This study investigated the relationships between patterning skills, executive function skills, vocabulary knowledge, and mathematical language with children's numeracy development. A total of 140 first-year Hong Kong kindergarten children in K1 who followed up on to K2 participated in this study. Chinese children were assessed on their patterning skills, mathematical language, oral vocabulary at K1, number counting, and number word comparison at K1 and K2. Mothers were asked to rate their children's executive function skills at K1. With the child's age, mothers' education and arithmetic competence in K1 were controlled; patterning skills, executive function skills, oral vocabulary, and mathematical language at K1 uniquely contributed to arithmetic competence at K2. These findings highlight the need to consider the impacts of these cognitive and language knowledge and skills in future research, shedding light on the multifaceted nature of mathematics achievement determining factors. Findings also suggest that the instructions and interventions integrating patterning, executive function, and language skills may be an essential avenue for enhancing children's numeracy development in the early years and future mathematics achievement.