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Opening video clip - suggest Julia reflects on learning from Sessions 1 and 2 where learners saw how a geometric sequence could be used to model an epidemic, but we also the need to move from the abstract world of maths to real-life because there is not an infinite population. Also, different factors might affect the spread. We have access to a wealth of data so we need to choose which factors to focus on so the model is helpful.
Perhaps a nod here to history - what we learned from previous outbreaks in history eg Spanish Flu and the Great Plague (which we remember with the rhyme Ring-a-Ring-a-Roses)
Moving on...in real-life you visit multiple locations every day- the school bus, your school assembly hall, your classroom etc etc, We can use mathematical modelling to investigate the spread of a virus in those locations
Think about a school bus. What might be the key factors to consider for your model. For example, if one passenger picks up an infection, does it mean that everyone else will get it too? Think about own experiences when a family member picks up an infection, does everyone else always catch it too? Do we 'all fall down?'
Clip 3.3 clip 3.3 3.4 3.5 4.1Teacher led discussion about possible factors such as layout of the bus, how many people have the virus and where they sit, how liable passengers and drivers are to get infected.
*Possible NRICH video modelling using the interactivity in the bus setting - focus on pre dicting infecting a 'white' dot passenger or driver and checking effect on number of infected passengers- do this multiple times to confirm answer*
Class use interactivity to predict average number of passengers who might get infected if a yellow dot passenger is infected, then investigate it using the interactivity. Repeat when infecting a blue.*
Julia video clip 2 - along the lines of: if we can use mathematics to model the effect a passenger with a virus on bus might have, then perhaps explain how that data might inform government policy re using buses during an outbreak bearing in mind average number of infections the students recorded when using interactivity to investigate different r numbers. To improve a model with one infected passenger, what could we change (number of pasengers having virus eg family members sat together or apart). How might that effect number of infections? Also, how might it affect school policies - should passengers have set seating positions so they can be tracked more easily on buses like happens on many trains?
Classes return to interactivity to investigate changing number of original infections, and the locations of those infections - thinking about whether it happens if they are spread across the bus or in clusters, why might a school decide to sit year roups together?
Investigate effect of changing r value - different groups investigate different r value and report back.
Important things to consider – what are we changing each time, what are we keeping the same?
· R value
· Number initially infected
· Initially clustered infections, or spread out?
Questions to consider:
Which are the most dangerous scenarios WRT infection spread?
Where is the safest place to sit on bus/in theatre etc?
What other factors are we not considering/might affect this (air con, …)
Video clip 3 Julia - perhap discuss different locations modellers considered when reporting on possible impact of opening schools - assembly halls with whole school attendace, single classrooms, buses, visits to theatres etc. Huge project, modelling is growing area towork in within maths. Perhaps also use place to add reminder that maths is not necessarily abstract, modelling can help keep people safe (note - this is a key consideration for many A Level students considering their degree choice of subject)
Classes investigate effect of changing different settings - perhaps working in different groups on different settings and reporting back their findings
Video clip 4 - reflect on what we've learn from modelling these situations - the bus ride home, the school assembly, sitting in class - - note that they were all similar scenarios -static - we've not static in real-life, we move about and mix with others so next generation of model needs to go further and reflect that too. Perhaps also mention the lessons learned from modelling which impacted our everyday lives for months on end, so there's also an ethical and social aspect to modelling (thought this might also appeal to those not necessarily hooked on the maths aspect but may be the social side of things -we find this with the Olympic Records activity which appeals to many students but in different ways according to their own interests - possibly link here to Motivate resources on ethics or update them).
Link to next session...The Ticket Conundrum