Hands-on sharing activities are necessary before students can understand the more abstract numeric representation of a fraction. Students need varied opportunities to practice sharing physical materials such as counters, pattern blocks, egg carton segments, marshmallows or stickers equally among a group of their peers. Increasing the number of recipients and redistributing the materials equally can help students understand why larger denominators mean smaller fractional amounts, an idea that is often counterintuitive for young learners. Sharing in this way also demonstrates how fractions can be part of a whole (sharing a pizza), parts of a set (sharing skittles) or larger than one (as in two and a half, or five halves).
As students share, they begin to identify situations where one fraction is larger or smaller than another. For example, students can compare a fraction they received to the whole amount and sort themselves into two groups: those who received less than half or more than half. Students will also find equivalent fractions informally when they compare. Again, if the fraction one-half is used as a benchmark, some students will find that amounts like three-sixths or five-tenths are neither bigger nor smaller than half.
Students should move gradually from representing fractions with concrete materials to using their own artwork. They should also explore other visual devices such as number lines and fraction strips. Fraction strips can be laid end-to-end to measure classroom objects, giving students a practical context for adding fractions. Number lines allow students to compare and order fractions using a familiar model from their study of whole numbers, deepening understanding of how fractions and whole numbers share the same space.
As students become comfortable with sharing activities, they should begin to discuss fraction names and solve problems aloud. For example, when comparing one-third and one-fourth of a pie, students should reason that if only three children share, everyone will get a larger piece. According to a study in the “International Journal for Mathematics Teaching and Learning,” music may be an overlooked context for talking about fractions since students typically develop literacy with whole, half, quarter and eighth notes. "Rhythm is a physical model of fractions in aural form," the report also states.
Students need opportunities to explore fractions in real-life contexts. Baking provides an opportunity for students to compare fractions, as they can see and feel that a half cup is larger than a quarter cup. Baking also encourages addition of fractions: A recipe may be doubled or quadrupled for a whole class, and students will need to problem-solve when they discover there is no three-quarter-cup measure in a set. As stated by the Institute of Education Sciences, measurement activities help develop the idea that fractions "allow for more precise measurement of quantities than do whole numbers." Even if your school has no access to a kitchen, students can measure the dry ingredients for a simple recipe, and a parent volunteer could finish baking it at home.