Flotation is usually taught in Indian schools after students have been introduced to the concepts of mass, density, pressure, volume and buoyancy. This paper describes an attempt to teach the principle of flotation to a class of sixth graders--who had not yet been taught these concepts--so they could understand (and perhaps, arrive at) Archimedes' principle. Using a modified version of the Predict, Observe, Explain (POE) pedagogy called PROVE (Predict, Reason Out, Verify), this paper describes how students began to use a process of iterative reasoning to develop their conceptual understanding of the law of flotation of objects, and how some of them came very close to understanding the principle, without the introduction of the necessary concepts. It also suggests the use of such pedagogy for the teaching of other concepts in science, to empower students to "first think their way through complex ideas" without getting bogged down by definitions and technical terms.