My homeschooled twice-exceptional 11 year old son also likes competition and plays the game Who Has the Biggest Brain on his iPhone. It posts his scores on Facebook so that his friends can see it and try to beat his score. He is competing with a college kid so he is motivated to keep increasing his mental math speed. He did very little math last year, but ever since he found online games like this and I let him use books with lots of the word problems he likes, he likes math again and will do it without being told to do it.
My son also loved competing in our state's spelling bee a few years ago. Without the competition I don't think he would have learned the thousands of words he learned. He loves trivia. Any kind of trivia. He is thinking about joining another 4H group now that does horse riding competitions, not because he is that interested in horse riding, but because the leader is a veterinarian and she is teaching the kids about veterinary medicine involving horses and she requires homework and they compete against each other with quizzes over the material.
My son seemed gifted in math when he was tested by an educational psychologist right after he turned 7. At that time the WIAT showed he was working at a 4th grade level but he lost interest and began to hate math when his motor dysgraphia made it difficult for him to do the writing that was required. Competition that doesn't require writing is helping rekindle his interest in math.
Even piano recitals are a competition for him and he will practice harder when he has a recital coming up.
