Number
Percentages
Can numbers help tell stories?
Exploration
Exploration
How can we use numbers to describe the world?
How does a virus spread?
How can we use numbers to describe the world?
The R number of a virus tells us how many people an infected person will go on to infect - on average. Pupils will explore number patterns and the impact of the R number.
We suggest completing the following activities over a number of sessions - usually 3-4 one hour sessions work well and can be delivered within a typical maths lesson format.
Exploration aims
Pupils will explore the R number and discover that this describes how fast a virus can spread.
They will investigate different ways of slowing the virus and discuss what would happen to infections.
Pupils will learn how to represent the number of infections using different methods (e.g. Lego or counters)
How might a virus spread?
Mystery glitter starter
Start the following without revealing anything about the project:
Spread a little biodegradable glitter on your hand (secretly) and ask the class to walk around "Hi-fiving" each other whilst you join in.
Ask the class to sit back down and look at their hands.
Some pupils will have some glitter and some won't.
Explain that you were the only person who had glitter at the start. Ask which pupils "Hi-fived" you and who didn't.
Class talk
Encourage pupils to discuss and relate this activity to the real world.
Some pupils may suggest that this is an example of how viruses might spread spread.
Introduce the project
(A) Describing a virus with numbers
Pupils explore different values of R and draw diagrams to show how fast a virus outbreak can happen on their whiteboards.
First, pupils explore the amount of infected people each day when R=2
The slide on the right can be used to explain what R means and as a class you can count the amount of infections up to day 2 and let them continue on mini-whiteboards.
Imagine that one person is infected with a virus in a population of 1000…
On day 0 there is one person infected
On day 1 of the virus outbreak the one infected person goes on to infect R more people
On day 2 of the virus outbreak the two new infected people go on to infect R more people ...each
On day 3 of the virus outbreak the new infected from day 2 go on to infect R more people ...each
etc.
Answers when R=2
Day 1
2 more people are infected - giving a total of 3 people infected
Day 2
4 more people are infected - giving a total of 7 people infected
Day 3
8 more people are infected - giving a total of 15 people infected
etc.
Pupils should now continue counting the infections up to day 7, using whichever method they prefer. Use the following questions to guide their exploration...
Take it Further
1.) What percentage of the population are infected each day?
2.) How long until everyone is infected?
Pupils who are able to calculate percentages of the population of 1000 people can find out this answer for different values of R.
Answer: on the 9th day the whole population will be infected
(new infections: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512... , total infections: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023...)
(B) Visualising infections
Here, pupils consider the amount of infections for a virus outbreak, first writing the infections into a table and then explore how to visualise them.
Pupils use worksheet (download here) to write the infection numbers into the table on page 1. Page 2 & 3 enable pupils to explore how to visualise infections with help from the slides.
(C) Methods of slowing down a virus
Pupils generate their ideas about the different methods that might slow down a virus.
(D) Flattening the curve
Together as a class the curve of infections is plotted for the same scenario as part (B) but from day 6 onwards R=1/2. This is simulating a restriction on daily life (as discussed in part (C) ). Pupils should be encouraged to write this into a table similar to part (B). Some pupils may be able to use the skills learnt in part (B) to visualise this outbreak.
Answer - The new number of infections for the first 10 days (starting at day 0), following the outbreak in part (B) would be
2, 4, 8, 16, 32, 64, 32, 16, 8, 4, 2
The total number of infections would be
2, 6, 14, 30, 62, 126, 158, 174, 182, 186 ,188
Finish with visualising this outbreak using methods from exploration (B).
These slides can help support thinking and structure teaching
VirusOutbreak_E_B.pdfStudents could use another print out of the worksheet from (B) (download here)
Take it Further
Can you create some other measures that might make the R value smaller or larger?
Pupils can try other values of R to see this effect - they will likely need to round up some numbers
What happens when R is less than 1 and what happens when R is more than 1?
Answer - when R is more than 1 the new infections grow and when R is less than 1 the new infections shrink. So we want R to be less than 1 to flatten the curve.
(E) Explaining an outbreak
Working as a class, use the Estimating new infections slide and/or print off copies for pupils.
Pupils should guess what might have happened at each point where the curve changes. Some may be able to use numbers to understand what the R value was for each part of the graph.
Its important to notice that when infections start rising again there is a few days before the R is lowered so that the amount of new infections goes down. This is analogous to real life when restrictions take some time to implement.
Pupils should now answer the 3 questions on the Estimating new infections worksheet.
Estimating new infections slide.
VirusOutbreak_E_E.pdfEstimating new infections worksheet (download here)
Take it Further
Pupils could plot the total infections as well as new infections
(they may need to create a key where the circle represents more than 4 people to fit on a page).
Have you completed this project?
Let us know what you thought and help us develop future projects for schools