## Wednesday, November 5, 2014

### The Game Begins

The mantra for working with numbers remains ‘Never be afraid to use pictures in mathematics no matter how simple the problem appears’. Even for simple addition and multiplication if necessary
So here we go building numbers using pictures.

This is One . Notice the capital letter. Numbers as objects will have capital letters, counting numbers do not. So  is of one One.

For clarity we need a location, so we are going to use a board to place our numbers on. You can think of the mathematics of numbers as a game played on a board with counters. Only counters on the board are counted.
 Board A                     Board B                         Board C
Board A has zero counters on it and shows Zero.
Board B has one One on it and shows One.
Board C also has one One on it and shows One. The Ones around it do not count for anything. They are not in play just like discarded draughts pieces.

 Board D                      Board E
Board D is two Ones, two Ones combine to make one Two.
Board E is one Two, or just Two.
Both Board D and Board E show the same number.

The thing about number objects is that they can quite happily join up and split apart.
The first set of numbers is directly created from the One object. For example Three is three Ones, Ten is ten Ones, a Hundred is a hundred Ones and Sixteen is sixteen Ones.