According to ri.net, gifted and talented children are highly inquisitive and always are looking for explanations and cause and effect relationships. They also are highly observant and tend to be linguistically fluent. One way to exercise all of these areas is to assign the child research and writing projects. For example, if the child has questions about a particular painting, encourage the child to look up information in the library or on the Internet. Then follow through with giving the child the assignment of writing down not only what they learned, but also why it is significant--according to the Connecticut State Department of Education, gifted children need to practice argument more than they do simple reporting. For example, rather than have the child write about the different kind of dinosaurs viewed at a museum, have them research something specific about dinosaurs, such as how each ate, or have them write a persuasive paper on which dinosaur was "best" and why.
Most math texts and courses concentrate on simply teaching the mathematical concepts and presenting story problems that fill in missing information (e.g., find out how many feet of wood you need to build Bridge A). For the gifted and talented child, this is simply drill work. The bigger challenge exists in locating mathematical anomalies and solving math difficulties. For example, instead of having the child repeatedly plug numbers into the same equation, have the child identify why one equation would work better than another, or have them identify how different mathematical procedures may result in different answers. The Connecticut State Department of Education recommends giving gifted and talented students a "Problem of the Day" to make sure they routinely use math skills. When doing this, encourage more story problems or oral work, as well as mental math.
Science may be the best area in which to challenge gifted and talented students because it provides an opportunity for the child to investigate on their own, make use of mathematical equations and concepts, and to analyze and report results linguistically. However, as with math, many lesson plans involve having students follow a rigid set of procedures with limited opportunity for analytical discussion. In addition to regular experiments, have gifted students do research projects related to science, such as figuring out the science behind making sodas, shoes or other objects. One suggestion from lessonplanet.com is to have the student evaluate different companies that use science to determine who has been the most successful. Field trips are encouraged so the student can investigate in person and has the opportunity to ask questions from those in the field.