Wellness Level 2 allows your Sim to discuss focusing methods. Children are more likely to start homework autonomously if they are focused. As soon as they start the homework, have your controllable Sim help with homework to keep them on task. If possible, do this in a locked room so no other Sims can talk to the child and distract them.
In addition to what Marian said in regard to logic and the chess table, Whiz Kid is fairly easy to complete. The first Milestone can be initiated by the controlled Sim (Be read to by an adult for two hours and play three games of chess). Completing the finish homework two times while focused is accomplished by using the above method. You can build mental skill with chess or travel to a community lot and fish together. The child can make the 3 required emotional potions on a free day. If you add the Good Schools lot trait, they will get to an A grade faster.
Keep in mind that the Science career has no skill requirement. It's also the only active career that Sims can progress in without following them to work. Sims can get breakthroughs while reading, showering or bathing, viewing art, using the telescope, and fishing. Again, going to a community lot and fishing together can get the breakthroughs while also building mental skill in children.
If any of your uncontrolled Sims are active, be sure to keep workout equipment on your home lot. They will go and work out whenever they are energized and it's possible that they will max that skill. Sims will also do yoga autonomously, but that skill builds slowly, so they may not max it. It does help to keep them slim, though!
Keep a stereo on all the time. Dancing skill is only 5 levels!
It's also a good way for Sim kids to autonomously gain motor skill if you don't have room on the lot for a jungle gym.
I got my heir to level 8 or 9 in several skills so that once she moved out, she only needed a point or two in order to max the skill.