For teachers: Lesson by lesson breakdown
These Contagious Maths resources are arranged in four parts, where each part might correspond to a lesson, plus a wrap-up section which can be used at the end of the final lesson. We have designed the resources so that they can form a coherent package for any of the following approaches:
After the final part that you select, the lessons can be rounded off by continuing to the section called Wrap up and Meet the Researchers.
We are very grateful to the schools who gave us valuable feedback in the pilot phase of this project. We would love to receive further feedback from any teachers who use these resources in their classrooms - do please email us.
Part 1: Build Your First Model
Introduction:
Video clip introduces a simple model to describe how an infectious disease might spread.
Key question:
How many generations might it take to infect a school/local community/nearest city/country/the globe?
Middle:
Video clip introduces R, the reproduction ratio.
Key question:
What is the effect of different R numbers?
Conclusion:
Video clip encourages students to consider how our simple model might need adapting.
Key questions:
What assumptions have we been making? How realistic are they?
Curriculum topics:
Arithmetic and Geometric progressions
Part 2: Lucky Dip
Introduction:
Video clip asks how we could improve our model so that it more accurately represents real life.
Key question:
What are the main limitations of the model we have been using so far?
Middle
Three linked video clips explain the 'Lucky Dip model', and invite us to consider the impact of herd immunity:
The Lucky Dip interactivity offers a chance to speed up the simulation of the spread of a disease, and then compare the outcomes of several outbreaks.
Key question:
What features do different epidemics have in common, and how are they different?
Conclusion:
Video clip explains that the improved model is an example of an SIR (Susceptible, Infected and Recovered) model.
Key question:
How could the model be improved further?
Curriculum topics:
Statistics: describing simple relationships between two variables in experimental contexts, and making connections between number relationships and graphical representations
Part 3: Everybody Is Different
Introduction:
Video clip introduces the need for a more realistic model, in which we don't all behave in identical ways.
Key question:
What is R, if there is variability in the number of people that infected people go on to infect?
Middle:
The Everybody is Different interactivity offers a chance to simulate the outbreak of an infectious disease, recognising that not everyone is the same.
Key questions:
How will this variability in the population affect the epidemic? Can we anticipate what will happen?
Conclusion:
Video clip explains the impact of R being greater than or less than 1.
Key question:
How could the model be improved further?
Curriculum topics:
Developing students' fluency, reasoning, and problem solving skills
Part 4: Get Moving!
Introduction:
Video clip highlights the need for models to take into account where we are spending our time.
Key question:
How does the spread of a disease differ when people are spaced differently?
Middle:
Video clip points out that models need to take into account how diseases spread across different communities when people move around.
The Get Moving! interactivity offers a chance to simulate the outbreak of an infectious disease when populations are not static.
Key questions:
Do diseases spread differently when people are moving? Can we anticipate what will happen?
Curriculum topics:
Developing students' fluency, reasoning, and problem solving skills
Conclusion:
Continue to Wrap up and Meet the Researchers which connects the activities in this Contagious Maths resources with the world of scientific and mathematical research. Professor Julia Gog draws the series to an end, sharing her enthusiasm for using maths to tackle real world problems, such as helping to control epidemics. There are a set of four further videos with individual researchers talking about their work.
Further directions and resources:
Disease modelling for beginners offers 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.