At what stage do children begin to understand and manipulate concepts related to "teen" numbers?

Children typically begin to understand and manipulate concepts related to "teen" numbers during the Second Level of Counting. At this stage, children develop a more sophisticated understanding of quantities beyond simple counting and start recognizing patterns within numbers. They begin to grasp that numbers from 11 to 19 represent quantities that include a base of ten plus additional units. This cognitive leap allows children to identify why numbers in this range follow a particular pattern (for instance, understanding that 13 is 10 plus 3).

Understanding "teen" numbers requires not just rote memorization but also the ability to relate these numbers to their constituent parts (like recognizing that 14 is one group of ten and four more). Mastery of this concept is crucial for building a strong numerical foundation, which will be essential as they encounter more complex mathematical operations as they progress in their education.

In contrast, the First Level of Counting generally focuses on the basics of counting and recognizing quantities up to a certain number, while the Preparatory Stage is more about developing foundational skills prior to formal counting. The Formal Operational Stage pertains to a later stage in childhood when logical thought becomes more advanced, typically occurring in adolescence, which is beyond the relevant age for manipulating "teen" numbers.