Introduction: In each situation, the group of people begins seated in a row of chairs. The first person in the row is numbered 1, the second is numbered 2, and so on until the last one is numbered 5 (if there are 5 people) or 10 (if there are 10 people) or 20 (if there are 20 people). The first person in the row gives the following directions:

• Every person whose number is a multiple of 1, change position so that each is now standing.
• Every person whose number is a multiple of 2, change position. If they were sitting, they stand or if they were standing they sit.
• Every person whose number is a multiple of 3, change position. If they were sitting, they stand or if they were standing they sit.
• Continue with this changing position exercise for every multiple up to the last numbered person (if there are 5 people, continue to multiples of 5. If there are 10 people, continue to multiples of 10, and so on.)

Problem:

1. Start in a group of 5 people. Follow the above directions. Which numbered people are standing when the exercise is finished?
2. Now do the exercise over again, this time starting with a group of 10 people. Follow the above directions. Which numbered people are left standing when the exercise is finished?
3. Do the exercise once again, this time starting with a group of 20 people. Follow the above directions. Which numbered people are left standing when the exercise is finished?
4. You might be able to find a pattern so you can predict who is left standing for a very large group, even without acting it out. If there were 100 people in the starting group and this standing and sitting exercise were repeated from multiples of 1 all the way to multiples of 100, who do you think would be left standing?
5. In each of the above exercises, the person numbered 4 should have been left standing. Can you explain why this is the case? Would this be the same reason for the others left standing? Explain.

Materials: pencil, paper, calculator, pennies or two-coloured counters

Patterns, multiples, factors, 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:

To try to find the pattern for larger groups of people, pennies could be used. A penny with heads up could be a person sitting and a penny with tails up could be a person standing.