This study is about the design of hypothetical teacher tasks (HTTs) on density of rational numbers, developed based on the anthropological theory of the didactic (ATD), and used to investigate pre-service lower secondary teachers (PLSTs)’ mathematical and didactical knowledge. The PLSTs’ knowledge considered in this paper concerns mathematical and didactical techniques to solve the specific tasks on the HTTs. The collective aspects, mutual engagement, joint enterprise, and shared repertoire, are considered during their discussion. The findings show that there is a link between mathematical and didactical techniques, and some didactical techniques purposed by PLSTs are too general.