Comparing E

Comparing Fractions

Fraction Learning Pathway

Compare fractions with unlike numerators and unlike denominators using models and symbols

Applying a variety of strategies to compare any two fractions, including comparing to benchmarks, using proportional reasoning or determining a common fractional unit (denominator) supports understanding of value.

Background

Comparing and ordering fractions allows students to develop a sense of fraction as quantity, as well as a sense of the size of a fraction, both necessary prior knowledge components for understanding fraction operations (Johanning, 2011).

Comparing and ordering fractions with different fractional units (or denominators) leads students to identify the need for equivalent fractions. When students determine an equivalent fraction they are changing the unit of measure by either splitting or merging the partitions of the original fraction. The following illustration demonstrates these concepts using an area model:

Splitting to determine an equivalent fraction for 23

A fractions strip with two thirds shaded in, equal to a fractions strip with four sixths shaded in.

Merging to determine an equivalent fraction for 68

A fractions strip with six eighths shaded in, equal to a fractions strip with three fourths shaded in.

The exploration of equivalence allows students to develop an understanding of equivalent fractions as simply being a different way of naming the same quantity; it also supports them in viewing the fraction as a numeric value. A solid understanding of equivalence helps students with fractions operations, especially addition and subtraction.

References:

Johanning, D. I. (2011). Estimation's role in calculations with fractions.Mathematics Teaching In the Middle School, 17(2), 96-102.