Introduce the task by reading the situation with the students. Highlighting the start time and the amount of time it takes for the disease to spread. State to students that goal of the activity is to see which types of viruses are more deadly and whether social distancing measures make a difference. To accomplish this, students will be placed in groups to model the spread of a virus using beans. All groups will receive a cup of pinto beans that represent a healthy student population. Each group will also receive a different kind of bean (Kidney, Black, Lima) that will represent an infected individual. [Note: Teachers are not limited to the suggested beans. If teachers implementing the lesson wish to use different color and size beans, they are encouraged to do so.]
To simulate the spread of the virus, all of the pinto beans will be evenly spread out in a box lid or serving tray so that no beans are on top of each other. [Note: Any flat surface that can hold the beans without the beans spilling over will suffice. Uniform sizes are encouraged so that comparisons across groups are more effective.] Next, students will then drop one infected individual into the healthy population, flattening all of the beans so that they are not on top of each other. Every pinto bean that is touching the virus bean has now become infected. Students will then remove the number of infected pinto beans from the healthy population and replace them with the same number of virus beans. Repeating the process and completing the table in the task sheet.
As students complete their data tables and begin plotting their values on the graphs provided, it is important that students understand the type of scale they are using along the vertical axis. Without an appropriate scale, students will have difficulty plotting all of their points on the graph.
Once students complete their graphs, they are asked to make sense of the key features of their graph and data table. The first part requires students to make sense of the rate of change as they are conducting their simulation and use that information to make a prediction about how many shakes (how much time) is needed before all of the healthy individuals are infected. Students are then asked to explicitly state what they believe the rate of change is based on their data table and graphs. This will be compared to their technology generated models.
Students will repeat the simulation two times. The first time is for students to see how the virus is spread without social distancing, and the second time with social distancing, modeled by using a larger serving tray or box lid.
Once students have answered the questions asking them to make sense of their table and graph features, they will rely on available technology to graph their points and create a model that best fits their data.
Teachers should model the procedure for creating a model with the available technology if students are unfamiliar.
If using the TI-84, TI-Nspire, Geogebra (https://www.geogebra.org/classic#spreadsheet), or Excel, students will recreate their table of values in a spreadsheet. It is important that the headings for each column are included so that the vertical and horizontal axis can be well-defined. Once the values are in the spreadsheet, students will need to generate a graph of their data values where the time is represented on the horizontal axis and the number of infected people is on the vertical axis. Students will then use their technology to create a regression model.
[Note: Students should be familiar with the idea of lines of best fit from their linear function knowledge. The regression model illustrates the same concept of finding the curve of best fit.] If using Desmos(https://www.desmos.com/calculator), students will need to insert a table and enter their data values. This will automatically plot their points on the graph. To generate an algebraic regression model, students will need to type into the row beneath their table. This will generate values below this entry for a and b that represent the initial value and rate of change for the model.
Once the algebraic model is generated for the curve of best fit (an exponential model) students will record their results and should be comparing their previous predictions to the technology generated rate of change. Discussion of why linear and quadratic models are not appropriate should be addressed. Discussion of whether the graph will extend infinitely should be addressed also.[Note: If appropriate, the correlation coefficient and the coefficient of determination should also be included during exploration for students to understand why exponential models are the best fit model.]