Counting Handshakes

1
Counting Handshakes ?

• After a sporting event, the opposing teams often
  line up and shake hands. To celebrate their
  victory, members of the same team congratulate
  each other with a round of high fives.
• Lets explore the of high fives or handshakes
  that take place.

2
Case 1

• Each member of a team gives a high five to each
  teammate.
• How many high fives will take place among an
  academic quiz team with 4 members?
• How many high fives will take place among a
  basketball team of 6 players?
• How many high fives will take place among a golf
  team of 15 members?
• Write an equation for the number of high fives,
  h, that will take place among a team with n
  players.

3
Case 2

• Two teams have the same number of players. Each
  player on one team shakes hands with each player
  on the other team.
• How many handshakes will take place between two
  basketball teams with 5 players each?
• How many handshakes will take place between two
  soccer teams with 10 players each?
• How many handshakes will take place between two
  volleyball teams with 15 players each?
• Write an equation for the number of handshakes,
  h, between two teams with n players each.

4
Case 3

• The number of players on the two teams differ by
  one. Each player on one team shakes hands with
  each player on the on the other team.
• How many handshakes will take place between a
  chess team with 3 players and one with 4 players?
• How many handshakes will take place between a
  water polo team with 10 players and one with 9
  players?
• How many handshakes will take place between a
  field hockey team with 15 players and one with 14
  players?
• Write an equation for the number of handshakes,
  h, between a team with n players and a team with
  n 1 players.