How Many Handshakes?

  For class, we were to find how many handshakes our group of 4 could do between ourselves. In order to find the number of handshakes total, we made small dot diagrams, similar to the one above, and we connected each dot in every way possible. Our solution, was that 4 people could do a maximum of 6 handshakes. In order to find the exact number of handshakes any group of any size could have, we had to find the function rule. For every rectangular function, the rule is n(n+1)÷2. So, we plugged in the number of people for "n" and got out the appropriate number of handshakes.