Number sequences are defined in terms of children's abilities to construct and transform units. Children operating with the initial number sequence (INS) construct units of 1. They construct other numbers as strings of 1s and can count on, by 1s, from one number to a subsequent number. A critical benchmark in children's further numerical development is the construction of units of units, or "composite units." This development corresponds to the tacitly nested number sequence (TNS) wherein numbers are nested within other numbers. We report on a large-scale quantitative study of children's available number sequences and their relationships with later mathematical development, such as multiplicative reasoning and fractions knowledge. This study involved 5747 children from three cohorts surveyed at the beginning of second grade in 2013, 2014, and 2015. We document strong relationships between children's early construction of an INS and a TNS and the likelihood of their later development of multiplicative reasoning, a measurement meaning of fractions, and general mathematics achievement, while controlling for rote computational skills. Implications for teacher instruction are discussed.