Introduction: Greetings everyone! Sometimes when people meet, they welcome each other by shaking hands or giving high fives. The more people at the party, the more handshakes take place. In this problem, you find out how many handshakes are needed so that everyone shakes each other person's hand once.

Problem:

1. Join with classmates or family members to form a group of three people. Make sure everyone in the group shakes the hand once of each other member of the group. List the pairs of people who shook hands. How many handshakes were there?
2. Now form a group of four people. Have everyone in the group shake the hand once of each other member in the group. List the pairs of people who shook hands. How many handshakes were there?
3. Make a chart (like below) showing the number of handshakes for groups with two, then three, then four, then five, then six, then seven people.

   

4. Look at the chart you made. Can you see a pattern that helps you predict how many more handshakes there are when a new person joins the group? Describe the rule for this pattern. Can you explain why this rule works? Use the rule to predict the number of handshakes when there are twelve people in the group.
5. You might imagine there would be a lot of confusion keeping track of all the handshakes in a group of twelve people. Describe the most organized way you can think of to help keep track of the handshakes.

Materials: people (with washed or gloved hands), pencil, paper, calculator

Numbers and patterns, critical and creative thinking, communication

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
Include in your portfolio?
Yes     No     Optional 
Toward Your Marks?
Yes     No     Optional 

  Hints:

If Pat and Chris are two members of a group, the handshake between Pat and Chris should only occur once. Make sure Pat does not shake Chris's hand and then Chris shakes Pat's hand. This would be two handshakes between Pat and Chris.