Overview

This part explores four strategies for comparing fractions (Van de Walle et al., 2009):

• More of the same-size parts (common denominator)
• Same number of parts, but parts of different sizes (common numerator)
• More and less than a benchmark such as one-half or one whole
• Distance from a benchmark such as one-half or one whole (could be distances more than or less than)

Knowing different fraction comparison strategies, situations in which they are useful, and ways of representing and explaining them helps teachers facilitate student learning. In particular, it provides a foundation for anticipating and analyzing student thinking.

Key Points

• Three ideas to keep in mind when considering fraction comparison strategies:
  • The connections between the strategy and the definition of a fraction being used
  • Situations in which the strategy is useful or questionable
  • Representations that are useful for explaining the strategy
• Equivalence can be used to make fractions easier to compare. For instance, to use the common denominator strategy to compare 2/5 and 3/8, each fraction can be rewritten as an equivalent fraction with a denominator of 40. Once the denominators are the same, one can simply compare the size of the resulting numerators. Or, to use the “more and less than a benchmark” strategy to compare 2/10 and 3/4, each fraction can be compared to an equivalent form of 1/2 (i.e., 5/10 and 2/4).