Young children 'solve for x' using the Approximate Number System.

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. 'Solving for x' in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems well into high school. Here we asked whether 4-6-year-old children could solve for an unknown addend using the ANS. We presented problems either symbolically, using Arabic numerals or verbal number words, or non-symbolically, using collections of objects while preventing verbal counting. Across five experiments, children failed to identify the value of the unknown addend when problems were presented symbolically, but succeeded when problems were presented non-symbolically. Our results suggest that, well before formal exposure to unknown-addend problems, children appear to 'solve for x' in an intuitive way, using the ANS.