The overarching intent of this supplement is to describe how children understand and learn mathematics. For the most part, describing how children come to know fractions depends on how fractions are taught or presented to children. More so than with numbers, children’s school experiences play a large part in their knowledge of fractions. Children possess some informal knowledge of sharing or partitioning by halves, thirds, and fourths, but most do not have everyday experiences with fractions. Other than sharing something equally, children are unlikely to encounter anything other than the most basic fractions such as 1/2, 1/4, and 1/3. Although some children may encounter fractions in recipes, their understanding is usually contextualized; they do not usually transfer this knowledge to other fraction contexts. Children simply do not come across fractions in their everyday experiences the way they do whole numbers and geometry. Consequently, their understanding or misunderstanding of fractions is most often dependent upon their experiences with fractions in the school setting. This section will describe children’s intuitive notions of fractions, the typical representation of fractions to elementary school children, other conceptions of fractions which are essential in children’s understanding of later mathematics, and many of the common misconceptions or errors that children make with fractions.