Children's Construction of ‘Fair’ Representations of One-Third

Abstract

This article discusses the development of the concept of the fraction one-third by children from pre-Grade 1 to Grade 4 in terms of their ideas of fairness and equality of sharing. Twenty-four children were interviewed and asked to share a pancake fairly among three dolls. The context was chosen to allow children to use out-of-school intuition and understanding if preferred. Four levels of development are identified leading to the idea of fair fractions as those where each part contains the same amount of pancake. The identification of intermediate strategies for sharing should assist teachers in planning activities to achieve a mathematical understanding of fair fractions.