U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.3. Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
1.1.4. Use models, benchmarks, and equivalent forms to judge the size of fractions.
N.2. Algebra (NCTM)
2.3. Use mathematical models to represent and understand quantitative relationships.
2.3.1. Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
N.11. Grade 3 Curriculum Focal Points (NCTM)
11.2. Number and Operations: Developing an understanding of fractions and fraction equivalence
11.2.1. Students develop an understanding of the meanings and uses of fractions to represent parts of a whole, parts of a set, or points or distances on a number line. They understand that the size of a fractional part is relative to the size of the whole, and they use fractions to represent numbers that are equal to, less than, or greater than 1. They solve problems that involve comparing and ordering fractions by using models, benchmark fractions, or common numerators or denominators. They understand and use models, including the number line, to identify equivalent fractions.