Educational Studies in Mathematics

, Volume 73, Issue 2, pp 105–120

# Children’s strategies for division by fractions in the context of the area of a rectangle

• Jaehoon Yim
Article

## Abstract

This study investigated how children tackled a task on division by fractions, and how they formulated numerical algorithms from their strategies. The task assigned to the students was to find the length of a rectangle given its area and width. The investigation was carried out as follows: First, the strategies invented by eight 10- or 11-year-old students, all identified as capable and having positive attitudes towards mathematics, were categorised. Second, the formulation of numerical algorithms from the strategies constructed by nine students with similar abilities and attitudes towards mathematics was investigated. The participants developed three types of strategies (making the width equal to 1, making the area equal to 1, and changing both area and width to natural numbers) and showed the possibility of formulating numerical algorithms for division by fractions referring to their strategies.

## Keywords

Algorithm Children’s construction Division by fractions The area of a rectangle The inverse of a Cartesian product

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