This article is the first in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation." The Nuffield report is soundly based on research about how children learn some of the concepts involved in mathematics. In this series of articles the author takes key ideas from the report and shows how they impact on school mathematics for all years, beyond those in which particular aspects of number are taught. The understanding of number which school children eventually need to develop comes from four threads of development: (1) counting discrete objects; (2) knowing about quantities of all kinds; (3) comparing quantities and collections of object; and (4) using notations for these. In this article, the author considers the importance of relations among quantities. (Contains 2 notes.)