Verizon's Innovative App Challenge is a contest that asks students in grades six through twelve to design an app. The contest does not require students to code the app. The contest is focused on the concept of an app and its presentation. Students can work in teams to to design an app that solves a real problem. Take a look at the Chow Checker app for an example of an app designed by students to solve a problem.
Verizon's Innovative App Challenge is accepting submissions until November 24th. Students must make a video to explain the concept of their apps and write a short essay about their apps. Complete entry rules are available here.
If your students do want to build an app either for this contest or for their own enjoyment, the MIT App Inventor offers a great way to do that. Students can build working apps in their web browsers before using them on their Android devices. Click here to read more about the MIT App Inventor.