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Objective: The authors investigated whether children with Down’s syndrome (DS) who have not started to produce number words understand the one-to-one correspondence principle (Experiment 1), and they looked at the relationship between number word knowledge and receptive vocabulary (Experiment 2). Method: Sixteen children with DS who did not recite the count list participated in Experiment 1, along with 2 comparison groups: 1 of 16 children with DS who recited up to 10, paired by chronological age, and another of 16 typically developing children paired by their ability to recite the list. The understanding of the principle was evaluated by a preferential looking task. Children saw 1 of 2 conditions. In the number condition, they heard number words and in the beep condition they heard computerized beeps. In both conditions, children saw videos depicting counting events that were principle-consistent or principle-inconsistent. Experiment 2 evaluated 25 children with DS using the Give-a-Number task and the Receptive Vocabulary subtest of the Wechsler Preschool and Primary Scale of Intelligence-III. Results: In Experiment 1, children in the number condition preferred principle-consistent videos, independent of their ability to recite the count list. Experiment 2 showed a strong correlation between number word knowledge and receptive vocabulary scores, independent of chronological age. Conclusions: The results suggest that the difficulty of children with DS in acquiring counting ability might not reflect a lack of understanding of the one-to-one correspondence principle, but might instead be related to vocabulary development.