We report from the first iteration of a small-scale project introducing elements of inquiry-oriented education in a first-year engineering Calculus course. In four of the exercise sessions we introduced problem solving in groups, using problems designed to provide alternative viewpoints on central topics of the course, for example limits, differentiation and integration, and containing elements of modelling and numerical methods. The theoretical perspective underlying the design was commognitive theory. We discuss some of the problems used in the intervention, focusing particularly on the numerical differentiation and integration problems. We also report some observations made during the first two iterations of the project, and how these have fed into the continued evolution of the project.