Number Devil Activites: The Eleventh Night

On the eleventh night, the Number Devil helps Robert understand why all the cool tricks he has taught him really matter.

1) Lord Russell:

Lord Rustle in the dream world, but Bertrand Russell in the real world searched for knowledge for his nearly 100 years on earth.  Among many other accomplishments, he is a famous mathematician.  Learn more about him and create a notebook page about him.  If you have a timeline, you can print his picture and add him to it.

2) Pigeon Hole Proof:

The Number Devil explains that proofs are used as stepping stones to understand more in the field of mathematics.  Explore the Pigeon Hole Proof to better understand what a proof is and why it is useful.

This website gives a clear, brief explanation of what the pigeon hole principle is and 16 fun applications to help understand it.   Have each student write 27 words on a piece of paper.  Explain to them that because of a mathematical proof you are sure that each of them wrote at least two words that start with the same letter.  This must be true because there are 26 letters in the alphabet and 27 words on their paper.  This is a demonstration of the pigeon hole principle.  Discuss some of the other examples on the website.  Try the proof again with a miniature chess board and eight dominoes.  The worksheet and the explanation of the proof can be found here.

3) Chocolate Bar Proof:

Start with a candy bar that is scored into smaller bars- at least 3 sections across and 4 in length.  Have children guess the minimum number of breaks it will take to break the candy bar into all the small sections.  In small groups pass the candy bar around letting each child make one break until the bar is in individual sections.  Count how many breaks you make along the way.  How many breaks did each group make?  (The number should be the same for every group).  How close were the children's guesses?  The proof says that there will always be one more piece than the number of breaks it takes to separate them.  For example at the beginning there was no breaks and one piece, then there was one break and two pieces, and two breaks and three pieces and so on.