Named "Best Serious Game" at the 2013 International Mobile Gaming awards, DragonBox+ is an awesome example of a game-based learning app that can be used by either children or adults.
It may cost $5.99 to download, but DragonBox+ succeeds where many modern mathematics lesson plans fail. It simplifies the process of solving algebraic equations and even makes it fun for children. While the game is certainly designed for the young ones, there's no question that it can be used to teach teenagers and even some adults who may be seeking a better understanding of the sometimes scary subject.
When you first open up the app, DragonBox+ asks you to pick an avatar. From there, the first few levels act as a sort of tutorial, establishing a few rules and helping you get the hang of moving pieces on the board.
The entire game revolves around a single objective: isolate the glowing box on one side of the screen. With small pictured tiles strewn about on both sides of each level, it is your job to follow the rules of the game (new rules are added in each chapter) in order to move the tiles to the side opposite the box. In the first chapter, the levels are relatively simple, as they have only a few established rules and there aren't yet an overwhelming number of tiles. In the later chapters, however, things get more complicated.
If you haven't figured it out by now, the glowing box represents the variable that needs to be solved for, the "X" if you will, while the other tiles represent numbers. Since your job is to move the other tiles away from the box, you are essentially isolating the variable on one side of the equation and therefore finding its value.
In order to ensure that you aren't just haphazardly moving tiles back and forth between the sides, each level gives you a certain number of moves you can use to complete your objective. Also, there's a reservoir of tiles that can be used in your problem solving.
The simplest operation that can be performed in DragonBox+ is addition. For example, if you have a lizard tile on the same side as your box, you can grab a "negative" version of the lizard and "add" it to both sides, which will help to isolate your box. You can also divide by tiles and multiply by tiles in later chapters. But of course, the beauty of the game is that these complex-sounding mathematical operations are disguised as simple game rules.
One thing I would add to DragonBox+ is more explicit explanation of the mathematical concepts being taught. While the game does slowly mix real numbers in with the pictured tiles, which is brilliant, I still think an explanation or a pictureless math chapter at the end of the game would go a long way in helping a student to apply the game-learned rules to the real world of algebra. That said, there is a fine line that shouldn't be crossed with such an explanation, otherwise it may turn a child off. Also, I think it would be great if you could "level up" your avatar by completing chapters or challenges.
Dragonbox+ is also available on iOS, Windows, and Mac.