Web sites like SuperKids.com allow teachers and students to create their own worksheets to practice averaging. These sites ask you how many values you want to average, whether the answer has to be in integer form (instead of decimals), and the highest number you want to use. With one click, you have a worksheet with averaging problems for practice.
Education.com is just one web site offering ideas for games for children to use to practice their averaging skills. "Choosing the Best Average" lets students use playing cards to practice adding and dividing to get the mean value of each playing card. For example, an ace is worth one point, and a king is 13. The player with the highest mean after 10 rounds is the winner.
The BBC has an educational activity web site that has math games for primary students. One of these is the adventure of the BAMZOOki Zooks, creatures that threaten to overrun everything if the player does not sort averages in time. This is a game students in first through fourth grades should enjoy, depending on their ability.
If you have some students who are ready for more challenging problems, you can give them some activities based on what's in their local newspaper. For example, ask them to look through the obituary columns and find the average age of the people who died. Or you can ask them to find the average cost of land for sale in the classified ads.