Final answer:
The first permanent tooth to typically erupt in a child's mouth is the molar, specifically the first molar, which appears between the ages of 6 and 7.
Step-by-step explanation:
The first permanent tooth to erupt in a child's mouth is most often a molar. Specifically, the first permanent molars, also known as the 6-year molars, typically emerge behind the last baby teeth without replacing any deciduous teeth. They usually appear between the ages of 6 and 7. Incisors are generally the first deciduous teeth to fall out and are replaced by permanent incisors. However, they are not the first permanent teeth to erupt. The sequence of tooth emergence can vary in individuals, but the first molars are most commonly the first to make an appearance in the permanent dentition.