Not sure how to keep your gifted toddler busy? Take your cue from him. Does he seem entranced by numbers? Try taking him to the grocery store and showing him the different prices on the products there. He can help you weigh produce on a scale, and you can show him how to find products by looking at the numbers on the aisles. Does your toddler love music? Let him play with an instrument, under careful supervision. Keyboards are especially helpful for toddlers, who can use them to explore several different types of sounds at once. Try some of these music games as well.
Of course, as soon as you see that your gifted toddlers are beginning to become restless or bored with a repetitive activity, switch gears. You should not view your job as actually teaching your child new concepts, but as exposing him to them to the extent that he shows interest.