Noticing young children's mathematics can involve talking to them and watching as they undertake mathematical tasks or answer questions. Interviews are a key methodology for researchers who focus on young children's mathematical learning, providing opportunities to notice what children are doing and gain insights into their thinking. This paper focuses on one-to-one task based interviews as a tool for noticing young children's mathematics and particularly the use of flexible, semi-structured interviews with children with Down syndrome. Such flexible approaches maximised the chances of children with Down syndrome showing what they knew and could do mathematically.