In an afternoon, as a lesson in electronics and building, Emily and I built a small robot. Although it has a small rechargable battery, the robot is based on ideas of BEAM robotics, which combine simple electronics with simple locomotion to produce insect-level behavior. This robot uses two photodiodes as eyes, and vigorously seeks out the brightest light source in a darkened room.
In order to make life easier, we used a kit for the robot that included directions, all parts and a pre-printed circuit board. Emily was able to solder all the joints herself, with me only needing to do some cleanup after the project was done.
You could tell that she was astonished when we charged it up, and it actually worked! Besides the discussions about basic electronics, it was a great way for Emily to learn how to follow written directions, and match parts to a schematic. See the rest of the pictures here.