A motion teaching apparatus includes a teaching motion detection device, a demonstration tool, and circuitry. A robot includes a leading end to move in a first coordinate system. A teaching motion detection device detects a position of the demonstration tool in a second coordinate system. The circuitry derives a relationship between the first and second coordinate system based on a position of the demonstration tool in the first coordinate system at at least one spot and based on the position of the demonstration tool in the second coordinate system at the at least one spot; obtains a transition of the position of the demonstration tool during the demonstration using the demonstration tool; and generates a motion command to control motion of the leading end of the robot based on the transition and the coordinate system relationship information.