These are designed to be used with dice, spinners, etc. The child would roll die or spin spinner, and then he/she would place that number of items (rocks, coins, erasers, etc.) on the gameboard -- one item per square. The child continues adding items until all of the squares are filled. Another idea that you could do with these gameboards is to use them as a matching game or memory, or as an art extension -- comparing and contrasting the artists.
I'm going to use them as a math manipulative, which I will be sharing with you over the next few weeks, on how we are introducing the basic addition facts up to 10 (this is similar to the Montessori black and white bead stair).