Building on research into the visual semiotics of slides and the multimodality of oral presentations, this paper analyses the speech-gesture-slide interplay in TED talks and considers implications for teaching about gesture in the academic presentation genre. Using two examples from presentations by award-winning science communicator Professor Brian Cox, an enactive-ecological approach to embodied communication yields fine-grained descriptions of relations between spoken language, visuals on the slide, and gesture including depictions, eye-gaze shifts, posture, and footwork. These demonstrate how the speaker's activity of showing slides is a person-environment dynamic of sense-making with the audience, and more specifically, how the speaker's speech-gesture-slide interplay animates, discloses, and decomposes aspects of the visuals on his slides while keeping his audience's attention intact. Whereas researchers of English for Academic Purposes have recommended raising students' awareness of multimodality or body language, this paper's findings suggest ways to sensitivise and engage students more directly and implicitly with the ecology of oral presentations.