Both, Common Core and Singapore Math emphasize that understanding of a unit fraction is a conceptual foundation for developing students’ understanding of fractions in the upper elementary grades. With this knowledge students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators (CCSS p.21). Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal and they develop methods for generating and recognizing equivalent fractions. (CCSS p. 27). Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. (CCSS p. 33)
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