E.R.
Find out what the policy is for your district- not just your school! My son tested out as gifted beginning in 2nd grade. He spent 2nd grade bored and we arranged a reading club for him and other advanced readers on our own. When he entered 3rd grade, the addition of more social studies and science curriculum kept him busier- just because it was something new. Has your child actually been tested yet? There is a big difference between a smart child and a 'gifted' one, both in ability and in behavior.
In our district they start pulling gifted kids out for small group instruction in 4th grade for reading and math, so my son will be leaving the classroom to work with the gifted teacher and a small group of other advanced kids this year.
However, even last year, within the classroom structure AND the grade level, they grouped the kids by where they were at for different subjects. So my son was in the advanced reading group and math group, but pretty much everyone was at the same level at that time for science and social studies.
It seemed to work well- he and his group often 'worked ahead' and got 2 homework assignments instead of one, etc. and no one seemed to mind. One child who is very good at math had completed most of the math coursework on his own before the year had ended, but was only a so-so reader. The teachers did a good job of individualizing the program for different kids, but we were lucky with teachers too.
Many schools allow teachers a lot of leeway in how they put these programs together, but there is usually an 'official' policy for the district and as a parent, you'll need to know about it.
Get together with other parents of advanced or gifted students and work together to get your kids some additional options, extra activities, etc. Don't try and do it alone, just for your kid- its a lot harder!