This task was used with third graders to develop fractional number sense. It emphasizes the relationship of the denominator to the size of a unit fraction. Students struggle with this fundamental understanding of fractions because it contradicts the relationship of whole numbers that they are familiar with (i.e. as the number in the denominator gets larger, the value of the unit fraction gets smaller). This task requires students to realize that the denominator signifies the number of equal parts in the whole. Consequently, the more equal parts there are in the whole, the smaller each fractional part becomes.
Microsoft Word version: 3_NF_FractionsComparing_Problem_Critique_ComparingFractions