The preteen life stage is only available in The Sims FreePlay. It is similar to the Child stage in other games.
The Community Center is mostly for preteens. They are able to learn karate or ballet there. However, there is also woodworking benches for Adult sims. Preteens can also learn how to Dive at the Swim Centre and how to Figure Skate at the Snow Park. After the Arcade is unlocked on the Mysterious Island at level 26, they can also practise the Skill Tester hobby.
The amount of money (allowance) and XP your preteen will earn from going to school depends on their grades. The higher their grade, the more Simoleons and XP they will come home with.
Your preteen can improve his or her grades by (1) going to school every day, as well as (2) studying with a Study Desk when they're at home. You can purchase a Study Desk from the Home Store, under the 'PreTeens' tab, for Simoleons or Lifestyle Points.