These are the electronic components necessary to build a basic robot for children that uses two vibration motors to move forward, left, and right. Two digital pins are used to control the vibration motors leaving 3 open GPIO pins. The Photo cell and LED can be used to detect the presence, and close proximity, of another robot. The Micro servo is an optional add on so that a simple claw (http://www.thingiverse.com/thing:18339) can be added.
Total: $20.98
This project will also need to have some parts like the brushes, sensor housing, and claw printed via a 3D printer. I recommend designing this robot to use the battery holder as the chassis and attach the 3D printed parts to it.
While we are at it, maybe we should give the kids a Robotics patch like this one $3.95