handshakes

a good task for the start of a new year
students can introduce themselves to each other by shaking hands (or a high five or a 'namaste')

maybe start with 5 or 6 students at the front of the room and get them to all shake hands with each other

then think about how this can be done (maybe more) systematically - to make sure everyone has shaken hands with everyone else

"and how many handshakes were there altogether?"

think of a way or ways to record or represent what they did (seeking some variety)

NCTM (USA) reflections on the 'handshake' problem

student recording

student recording

student recording

if 5 people shake hands with the 4 other people this suggests there would be 20 handshakes
why do you half this?

various methods for recording 'handshakes' can be compared

the 'handshake' numbers are triangular numbers
the rule for the number of handshakes for 'n' people is n(n - 1)/2
since for 1 person there are 0 handshakes

[note that the usually quoted rule for the nth triangular number 1, 3, 6, 10 ... is n(n + 1)/2]