In kindergarten, children are usually engaged with both verbal activities and non-verbal activities, often requiring the manipulation of physical objects. During technical tasks (e.g., problem solving), children can use argumentation as one of the languages of science that mediates how they interact with the surrounding world. In this paper, we focused on technical tasks in kindergarten in order to understand to what extent activities requiring the manipulation of physical objects also leave space for argumentation. The study involved 25 children engaged in three problem-solving activities requiring the manipulation of Lego® and some recycled materials. To analyze the non-verbal (embodied) side of the argumentative activities, we firstly identified the argumentative structure of each exchange involving the participants. Then, we focused on segments of "incomplete" argumentative dialogues (i.e., presenting only some elements typical of children's argumentation) by appealing to multimodal representations (speech, gestures, and physical objects). The findings of the study showed that even apparently incomplete exchanges can have an argumentative function generated by non-verbal elements of the interactions. Investigating the role of embodied argumentation during technical tasks in kindergarten can allow teachers to recognize and further develop children's argumentative resources.