Events that will be used to introduce the project to studentsZombie Outbreak News
**Simulated News Broadcast:** A breaking news report interrupts class, detailing a rapidly spreading 'unknown virus' outbreak with initial reports of erratic behavior and aggression. Students must analyze the (initially limited) data presented in the broadcast to predict the virus's spread and potential impact, using early exponential models.Zombie Data Breach
**'Classified' Zombie Research Data:** Students receive a 'leaked' file containing data points on zombie population growth over time, but the data is incomplete and partially corrupted. They must use their knowledge of exponential and logarithmic functions to clean, analyze, and extrapolate the data to predict future zombie population sizes and resource depletion rates.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Exponential Outbreak: Initial Modeling
Students will create a basic exponential model to represent the initial spread of the zombie virus based on the data from the 'Zombie Outbreak News' entry event.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA graph and equation representing the initial exponential growth of the zombie population, with clearly labeled axes and a written explanation of the model's assumptions.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Understand and apply exponential functions to model the spread of a zombie outbreak.Logarithmic Analysis: Predicting the Apocalypse
Using the 'Zombie Data Breach' information, students will convert exponential models into logarithmic models to solve for time, given a specific zombie population threshold.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA set of logarithmic equations derived from the exponential models, along with solutions for the time it takes to reach specific zombie population milestones (e.g., 1000 zombies, 10,000 zombies).Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Understand and apply logarithmic functions to model the spread of a zombie outbreak. Learning Goal: Analyze and interpret the parameters within exponential and logarithmic models in the context of the outbreak.Refining the Model: Factors and Limitations
Students will refine their models by incorporating factors that influence the rate of zombie outbreak, such as population density, resource availability, and potential countermeasures. Students will create a report detailing how the refined model changes predictions.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA written report that includes the initial and refined models, a comparative analysis of the predictions, and a discussion of the limitations of both models. The report should also suggest further refinements for increased accuracy.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Make predictions about the spread of the zombie outbreak based on the model. Learning Goal: Evaluate the limitations and assumptions of the model.Presenting the Pandemic: Communicating the Model
Students will create a presentation that communicates their findings, predictions, and the limitations of their zombie outbreak model to an audience of stakeholders (e.g., classmates, teachers, community members).Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA visually engaging presentation (e.g., PowerPoint, Prezi) that includes: an overview of the initial exponential model, the logarithmic analysis, the factors influencing the spread, a discussion of the model's limitations, and predictions about the future of the outbreak.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Communicate the findings and predictions of the model effectively.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioZombie Apocalypse Model Rubric
Exponential Modeling
Focuses on the student's ability to create an accurate exponential model and understand its limitations.Exponential Equation Accuracy
Accuracy of the exponential equation in modeling the initial spread of the zombie outbreak, based on data from the 'Zombie Outbreak News'.
Exemplary
4 PointsExponential equation accurately reflects the initial conditions and growth rate from the news report. Graph is clearly labeled and precisely represents the equation. All assumptions are explicitly stated and justified.
Proficient
3 PointsExponential equation mostly reflects the initial conditions and growth rate from the news report. Graph is labeled and generally represents the equation. Most assumptions are stated.
Developing
2 PointsExponential equation partially reflects the initial conditions and growth rate from the news report. Graph is somewhat labeled and roughly represents the equation. Some assumptions are stated.
Beginning
1 PointsExponential equation does not accurately reflect the initial conditions and growth rate from the news report. Graph is poorly labeled and does not represent the equation. Assumptions are missing or unclear.
Explanation of Assumptions and Limitations
Clarity and completeness of the explanation of assumptions made in the model, including limitations.
Exemplary
4 PointsExplanation is comprehensive, insightful, and addresses the limitations of the assumptions in detail. Demonstrates sophisticated understanding of the model's constraints and potential biases.
Proficient
3 PointsExplanation is clear, complete, and addresses the limitations of the assumptions. Demonstrates thorough understanding of the model's constraints.
Developing
2 PointsExplanation is somewhat clear and complete, but only partially addresses the limitations of the assumptions. Demonstrates basic understanding of the model's constraints.
Beginning
1 PointsExplanation is unclear, incomplete, and does not address the limitations of the assumptions. Demonstrates minimal understanding of the model's constraints.
Logarithmic Modeling and Prediction
Assesses student's ability to apply logarithmic functions to the zombie outbreak model to solve for time, given zombie population milestones.Logarithmic Equation Accuracy
Correctness of the logarithmic equations derived from the exponential models.
Exemplary
4 PointsLogarithmic equations are derived flawlessly from the exponential models. Solutions for time to reach zombie population milestones are calculated precisely. Demonstrates sophisticated understanding of logarithmic functions.
Proficient
3 PointsLogarithmic equations are correctly derived from the exponential models. Solutions for time to reach zombie population milestones are calculated accurately. Demonstrates thorough understanding of logarithmic functions.
Developing
2 PointsLogarithmic equations are mostly correctly derived from the exponential models. Solutions for time to reach zombie population milestones are calculated with some errors. Demonstrates basic understanding of logarithmic functions.
Beginning
1 PointsLogarithmic equations are incorrectly derived from the exponential models. Solutions for time to reach zombie population milestones are calculated with significant errors. Demonstrates minimal understanding of logarithmic functions.
Logarithmic Analysis Quality
Quality of the analysis explaining how the logarithmic function helps in predicting the long-term spread of the outbreak and identifying critical intervention points.
Exemplary
4 PointsAnalysis is insightful, comprehensive, and demonstrates a deep understanding of the application of logarithmic functions in predicting the spread of the outbreak. Intervention points are identified and thoroughly justified.
Proficient
3 PointsAnalysis is clear, complete, and demonstrates a good understanding of the application of logarithmic functions in predicting the spread of the outbreak. Intervention points are identified and justified.
Developing
2 PointsAnalysis is somewhat clear and complete, but only partially demonstrates the application of logarithmic functions in predicting the spread of the outbreak. Intervention points are identified but lack justification.
Beginning
1 PointsAnalysis is unclear, incomplete, and does not demonstrate the application of logarithmic functions in predicting the spread of the outbreak. Intervention points are not identified or are poorly justified.
Model Refinement and Limitations
Evaluates how students refine their models by including real-world factors and recognizing limitations.Integration of Influencing Factors
Integration of factors influencing the spread (e.g., population density, access to resources, quarantine measures) into the models.
Exemplary
4 PointsFactors are seamlessly integrated into the models, and their impact is thoroughly analyzed. Model adjustments are sophisticated and demonstrate a deep understanding of their effects.
Proficient
3 PointsFactors are successfully integrated into the models, and their impact is clearly analyzed. Model adjustments are effective and demonstrate a good understanding of their effects.
Developing
2 PointsFactors are partially integrated into the models, and their impact is somewhat analyzed. Model adjustments are basic and demonstrate a limited understanding of their effects.
Beginning
1 PointsFactors are poorly integrated into the models, and their impact is not adequately analyzed. Model adjustments are ineffective and demonstrate a minimal understanding of their effects.
Discussion of Limitations and Refinements
Depth of the discussion regarding the limitations of the refined model and suggestions for further refinements.
Exemplary
4 PointsDiscussion of limitations is insightful and comprehensive, addressing potential biases and uncertainties. Suggestions for further refinements are innovative and demonstrate advanced critical thinking.
Proficient
3 PointsDiscussion of limitations is clear and complete, addressing potential biases and uncertainties. Suggestions for further refinements are effective and demonstrate thorough critical thinking.
Developing
2 PointsDiscussion of limitations is somewhat clear and complete, partially addressing potential biases and uncertainties. Suggestions for further refinements are basic and demonstrate limited critical thinking.
Beginning
1 PointsDiscussion of limitations is unclear, incomplete, and does not adequately address potential biases and uncertainties. Suggestions for further refinements are ineffective and demonstrate minimal critical thinking.
Communication and Presentation
Focuses on the student's ability to effectively communicate their model and its implications to an audience.Visual Aid Clarity and Effectiveness
Clarity and effectiveness of visual aids (graphs, charts, maps) in illustrating the spread of the zombie outbreak.
Exemplary
4 PointsVisual aids are exceptionally clear, engaging, and effectively illustrate the spread of the zombie outbreak. They enhance the audience's understanding and provide valuable insights. Design shows leadership and innovation.
Proficient
3 PointsVisual aids are clear, engaging, and effectively illustrate the spread of the zombie outbreak. They enhance the audience's understanding.
Developing
2 PointsVisual aids are somewhat clear and partially illustrate the spread of the zombie outbreak. They provide some enhancement to the audience's understanding.
Beginning
1 PointsVisual aids are unclear and do not effectively illustrate the spread of the zombie outbreak. They provide minimal enhancement to the audience's understanding.
Communication Effectiveness
Effectiveness of communication of the model's assumptions, limitations, and predictions about the future of the outbreak.
Exemplary
4 PointsCommunication is exceptionally clear, persuasive, and engaging. Assumptions, limitations, and predictions are presented with clarity and insight. Audience is actively engaged, leading to productive discussion. Countermeasures are thoroughly discussed.
Proficient
3 PointsCommunication is clear, persuasive, and engaging. Assumptions, limitations, and predictions are presented with clarity. Audience is engaged in discussion.
Developing
2 PointsCommunication is somewhat clear and partially engaging. Assumptions, limitations, and predictions are presented with some clarity. Audience is passively involved in discussion.
Beginning
1 PointsCommunication is unclear and unengaging. Assumptions, limitations, and predictions are presented without clarity. Audience is not engaged in discussion.