Noughts and crosses, sometimes called Tic Tac Toe, is a simple game which has been handed down through successive generations of people.

The game is thought to have originated in England centuries ago. (Interestingly Tic Tac Toe is virtually unknown in Germany ). As school children we have all played O's and X's ( I seem to remember it as a 'spatial adventure' the child next to me passed on in Grade 4. We played it at the back of the room, out of sight of the teacher if we were bored.

But ! : In retrospect the two of us were actually investigating geometrical relationship and simple game play rules and conditions. We were 'self learning' important ideas. 

Below is a lesson concerning Noughts and Crosses which the Constellations group sends out in its lesson notes with its computer series. 

Noughts and Crosses is the preliminary learning concept in the Constellations Arithmetic Technique. The Noughts and crosses grid is later overlaid with magic number grids and the patterns turned into fantastic pictures of science fiction 'Stargates' for nought and crosses players to travel the infinite Universe. Magic Turtle uses the original traditional 3x3 grid and later on the Stargate and Star Chaser Trainer use the uniquely Australian developed 4x4 grid.

The ability to develop geometrical concepts and handle spatial relationships can be initiated by the simple game of noughts and crosses on a 3 x 3 grid.

By showing players how to NEVER LOSE AT NOUGHTS AND CROSSES, game strategy and player concentration can also be developed. A winning row of three, either horizontally, vertically, or diagonally can always be blocked by the correct response to the opening move. BLOCKING TACTICS: If you are 'X', the way to block any of the three basic opening moves and force a drawn game, is to AVOID the shaded areas shown below. In the illustration below, player 'O' has made the three possible opening moves. The second player should play any of the unshaded areas and AVOID shaded areas.

Although only nine positions on the 3x3 grid are used by players, there are 15,120 different sequences of play for the first five moves of the game. However the game is reduced to a few basic patterns because the grid can be rotated around the central square. With practice, two players of equal ability will draw game after game. Winning only occurs when the second player fails to correctly block the opening move, e.g. , 

(a) 'O' , the opening player, begins in a corner and 'X' responds in the corner beneath: 

(b) 'O' , then places the next 'O' symbol in the opposite corner from the first, and threatens 'X' with a diagonal. Player 'X' has no choice but to claim the centre square: 

(c) 'O's next move which is a winner, is to put an 'O' in the remaining corner, leaving 'X' with the problem of blocking two lines simultaneously - horizontal and vertical rows: 

A centre opening will also lead to a win if the second player fails to claim a corner square. For example, in the game illustrated below, 'X' makes the mistake of going to a bordering square beneath 'O': 

LESSON 1. The teacher illustrates the classic blocking tactics on the Black/white board or on three large squares of cardboard. The cardboard charts can be rotated to illustrate various orientations of the basic play patterns. Ask the students to play noughts and crosses on paper. As a game variation, change the winning definition: 'The LOSER is the player who places a row of three, either horizontally, vertically or diagonally.