First up-- MineCraft, Pocket Edition. This game is pretty incredible and the kids eat it up. It's an open world filled with opportunities to build and create. Plus, kids communicate and interact through the game and with one another. It's awesome. I apologize if you don't like Minecraft.
Cargo Bridge. The objective is to build and construct bridges that will hold people, animals, cargo, and more. The fun comes when you get to test your bridges and realize you need to do just a little more work.
Tangrams. A simple app of building and creating images with geometric shapes. It's filled with multiple levels and the images kids create are spectacular. It's great for all ages.
Casey's Contraptions: Rube Goldberg would be proud of this app. Simple and executed well, but the levels are very challenging for all the kids. They have to think, test, rethink, and retest--sometimes over and over. It's good.
Inventioneers is much like the previous app, using objects to complete tasks and find answers to problems. My students have just started with some of the tasks and really have to work together to solve the tasks.
a-MAZE-ing: Part puzzle, part maze, with a little eye-spy mixed in for good measure. Roxy's a-AMAZE-ing is a huge app with many obstacles and activities to complete. It's massively great.
I first used Lightbot during Hour of Code. Loved it and the idea of making kids think directionally within a game. Same rules apply for the app--plus, the robot is cool.
Kodable is a variation of coding for kids. It's tough and there are rules that have to be followed to be successful--but it's outstanding. I highly recommend it. Seeing kids pump their fist when they pass a level is pretty cool.
Enjoy this peak into my classroom and iPad world. If you think I left a good problem solving app out, let me know. I'd love to know what you use with your students!