Recent research has suggested that some children, after they learn the meaning of “four,” proceed to learn the next few numbers one at a time (Krajcsi & Fintor, 2023). This claim is in direct contrast with previous theories that argued for an inductive leap after learning “four” (Carey, 2009). We assessed children’s number knowledge using an adapted Give-N method that captured higher set sizes, and tests of executive function and working memory as an exploratory window onto the changes across stages. First, results support the claim that children exhibit partial-number knowledge beyond “four”. Second, executive function was associated with children’s jump from knowing numbers up to “four” (subset-knower stages) to knowing numbers above four, while working memory was associated with the change from partial to putatively full knowledge of number word meanings. These findings offer new insight into the conceptual change process and suggest a potential two-fold sequence in children’s induction of cardinality.