For 11 year-olds, there are a lot of ways for making money before they are able to get a real job. One option would be to ask their mom to bake cookies for them and sell them in their neighborhood to preferably neighbors they know.
Alternatively in the summer they can fill up a cooler with lemonade, get some cheap cups (8oz/12oz) and set up a table right in front of their front lawn selling lemonade at a marginal price (not too expensive). 1$ a cup is a good start. On a hot day in the summer they could make lots of money from thirsty passersbys or children from the neighborhood.
Another good idea is to offer their brothers and sisters to cook their meals for 25 cents each. Older siblings would most likely to stay in front of the TV than make scrambled eggs or sandwiches. Since the food is already provided by the parents, the income is pure profit.
Computer literate kids can show old folks how to use a computer and the Internet for a fee. Letting grandparents spread the word would be a good marketing tool.
Collecting returnables such as cans and bottles is another way for making some extra pocket money. Especially during big events around the neighborhood (carnivals, community gatherings) people just leave cans and bottle around. All a kid needs to have in mind is to wear gloves, leave broken cans and bottles alone and use hand sanitizer.
If there are many people in the family, a great way for kids to make money is to sell their services. They can make a list of things they would do and how much they would charge for each. It might include washing windows for 50 cents each, for example, or maybe $1.50 to walk the dog. Another good way to earn money is to buy cheap candy at the store and then sell it in your neighborhood! You'll get more $$.