Progressions for the Common Core State Standards for Mathematics

Description: One of a series of documents describing the progression of a topic across several grade levels, informed both by research on children's development and by the structure of mathematics. In Grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares. In Grade 3 students start with unit fractions (fractions with numerator 1), which are formed by partitioning a whole into equal parts and taking one part, e.g., if a whole is partitioned into 4 equal parts then each part is 14 of the whole, and 4 copies of that part makethe whole. Next, students build fractions from unit fractions, seeing the numerator 3 of 34 as saying that 34 is the quantity you get byputting 3 of the 14 's together. Initially, students can use an intuitive notion of congruence ("same size and same shape") to explain why the parts are equal, e.g., when they divide a square into four equal squares or four equal rectangles.