After listening to the story of Archimedes' discovery, students were asked to think about and discuss whether his principle had 'Mathematical Merit". A couple of examples of their discussion points were that the Science of Math can be used to solve a problem (determining the volume of the gold in the crown), and that 'merit' implied a level of reliability and quality.
Their conclusions demonstrated the relationship between the number of centimetre cubes added to the water in a graduated cylinder, and the corresponding change in the level of the water. Their 'Eureka' moment came when they showed that 1 cubic centimetre displaces 1 millilitre of water, and that this represents the volume of an object. Further food for thought was to consider how this information could be used in other applications and problems.