This data set includes the supplementary material for the article "Reaching Meaning through Language: What can Children Tell Us about Distributivity?". All content is documented in the README.md file. Abstract: Sentences with a plural subject receive a distributive reading if the predicate refers to the atomic members or a collective one if it relates to the whole group. Previous accounts suggest that the distributive representation includes an additional semantic operator, and comprehension experiments show that adults interpret an ambiguous sentence as collective. However, children accept distributive readings more often, questioning their presumed greater difficulty. The current study investigates these interpretations in a novel way through a production study. Italian adults and preschoolers described distributive and collective pictures. We found that adults produced more distributive expressions, in line with semantic theories and psycholinguistic findings. Children were not fully sensitive to the need to express markers disambiguating the two readings. However, when they recognised the difference between pictures, they produced more collective markers, different from adults. We discussed our results at the intersection of language acquisition, semantic theories, and cognitive development.