# Making the Pythagorus Board

BW is continuing his love for numbers in making his own primary Pythagorus Board.  He spent a good bit of time thinking about the board today.

First we noticed that all the numbers have matches – except the squares that travel in a diagonal down the middle of the board.

So then we began to see that the two x one and the one x two added together  make four.  Four is the square of two.  So two has two squares.

We spent the better part of the morning finding the pairs.  He has yet to discover that the smallest and the largest non-square of a number go together to make the square.  He was very excited to discover that each group of squares has exactly the same number of squares as the primary multiplier.

BW figuring out how to make the squares out of all the multiples.

Once complete BW began to reset the board and glue it to a piece of special paper to make his own board.

He laid it out and began to move the pieces to the special paper beginning with the 100 square as he glued them.

He was amazingly careful applying glue to his work.

We then decided to trim off the excess.  This was BW’s first time using a blade by himself.  He did a great job.

Tomorrow we are going to write the title of the board and our three observations.  Doing this work without working out some observations is not really doing the work.  Understanding is not drawn from blindly doing the work.  For the child to make a deep connection with work in elementary, the child must talk about what he has discovered.