In this article we present an activity theory based framework that can capture the complex situations that arise when modern technology like multi-touch devices are introduced in classroom situations. As these devices are able to cover more activities than traditional technologies, even computerbased, media, we have to accept that they now take a larger role in the model of interactions. We reflect this fact by moving the artefact into the centre of our observations, leading to an artefact-centric activity theory (ACAT). The theory was developed in the need of analysing learning environments for primary maths education.