Jumbo Checkers
The game of Checkers is great for developing reasoning and eye-hand coordination skills. The board and checkers are made of plastic designed to be used indoors or outside. The checkers are 1 5/8" in diameter, and 3/16" in height, and are called "jumbo" by the manufacturer. They are actually larger than regular checkers, but not the jumbo size you would pay a great deal more for at places like Cracker Barrel.
Plastic pieces and board may be cleaned with water, and are a good size for both small and large hands.