Educational technologies develop quickly. Which functions of face-to-face education can be substituted by technology for distance learning? One of the risks of online education is the lack of embodied interactions. We investigate what embodied interactive technologies might offer for teaching trigonometry when learning at a distance. In a multiple case study, we analyze the potential of embodied action-based design for fostering conceptual understanding of a sine graph. It appears that independent learning with tablet-based activities leads to acquiring new sensory-motor coordinations. Some students include these new embodied experiences into mathematical discourse and trigonometry problem solving themselves, while others still need some support from a teacher. However, distantly acquired embodied experiences can be easily recalled in a few days after learning and serve well as a substrate for further conceptualization and problem-solving. The results speak for a clear contribution that embodied design might provide for grounding conceptual understanding in distance learning. However, we expect embodied design to be particularly helpful in a blended learning format.