Flower Garden, Port and city Jigsaw Puzzles. For games, you should make the first few levels pretty easy to ace. Increase the difficulty, but give kids the feeling of accomplishment and mastery early on. As the levels go up, naturally, you'll make them more difficult, but keep the delta between levels pretty consistent.
For educational sites and apps, it's best to establish patterns of progression early on, so kids know the mechanics of what they need to do on each screen before they get there. This pattern lets them anticipate what they'll come up against as they move through the interface. For example, when designing an interface to teach math, keep the general layout of the math problems the same across screens, but just increase the difficulty of the problems. You can change stuff like colors, icons, and animations on each screen, but make the basic structure consistent so that kids can feel a sense of comfort and familiarity. If users feel like they might not be able to accomplish something at first glance, they'll be less likely to engage.

Life on the Allotment, Gibsons

Lake Windermere, Gibsons
Fizzy's Lunch Lab lets kids level up in interesting ways.

Newcastle, Gibsons
Explain, Explain, and Explain Again
While younger children prefer to explore and learn as they go, 6-8s want all the information up front, to make sure they get it right the first time. Starting at age 6, opinions of others become super-important to kids, even if that other is a digital interface. They don't want the game, or app, or device to think they're dumb or unsophisticated. Having all the rules established before they begin makes these kids feel better prepared to excel.It's important to note, though, that if you find your interface requires a lot of explanation say, more than a couple of short sentences it's probably too complicated and will likely turn kids away. These youngsters have just started to read, and if the directions make the experience sound too difficult, they won't want to participate.

Steep Hill, Gibsons
Although this process is broken up into several steps, it gives users a chance to fully understand what they need to do along the way and sets them up for success. While adults prefer to move through tasks quickly, 6-8s are more concerned with doing the task in the right way, so a greater number of clearly outlined steps works better for them.