One of the fundamental problems in education is that of applying skills and knowledge which learners have gained in school to problems they encounter outside school. This is particularly so in the area of mathematics, where the problems encountered by learners in applying mathematical knowledge are well documented. Using and applying mathematics is a central component of the National Curriculum in mathematics. However, it has been interpreted in many different ways by teachers trying to implement the National Curriculum in their classrooms. This text aims to help teachers with their understanding and practice in this area. It is based on the findings of a major research study, funded by the Nuffield Foundation, in which a group of primary teachers worked closely with conceptual analysis of the problem of application, together with extensive examples of ways in which teachers can address it in their classrooms. A novel feature of the book is that it includes first-hand accounts of practice in Japanese classrooms, and outlines what teachers in the UK and elsewhere may learn from Japanese methods.