games,  mathematics

3D tic tac toe and spatial reasoning

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I pulled out the 3-D tic tac toe frame again. Our frame has three layers of wood with indents to hold marbles. The kids and I played with it in a couple of ways. We played the game, but then we made patterns with the different colored marbles on it. I pulled out some paper and we experimented with drawing the board.

sixyearoldsmarblepatternMy six year old started by drawing the frame, but then switched to drawing the three separate platforms side by side. He made a couple of different patterns. The one I’m showing here involves a blue triangle being filled different ways, with two white marbles next to it, and on the side a diagonal line of white marbles.

I experimented with cubes. What if we thought of the marbles as cubes stacked together to make a larger cube? (Empty holes become a third color of cube, a placeholder.)

If we think of the marbles as representing points on a cube, then a marble could be placed on a vertice, the center of an edge, the center of a face or the center of the cube itself. There are really only four opening moves for 3D tic tac toe (up from three opening moves in the 2D version), and the number of lines which could potentially be made with that marble can be mapped out – easily seen but a challenge for me to draw.3 Dimensional tic tac toe possibile lines from a sample position.

I don’t have a picture of it, but my nine year old got into trying to slice the cube apart through lines that joined three blue marbles together. It was one of those odd days where we all found our own ways of exploring the spatial relationships in different ways.


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