Kenyan Handshake (Grades 4-8)

Blog by Jacob (grade 7)

"In Kenya, everyone in the congregation shakes hands with each other after church. To do this, at the end of the service, the pastor walks out. The next person walks by and shakes his hand, then goes next to the pastor. Third person shakes the pastor's hand and then lines up behind the second person. This goes on until the whole congregation is in a circle. Our job is to find out how many handshakes will happen if there were 50 people. 

My prediction is 100."



The students brainstormed ways to model this problem. Acting it out, making a table, making a graph, make a smaller (easier) problem and multiplying it to get the final answer.









After making a long chart, they discovered that number of handshakes was 1225. They also discovered that the handshakes didn't grow at the same rate, so an easier problem wouldn't work.

The next day we modeled the handshakes with polygons. Each dot was a person, each line was a handshake.



Each new person (n) shook hands (n-1) times. The 6th person shook hands with 5 people and this happened 6 times. Because this method counts each handshake twice, we divided it by 2.

Handshakes = n(n-1)/2

For more information about the math behind the handshake problem, go here.