The Connecticut Middle School League will use the Middle School Public Debate Program format, which is becoming popular across the country. It is a variant of Parliamentary debate, which is the most popular debate format in the world.
In this format, two teams debate a motion, one side arguing in favor, the other side against. Each team has three members, each of whom presents one speech: a first constructive, a second constructive and a rebuttal. The speeches alternate between the teams, with the team arguing in favor leading off. The order of the rebuttals is reversed, however, with the opposing team speaking first, giving the supporting team the last word. This is similar to a court trial where the prosecution has the burden of making its case, and is given the first and last word to support that burden.
We have a two page description of the format with more details. You may download the pdf file CTMSDL Debate Format. You may also find the Middle School Public Debate Program website a useful source of additional descriptive and educational material.