The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were small, 13% of the variance in arithmetic skills could be explained by the sample, replicating the pattern, previously found with older children in PISA. Furthermore, the same cognitive skills were related to early arithmetic in these diverse populations. Only understanding of symbolic number explained variation in mathematical performance in all samples. We discuss the results in terms of potential influences of socio-demographic, linguistic and genetic factors on individual differences in mathematics.