We test children's distributive and collective sentence interpretations and the variables that predict them. In our first experiment, we establish that adult English collective sentences with "the" or "some" in the subject are categorically collective in their interpretations. We further demonstrate that children's collective and distributive interpretations are predicted by an independent measure of lexical growth, consistent with the lexical refraction hypothesis, and that their collective interpretations are predicted by their distributive interpretations, consistent with the pragmatic scale hypothesis. Furthermore, the distributive interpretations produce complete mediation between lexicon and collective interpretations in a mediation analysis. In our second experiment, we take independent measures of Spanish-speaking children's knowledge of the Approximate Number System, inhibition, lexicon and phrasal syntax. We then fit a Piecewise Structural Equation Model with these variables, with high statistical power and showing high goodness-of-fit. We consider the contrast between this model of collective interpretations, which are putatively conversational implicatures, and quantity implicature models from previous studies.