Purpose: Certain researchers have expressed concerns about inequitable discipline representations in an integrated STEM/STEAM (science, technology, engineering, arts and mathematics) unit that may limit what students gain in terms of depth of knowledge and understanding. To address this concern, the authors investigate the stages of integrated teaching units to explore the ways in which STEAM programs can provide students with a deeper learning experience in mathematics. This paper addresses the following question: what learning stages promote a deeper understanding and more meaningful learning experience of mathematics in the context of STEAM education? Design/methodology/approach: The authors carried out a qualitative case study and collected the following data: interviews, lesson observations and analyses of curriculum documents. The authors took a sample of four different STEAM programs in Ontario, Canada: two at nonprofit organizations and two at in-school research sites. Findings: The findings contribute to a curriculum and instructional model which ensures that mathematics curriculum expectations are more explicit and targeted, in both the learning expectations and assessment criteria, and essential to the STEAM learning tasks. The findings have implications for planning and teaching STEAM programs. Originality/value: The authors derived four stages of the STEAM Maker unit or lesson from the analysis of data collected from the four sites, which the authors present in this paper. These four stages offer a model for a more robust integrated curriculum focusing on a deeper understanding of mathematics curriculum content.