Comparing fractions using like numerators or like denominators helps students to develop a deep understanding of the role of the numerator and the denominator in a fraction as well as the difference in change of magnitude in each (i.e., asthe digit in the denominator increases, the size ofthe fractional unit decreases; as the digit in the numerator increases, the size of the fraction increases).
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 2/3
Merging to determine an equivalent fraction for 6/8
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.
Johanning, D. I. (2011). Estimation's role in calculations with fractions. Mathematics Teaching In the Middle School, 17(2), 96-102.
Comparing Fractions with Like Numerators or Like Denominators
This is a set of prompts consisting of purposely paired fractions to elicit the use of various strategies. The prompts may be used on different occasions depending on student readiness. Repeated practice and exploration in making comparisons between fractions will deepen student understanding. Encourage students to build models/representations and create contexts to support visualization of fractions, which in turn supports meaning-making.