Do you have a bag of dried beans and a watch/phone that can time seconds? Then you can talk to your kids about exponential growth as you talk about why COVID-19 is so frightening.
Materials:
128 (at least) dried beans in a pile, bowl, stash, or whatever.
1 plate or bowl.
Timing device
One player is the shouter (keeps track of time) and one player is the doubler (counts beans).
Discuss in advance how often your beans will double (I recommend 5 seconds to start).
The doubler puts one bean from the stash on the plate. The shouter starts keeping track of time; when time has elapsed, shouter shouts, "Double!"
For the doubler:
Round 0.
Put one bean from the stash on the plate. (Plate: 1 bean)
Round 1.
Put another bean from the stash on the plate, count the beans. (Plate: 2 beans)
Round 2.
Put 2 more beans from the stash on the plate. (Plate: 4 beans)
Round 3.
Put 4 more beans from the stash on the plate. (Plate: 8 beans)
[this should have been pretty leisurely so far]
Round 4.
Put 8 more beans from the stash on the plate. (Plate: 16 beans)
Round 5.
Put 16 more beans from the stash on the plate. (Plate: 32 beans)
Round 6.
Put 32 more beans from the stash on the plate. (Plate: 64 beans)
...
Round \(n\).
Put \(2^{n-1}\) beans from the stash on the plate. (Plate: \(2^n\) beans)
You get the idea. This game gets frantic pretty quickly, and that is the kind of overwhelmed state exponential growth should invoke: "this is getting really big really fast!"
To compare to other modes of growth, you can do growth rates like Round \(n\): put \(n\) [or \(n^2\) if you have a fast counting doubler] beans on the plate -- see how much longer it takes for this type of growth to get frantic.
Enjoy!
(This is an activity I developed as part of my Project FULCRUM fellowship at the University of Nebraska-Lincoln when I was a graduate student.)
