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Handshakes & Plinko

How it works

Imagine you are in a group of people you have just met. Everyone in the group shakes hands with everyone else in the group exactly once. How many handshakes would that entail in total?

In this activity, students investigate the answer to this question depending on the number of people in the group, and then explore what happens when different numbers of people are involved in the handshake.

After shaking hands, students explore an activity called Plinko, a game where a ball moves down a hexagonal grid by randomly falling either to the left or right at every step. They look at all the possible paths the ball could take on its way to its final destination.

Handshakes handout
Plinko handout
Pascal’s Triangle handout

Why we like this activity:

  • It’s fun! Students get to find creative ways to greet everyone in the group.

  • It helps to develop combinatorial reasoning as well as enumeration strategies.

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

    • Finding and using strategies to ensure they have every possible handshake in their group or paths on their Plinko board.

    • Making observations about the number of pathways to each hexagon on the Plinko board and how they increase as you go further down.

    • Wondering what kind of connection exists between the two activities and the cause behind it.

To find out more about our approach to math and math education, click here.