Computer-based interactive simulations that model the processes of sampling from a population are increasingly being used in data literacy education. However, these simulations are often summarized by graphs designed from the point of view of experts which makes them difficult for novices to grasp. In our ongoing design-based research project, we build and test alternative sampling simulations to the standard ones. Based on a grounded and embodied learning perspective, the core to our design position is that difficult and abstract sampling concepts and processes should: be grounded in familiar objects that are intuitive to interpret, incorporate concrete animations that spontaneously activate learners’ gestures, and be accompanied by verbal instruction for a deeply integrated learning. Here, we report the results from the initial two phases of our project. In the first iteration, through an online experiment (N=126), we show that superficial perceptual elements in a standard simulation can lead to misinterpretation of concepts. In the second iteration, we pilot test a new grounded simulation with think-aloud interviews (N=9). We reflect on the complementary affordances of visual models, verbal instruction, and learners’ gestures in fostering integrated and deep understanding of concepts.