Physical manipulatives, such as rods or tiles, are widely used for mathematics learning, as they support embodied cognition, enable the execution of epistemic actions, and foster conceptual metaphors. Counting them, children explore, rearrange, and reinterpret the environment through the haptic channel. Vision generally complements physical actions, which makes using traditional manipulatives limited for children with visual impairments (VIs). Digitally augmenting manipulatives with feedback through alternative modalities might improve them. We specifically discuss conveying number representations to children with VIs using haptic and auditory channels within an environment encouraging exploration and supporting active touch counting strategies while promoting reflection. This paper presents LETSMath, a tangible system for training basic mathematical skills of children with VIs, developed through Design-Based Research with three iterations in which we involved 19 children with VIs and their educators. We discuss how the system may support training skills in the composition of numbers and the impact that the different system features have on slowing down the interaction pace to trigger reflection, in understanding, and in incorporation.