10.5.9

The Handshake Problem – Do on a piece of loose graph paper to turn in.  Remember to read the instructions clearly and use your blue sheet.

If everyone in the class shakes hands with everyone else, how many handshakes will happen?

• With one person, there are no handshakes
• With two people there is one.  
• With three people, there are three handshakes.

 1.   Continue the pattern using a table.  Try to find a rule.

 2.   Show all your work and explain your thinking and your rule.

 3.   Finally, graph the handshakes. The number of people should be on the x-axis (horizontal) and the number of handshakes should be on the y-axis (vertical).

 4.   When your graph is finished for up to at least 5 people, answer the following questions on the back of the page your graph is on:

• Describe the shape of this graph.
• How is this different from or the same as the other graphs you have made?
• Explain how the shape of the graph is related to the problem.