Learning to map number words onto their ordinal and quantitative meanings is a key step in the acquisition of formal mathematics. Previous neuroimaging work suggests that the intraparietal sulcus (IPS), the inferior frontal gyrus (IFG), and the fronto-temporal language network may be involved in representing number words. However, the contribution of early-developing numerosity representations to the acquisition of counting has not been tested in children. If regions that support numerosity processing are important for the acquisition of counting, then there should be functional overlap between numerosity representations and number word representations in the brain, before children have mastered counting. Using functional magnetic resonance imaging (fMRI), we identified numerosity processing regions in 3- to 5-year-old children during a numerosity comparison task. To identify neural representations of number words, we measured changes in neural amplitudes while those same children listened to number words and color words and while they listened to counting and alphabet sequences. Across multiple whole-brain analyses, we found that the bilateral IPS consistently supported representations of numerosities, number words, and counting sequences. Functional overlap between numerosities and unknown counting sequences was also evident in the left IFG, and in some cases number word representations emerged in the left hemisphere fronto-temporal language network. These results provide new evidence from children that primitive numerosity processing regions of the brain interface with the language network to ground the acquisition of verbal counting.