Multiple Strategies: Quadratic Sequences and the Handshake problem

In a classroom of 30 students, how many hand shakes would there be if every person shook hands once with every other person? How many handshakes would there be between 100 people? or any number of people?

I sent this via email as a homework problem to half of my year 9 top set and sent the same problem, put into another context, to the other half of the class. The other context I used was based around how many phone calls there would be between 30 people that’d been invited to a party.

When I came to mark the students’ homework I was astounded by the number of different strategies used. In addition, some of the students even tried to understand why the formula works – this excites me! When the students use a number of different methods I often make a PowerPoint showing some of the most interesting or clearly presented strategies. In this way the students can feel proud when their work is presented on the board. It also teaches the other students who struggled with the problem a lot about structuring a solution with the information coming from their peers and not from me.

Here´s the PowerPoint we looked over the next class. (contains solutions from 3 students)

Add on: How does all of this relate to the picture below? (Click on the picture to open the applet)

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