Kids really like guessing games. However, when they are very little they cannot tell the difference between random guessing and estimation based on partial information. For example, you might play a game with them where you show them some number of objects and ask them to “guess” how many there are without counting. When they inevitably then ask to give you a problem in return, they will hide their objects from you and ask you to solve the analogous problem.
As they get older, they will be able to make the distinction, although they may still enjoy games of both types. Whereas the pure guessing games can be amusing, the games involving estimation are both fun and teach a valuable life skill.
To practice estimation, we played a simple game in our last class. In a large room, a stuffed dog was placed some distance away from where the kids was standing. The task of each child was to predict how many steps it would take him/her to reach the dog. Overall, the kids were quite good at estimating the number of steps. Occasionally, someone would say a really large number, like 100, but this was mostly done for general amusement and did not reflect what the kids were thinking. It was also amusing to see how some kids really wanted their predictions to be accurate and they would adjust the size of their steps as they were getting closer. (We tried to control the size of the steps that the kids took and suggested that they they put one foot in front of the other but it didn’t always work)
At some point, it took two kids an identical number of steps to reach the dog, even though one of them was standing noticeably closer. When we asked the kids to explain how this was possible, a few immediately pointed out that one of the walkers had larger feet.