In this paper we describe and reflect on the design of a mathematical learning activity developed incollaboration between teachers, researchers and technical developers. By making use of augmentedreality (AR) as a technology supporting augmentation of a real-world projection with computergene-rated images, we have designed an activity that promotes unique action and learningtrajectories. These trajectories require the learners to engage in interactive-constructive actions thatinvolve and stimulate the development of their self-regulatory skills by inviting them to vary andcoordinate across the contextual affordances of the technologies and the physical resources in theclassroom. Our learning activity is designed as a collaborative guided inquiry, implemented in aregular classroom and involved mathematical problem solving in relation to the geometric conceptof scale. In order to successfully complete the activity, the learners are challenged to coordinateaffordances from three distinct referential contexts by involving physical and virtual artifacts. In thedesign process, we identify critical aspects of the activity and embed affordances for correspondingscaffolding actions which turn out to play a crucial role when the activity is implemented with agroup of four 15-year-old students. Although the AR technology has served us well in developingthis particular activity, this specific technology appears to have limited applicability in mathematicseducation beyond geometry. We recommend that future research efforts move beyond AR andconsider the broader context of embodied design with tangible user interfaces, that have recentlyshown great potential for the design of innovative activities for the learning of mathematics.