Mathematical tasks have always been and still are a major object of concern in the mathematics classroom. Teachers’ daily work includes planning, implementing, and evaluating the mathematical tasks that student engage in during class by making use of material and immaterial artefacts. We argue that teachers’ mathematical knowledge has to include instruments for controlling how these artefacts become involved when students engage in solving mathematical tasks. We propose to meet this demand by coordinating the matching notions of affordances (for planning) and objects of activity (for evaluation). We briefly illustrate how these notions can be used as analytical instruments in a fashion that connects to what teachers already do in their daily work.