Sites like Mensa for Kids and Free Puzzle Games (see Resources) provide a series of challenging puzzle and number-based activities. The games on these sites, which are updated regularly, are a good way of developing your bright child's math skills and teaching her how to apply mathematics to everyday scenarios. Playing games like Sudoku will also help to improve the way your child works with numbers as well as providing a fun way to wile away leisure time.
As well as being fun and stimulating to play, chess and other strategy games can help develop your child's creative and strategic thinking and teach her to analyze, think critically and focus her concentration. Studies have shown a strong link between chess playing and academic achievement. Other strategy games suitable for bright kids include Risk, Axis & Allies and Stratego. All of these games will encourage your child to plan ahead and appreciate the consequences of her actions.
Although it's possible to buy junior versions of word games like Scrabble and Bananagrams, it will stretch your child further if you encourage her to graduate to adult versions as soon as possible. If you're looking for a cheaper way to keep your smart kid on her toes, encourage her to complete the crossword in your daily newspaper or download free hangman templates from the Internet. You could even just supply your child with a pen and paper and test her spelling abilities by calling out awkwardly spelled words.
Playing quiz-based games like Trivial Pursuit, Jeopardy and What is What? is a good way of testing your child's general knowledge. Anomia, which was awarded the Mensa Select Seal of approval in 2010, is another good choice. As well as testing your child's memory and power of recall, these games encourage her to think and respond quickly under pressure. If you have a group of smart children to entertain, consider compiling a series of tough questions yourself and holding a pub quiz-style game.