This one is so well known that I was surprised when I realized that we had yet to feature it. The Redistricting Game (at redistrictinggame.org) is a great online tool for learning about districts, redistricting, and gerrymandering. Players work on behalf of one of the political parties and are tasked with redrawing district lines on several different missions, from simply making population size equal and districts compact and contiguous to partisan gerrymandering or ensuring minority representation. The gameplay is a map with small dots representing the people according to their party affiliation and ethnicity, and cities are noted with little house icons and high population density (i.e., lots of dots). As you redraw the lines, elected officials give you feedback through their animated expressions as well as written comments–happy if their reelection is ensured, concerned if the divide is a toss up between parties, and outraged if their district will flip to the other party. Once you meet the mission’s objectives, you submit the plan for a vote and eventually the Governor’s signature.
Its a great game to assign students either before or after learning about redistricting. It takes what can be a bit dry of a lesson–the rules and regulations of district sizes and shapes–and makes it concrete and active. Its also quite user-friendly and is entirely free. As a supplement to traditional class readings and lectures, it works really well in teaching the basics of the subject and you may find that students will play it for far longer than assigned.