Geometry belongs to branches of mathematics that develop students' visualisation, intuition, critical thinking, problem solving, deductive reasoning, logical argument and proof (Jones, 2002). It provides the basis for the development of spatial sense and plays an important role in acquiring advanced knowledge in science, technology, engineering, and mathematics. The "Australian Curriculum: Mathematics" (Australian Curriculum Assessment and Reporting Authority (ACARA), n.d) emphasises the need to help children develop an increasingly sophisticated understanding of geometric ideas, to be able to define, compare and construct figures and objects, and to develop geometric arguments. This article will look at some of the issues involved in the teaching and learning of two-dimensional shapes and illustrate how activities such as paper-folding tasks can be used to encourage visualisation and geometric reasoning.