Brain Training:
In addition to the educational games linked above and at the bottom of this page, the games and activities at lumosity.com and happy-neuron.com may be useful for your gifted children. Both sites have games designed to improve visual memory, attention, processing speed and other mental functions. Both have free games as well as additional features and games which are available via subscription.
While it may seem counterintuitive to recommend brain training games for a gifted child, asynchronous, or uneven, development is very commom among gifted children.
The Columbus Group (1991) defines gifted as:
...asynchronous development in which advanced cognitive abilities and heightened intensity combine to create inner experiences and awareness that are qualitatively different from the norm. This asynchrony increases with higher intellectual capacity. The uniqueness of the gifted renders them particularly vulnerable and requires modifications in parenting, teaching and counseling in order for them to develop optimally.
I must temper this with the caveat that I wouldn't expect brain training exercises to make significant changes in how your child functions in life. There have been some recent studies which have called into question the value of brain training exercise in creating functional gains. I have seen in my own children that some aspects of the asynchrony we saw when they were younger has leveled out simply through the process of getting older. Some aspects of their unevenness remains, though, and I suspect that some gifted children will just be slower, more meticulous people throughout their lives despite efforts to make them process faster. That is okay, too. If practicing speed and memory games helps with reducing anxiety surrounding timed tests or reduces perfectionistic tendencies or even just speeds along that maturation process where the asynchrony levels off, though, that is all good.
Board/Card Games and Books:
Created by 15 year old Anshul Samar, the card game Elementeo is an engaging way to learn chemistry concepts. Elementeo has won its creator numerous awards including the prestigious $25,000 Davidson Fellows Scholarship in 2009.
Another option for game recommendations are the games chosen as Mensa Select games. American Mensa hosts an annual Mind Games competition during which Mensa members gather to play and rate new board and card games. Five games are selected each year to receive the Mensa Select seal. Visit the Mind Games site to view a list of winning games.
For book ideas for precocious readers, check out: