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Using a variation on Knight's Tours, in 2004, I created a challenge to find Knight's Polygons.  The goal is to create a polygon with the most number of sides on an 8x8 chess board moving like a knight.  You start on anyone of the 64 squares from the middle of the square and make a straight segment to the center of the next square moving like a knight.

All of the Mathletes learned about or rediscovered the mystery and challenge of Knights Tours.  This is an ancient puzzle that challenges us to place a number anywhere on an 8x8 grid and move as a Knight on a chess board (2-1 L shape) until you reach 64. As only a Knight can do, it may jump over other numbers but may not repeat a square. If you are stuck, use the method of recursion where we erase the last number on which we hit a wall until we can travel more moves in a different direction.

The children are becoming experts at following very difficult algorithms.  In particular, the Stair Step Method for creating Odd ordered magic squares is very challenging.  It creates completely different Magic Squares than the method they learned the previous week by going in an upper right pattern.

Follow the attached pdf instructions and create as large a square as they can.

The children explored patterns in numbers placed diagonally in a pyramid like grid (see attached pdf).

They should create these diagonals in 7x7, 9x9, up to 15x15 grids and go pattern hunting.

They also received large graph paper in class that they can use to make their diagonals.

In addition, they all received a tennis ball that they wanted to decorate with math related drawings.   This can include numbers, shapes, diagonal squares, or anything they want.

Kindergarteners should choose rows, columns or diagonals in the Magic Squares Patterns.pdf and add the numbers using the vertical method.  

1. have the children copy the numbers vertically by lining up the ones place, tens place, etc.
2. add the ones place numbers first
3. put the ones place from the sum in the total and carry the tens place number on the top of the next column.
4. add the tens place numbers including the carry number and put the result in the total.