- Fractions(Content)

**Comparing** requires students to determine which fraction is the larger or the smaller. Comparing fractions assumes that the two fractions have the same whole, so is based in the part to whole meaning of fractions. Students should understand a fraction as a number and use benchmarks, such as 0, 1, ^{1}⁄_{2}, and ^{3}⁄_{4} to compare fractions. There are a variety of strategies for comparing fractions beyond determining a common denominator, including consideration of the relationship between the numerator and denominator. For example, students could quickly compare 1^{134}⁄_{2025} and 1^{1963}⁄_{2000} by realizing that the first fraction is closer to 1 since there is a greater difference between the numerator and denominator than in the second fraction Older students may use their knowledge of fraction as a quotient to determine decimal equivalencies for comparison.

Research Findings:

In this fractions research project, students frequently doubled the numerator and denominator of a fraction to generate equivalent fractions but demonstrated little understanding of how this procedure connects to the repeated partitioning of a measure, such as area (^{1}⁄_{4} = ^{2}⁄_{8} or ). Many students did not have consistent success with determining equivalent fractions by merging pieces, such as ^{18}⁄_{36} = ^{9}⁄_{18}