Children move their hands to explore, learn and communicate about hands-on tasks. Their hand movements seem to be “learning” ahead of speech. Children shape their hand movements in accordance with spatial and temporal task properties, such as when they feel an object or simulate its movements. Their speech does not directly correspond to these spatial and temporal task properties, however. We aimed to understand whether and how hand movements' are leading cognitive development due to their ability to correspond to spatiotemporal task properties, while speech is unable to do so. We explored whether hand movements' and speech's variability changed with a change in spatiotemporal task properties, using two variability measures: Diversity indicates adaptation, while Complexity indicates flexibility to adapt. In two experiments, we asked children (4–7 years) to predict and explain about balance scale problems, whereby we either manipulated the length of the balance scale or the mass of the weights after half of the trials. In three out of four conditions, we found a change in Complexity for both hand movements and speech between first and second half of the task. In one of these conditions, we found a relation between the differences in Complexity and Diversity of hand movements and speech. Changes in spatiotemporal task properties thus often influenced both hand movements' and speech's flexibility, but there seem to be differences in how they did so. We provided many directions for future research, to further unravel the relations between hand movements, speech, task properties, variability, and cognitive development.