Number Devil Activities: The Eighth Night

1) Permutation Relay:

Since we don't live in the dream world, it is important to know the real world names for things that the Number Devil introduces.   When Robert tries to find all the possibilities for how to seat his classmates this is called "permutations".  Let's have fun with permutations doing a permutation relay.  Give each child a red square of paper, a blue square of paper and a white square of paper.  Separate the group into two teams.  Have the teams line up for a relay style race.  The first child from each team runs to the board/wall and puts up their 3 papers in a line, in any order.  They run back, tag the next person who then runs to the board and puts up their 3 papers in a line, in any order except the order of the other person on their team.  This continues until all six permutations have been discovered.  The team that gets all their permutations up first is the winner.

2) More about Permutations?

Want to learn more about permutations?  Watch this online video to learn how to make tree diagrams to understand better how permutations work.

3) Vrooms! are Factorials:

Factorial worksheet

Answer key

The Number Devil calls them "vrooms", but we know them as factorials.  The factorial symbol is "!"  The Number Devil shows us that factorials are useful in figuring out permutations or in other words, how many different ways a certain number of things can be arranged.  The Number Devil shows Robert that to figure out how many possible ways to arrange his classmate's seats all Robert has to do is multiply the number of people by all the whole numbers below the number of people except zero.  Pretend you're in Robert's class and you want to figure out the number of possibilities for arranging your classmate's seats.  Fill in the blank spaces to complete the chart.  For more information about factorials check out this website.