Pool Testing

How it works

Imagine there are a bunch of people and one of these people is infected with a virus. We want to try to figure out which person is infected before the virus spreads to the others.

We can test people in groups, or pools: If the infected person's sample is in the pool we're testing, the test will come back positive, and if not, the test will come back negative.

For a given number of people, what is the smallest number of rounds of testing we'll have to do in order to guarantee we can find the infected person, even if we get as unlucky as possible with our test results?

In this activity, students start by exploring how to use testing to find the infected person. Next, they focus specifically on the number of rounds of testing they're doing. Students try to figure out whether it's possible to find infected person every time with a given number of people when they're only allowed to do a specific number of rounds of testing.

Why we like this activity

• It’s fun! Students enjoy trying to find the infected person.

• It helps students develop algorithmic reasoning.

• It helps students develop numerical reasoning.

• It requires students to engage in mathematical habits of mind:

  • Finding and using strategies to find the infected person.
  • Making and testing predictions about how many rounds of testing you'll need to find the infected person every time.
  • Finding and using strategies to find the infected person every time with a specific number of rounds of testing.
  • Understanding and explaining why it is or isn't possible to find the infected person every time with a specific number of rounds of testing.

• It has a low floor and a high ceiling: It's easy for students to get started trying to find the infected person through trial and error, but figuring out the minimum number of rounds of testing you need to do with each number of people to guarantee you'll find the infected person every time is challenging!

Learn more about our approach to math and math education