In this chapter we explore the teaching of ancient history in an Australian junior secondary school classroom, focusing particularly on how the knowledge of government in city-states in Ancient Greek are developed. We show that an important part of knowledge building in ancient history involves ‘factoring out’ the meanings which are condensed in technical terms – characterised informally as ‘flexi-tech’ because of the weakly classified nature of the terms. Throughout two history lessons, the teacher guides the students to think ‘critically’ about how types of government are categorised. We show that while Spartan government is referred to in different pedagogic materials as a monarchy, an oligarchy, or a military state, as the lessons unfold the teacher repositions Spartan government as a complex structure – comprising elements of different kinds, including specific elements of democracy. Our analysis focuses on how this repositioning is achieved and what kind of ‘critical thinking’ is involved.