In UK we call this game Draughts. You may know it by other names. This afghan doubles as a floor game and has a bag to hold all the playing pieces so it can be used as a small pillow and to prevent them from getting lost. Draughts is a traditional game which is not inherently mathematical. Games help to develop logical thinking and planning.
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The 64 squares are granny squares (Hence the name) which are worked individually and stitched, or crocheted together. The playing pieces are simple crochet circles.
Any yarn, in two colours, can be used. The size of the squares can be changed with more, or fewer rounds of crochet. The pattern includes instructions for the playing pieces and a bag to keep them in which forms a small pillow.