Epidemic Spread Simulation with Exponential Functions
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we effectively use exponential functions and technology to model and predict the spread of diseases in communities, and what are the implications for decision-making during an epidemic?Essential Questions
Supporting questions that break down major concepts.- How do exponential functions help us understand and predict the spread of diseases in communities?
- In what ways can mathematical modeling impact decision-making during an epidemic?
- What are the key features of exponential functions that make them suitable for modeling real-world phenomena like disease spread?
- How can technology be used to accurately represent and analyze exponential growth and decay in a real-world context?
- What challenges might arise in using mathematical models to predict real-world events and how can we address them?
- How does understanding the domain and range of exponential functions influence our interpretation of graphs related to disease spread?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will understand the concept of exponential growth and decay as it applies to real-world phenomena, particularly disease spread.
- Students will be able to graph and interpret exponential functions, identifying key features like y-intercepts and asymptotes.
- Students will effectively use technology to model and analyze exponential functions related to disease transmission.
- Students will develop problem-solving strategies to apply exponential models in decision-making processes during an epidemic.
- Students will be able to communicate their analytical processes and conclusions about epidemic spread using multiple representations.
Provided Standards
Entry Events
Events that will be used to introduce the project to studentsVirtual Field Trip to a Disease Research Lab
Use virtual reality technology to take students on a tour of a disease research lab where scientists use math to combat viruses. This experience gives students a first-hand look at how exponential functions apply in critical research work, enhancing engagement through a blend of technology, math, and real-world application.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Exponential Function Explorer
Students will start by exploring the fundamental concepts of exponential functions by investigating how they work and their applications in modeling real-world phenomena like the spread of diseases.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 concept map displaying understanding of exponential growth and decay functions, highlighting real-world applications.Alignment
How this activity aligns with the learning objectives & standardsAligns with A.9B-C, focusing on interpreting exponential function components in real-world problems.Graphing the Epidemic
Students will graph exponential functions to visually represent and analyze simulated data of disease spread, utilizing graphing technology to observe critical features such as y-intercepts and asymptotes.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 graphs annotated with critical features, demonstrating understanding of the graph's shape relative to real-world epidemic simulations.Alignment
How this activity aligns with the learning objectives & standardsSupports A.9A-D by graphing exponential functions, emphasizing key features and their meanings.Tech-Savvy Simulations
Leveraging technology, students will create simulations of exponential growth and decay by entering modeled data into software, allowing them to predict disease spread outcomes and propose intervention strategies.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activitySimulation reports displaying modeled outcomes and proposed interventions backed by data analysis results.Alignment
How this activity aligns with the learning objectives & standardsAligns with A.9E, focusing on using technology to model exponential functions and predict real-world scenarios.Epidemic Model Communicator
Using multiple forms of representation, students will compile and present their findings on epidemic simulations, effectively communicating their analytical processes and conclusions.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityAn interactive presentation that synthesizes the entire modeling process, analysis, and conclusions about epidemic spread.Alignment
How this activity aligns with the learning objectives & standardsAddresses A.1A-G by communicating mathematical reasoning and findings through multiple representations, both oral and written.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioEpidemic Spread Simulation Rubric
Understanding Exponential Functions
Assessment of students' comprehension of exponential growth and decay, and their ability to interpret exponential functions in real-world contexts.Conceptual Understanding
Evaluates students' grasp of exponential functions, including their components and behavior.
Exemplary
4 PointsThe student demonstrates a sophisticated understanding of exponential functions, accurately explaining components like 'a' and 'b' and their impact on the function's behavior. The student consistently links exponential models to real-world scenarios with clarity and insight.
Proficient
3 PointsThe student demonstrates a thorough understanding of exponential functions, explaining components like 'a' and 'b' and their impact on the function's behavior. The student relates exponential models to real-world scenarios accurately.
Developing
2 PointsThe student shows an emerging understanding of exponential functions, with basic explanations of components like 'a' and 'b'. The connection to real-world scenarios is inconsistent or lacks depth.
Beginning
1 PointsThe student shows initial understanding of exponential functions, struggling to explain components like 'a' and 'b'. The connection to real-world scenarios is weak or absent.
Application of Mathematical Concepts
Evaluates how well students apply exponential functions to model real-world problems, such as disease spread.
Exemplary
4 PointsThe student applies exponential functions innovatively to model complex real-world problems, demonstrating exceptional critical thinking and problem-solving skills.
Proficient
3 PointsThe student applies exponential functions appropriately to model real-world problems, showing effective critical thinking and problem-solving skills.
Developing
2 PointsThe student applies exponential functions inconsistently to model real-world problems, with basic critical thinking and problem-solving skills evident.
Beginning
1 PointsThe student struggles to apply exponential functions to model real-world problems, showing minimal critical thinking and problem-solving skills.
Use of Technology
Evaluation of students' proficiency in using technology to simulate and graph exponential functions, and analyze data related to disease spread.Graphing and Simulation Skills
Assesses the ability to use technological tools for graphing and running simulations.
Exemplary
4 PointsThe student uses technology with exceptional proficiency to create accurate graphs and simulations, demonstrating advanced analytical skills.
Proficient
3 PointsThe student uses technology effectively to create accurate graphs and simulations, demonstrating solid analytical skills.
Developing
2 PointsThe student uses technology inconsistently to create graphs and simulations, demonstrating basic analytical skills.
Beginning
1 PointsThe student struggles to use technology to create graphs and simulations, showing minimal analytical skills.
Data Analysis and Prediction
Evaluates the success in analyzing simulated data and making informed predictions.
Exemplary
4 PointsThe student analyzes simulation data with exceptional depth, making highly accurate and insightful predictions.
Proficient
3 PointsThe student analyzes simulation data effectively, making accurate predictions.
Developing
2 PointsThe student analyzes simulation data with limited depth, making basic or inconsistent predictions.
Beginning
1 PointsThe student struggles to analyze simulation data, making inaccurate or superficial predictions.
Communication of Findings
Assessment of students' ability to effectively communicate their modeling process, analysis, and conclusions through various representations.Presentation Skills
Evaluates the clarity and effectiveness of the students' presentations and their ability to communicate findings.
Exemplary
4 PointsThe student's presentation is exceptionally clear and engaging, with advanced integration of data and visual aids. The student communicates findings with depth and insight, showing leadership in peer discussions.
Proficient
3 PointsThe student's presentation is clear and well-structured, effectively integrating data and visual aids. The student communicates findings with clarity and participates effectively in peer discussions.
Developing
2 PointsThe student's presentation is structured but lacks depth or engagement, integrating basic data and visual aids. The student communicates findings with limited clarity.
Beginning
1 PointsThe student's presentation is unclear and poorly structured, with minimal use of data and visual aids. The student struggles to communicate findings effectively.