WSP Handshakes

  • Handshakes

    Grade: 3rd to 5th, 6th to 8th

    When the nine justices of the Supreme Court meet, they greet one another with a handshake to show harmony of purpose, even though their views may differ. How many handshakes occur? In general, how many handshakes occur when there are n people?



    How to Use

    • Use the red points (people) to enlarge or decrease the size of the display.
    • By highlighting two or more points, the location of the display can be moved.


    The buttons are meant to be used sequentially.

    • All the green buttons will show:
      • The number of handshakes between the specified number of people.
      • A diagram that shows how the handshakes are shared.
    • The gray buttons will toggle on and off to show or hide values and/or segments.
    • Use the Reset button to start over.



    • What patterns do you notice between the number of people and the number of handshakes shared?
    • If possible, what is a general formula showing the number of handshakes shared between n people? Assume that everyone shakes each other’s hand.


    Objectives and Standards

    NCTM Standards and Expectations
    • Probability / Data Analysis and Statistics
    • 3-5
    • 6-8
    • Data Analysis and Probability