I like the idea of the checkboard quilt/mat. I made one for my kids a few years ago (they are now 6 and 7) and before they were really playing checkers,they would put their toys on each square and play that way. I did my son's side with hockey fabric and used horses for my daughter's side, with a darker tan as the common "off square" color.
What lucky granddaughter's to have a grandmama like you!