Whereas the data in Chapters 4 to 6 are unified personally by informant (e.g. Susie) or thematically by phenomenon (e.g. hedges), those to be presented and considered here are more diverse in origin and nature. There is another important distinction: whereas the data in the earlier chapters were collected in the course of research interviews, the data presented here are transcripts of a variety of teaching and learning situations. Many of these transcripts were supplied by members of an ‘Informal Research Group’ of school teachers which met to consider the place of vagueness in mathematics talk, and the implications for their interactions with pupils. I shall apply the complete linguistic toolkit assembled in the book to the analysis of a number of ‘cases’—transcripts or fragments-demonstrating further the role of vagueness in mathematical discourse by reference to a number of episodes in teaching and learning. These cases come from a variety of sources, including the Informal Research Group.