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This is the third of four parts, designed to be used in a sequence of lessons - here is a lesson by lesson breakdown.
Everybody is Different follows on from Build Your First Model and Lucky Dip, and introduces the need for a more realistic model, in which we don't all behave in identical ways. Until now, we've assumed that every infected person exposes the same number of people to the infection. In reality there is variability in the number of people that infected people go on to infect. Students are encouraged to explore the similarities and differences that occur when running several simulations of the updated disease model, and to consider how variability affects the epidemic.
This lesson, and the next, meet the curriculum aims of developing students' Fluency (moving freely between different representations), Reasoning (making connections between number relationships and graphical representations), and Problem Solving skills (begin to model situations mathematically).
The teaching materials include video clips featuring Professor Julia Gog introducing the need for a more realistic model, and then explaining the impact of R being greater than or less than 1.
Everybody is Different is intended as an activity for students who have already explored Build Your First Model and Lucky Dip.
Introduce the Everybody is Different interactivity
The meaning of the different colours is explained in the problem page.
Model running the activity by clicking on the 'Infect a random person' tab. The random person will be highlighted in red - encourage the class to predict how the disease might spread from that person to others and justify their responses. Allow time for students to explore the interactivity by infecting random people and varying the value of R.
The Save / Load feature generates a code, which allows you to select and share a layout, which can be used as a common basis for exploration and discussion in the classroom. You can challenge the class to select individuals on the grid who they think would be likely to kick-start an epidemic, and explain their reasoning behind their choices. Allow time for students to test their theories. Then ask students to consider which individuals might be less likely to spread the disease widely, and test out those ideas too.
You can ask how important R is in determining what will happen, and how much it matters who the initial infected person is. What difference does it make if you start by choosing several infected individuals?
Finish by showing this video clip in which Julia explains the impact of R being greater than or less than 1.
Bring the session to a close by noting that the individuals in the models so far, have been static. Why might it be useful to include movement in a model?
Exploring models which incorporate movement is the basis of the final session, Get Moving!.
What do you think will happen to the spread of an infectious disease if different people infect different numbers of other people?
Do different layouts affect the spread of a disease?
What else could we consider exploring with our model?
Students could take screenshots to help them compare the outcomes of the spread of the disease each time they run the model.
Once students have finished these Part 3 activities they may like to explore Part 4: Get Moving! which looks in more detail at the importance of how people are connected and the effect of travel on epidemics. Alternatively, if you are finishing here, please continue to Wrap up and Meet the Researchers for a short concluding video and also clips from individual researchers to explore.
Students may be interested in Disease modelling for beginners, a collection of articles which explain how mathematics helps us understand how infectious diseases spread.
These Contagious Maths resources were developed and written by Julia Gog and the MMP team, including both NRICH and Plus, and funded by the Royal Society’s Rosalind Franklin Award 2020. We have tailored these resources for ages 11-14 on NRICH, and for older students and wider audiences on Plus.