Learning to measure the area of composite shapes

Abstract

Learning to calculate the area of composite shapes is an important application of area measurement but evidence suggests that many middle school students struggle to calculate the area of even simple composite shapes. In this article, I report the findings of a classroom design study conducted to investigate the collective development of strategies for measuring the area of composite shapes. I used the theory of strategy choice from an emergent perspective to analyze the collective strategy choice of two Year 8 mathematics classes (n = 31) and the findings revealed that the classes developed a repertoire of strategies to decompose the shapes, measure the area of the constituent shapes, and recompose those areas to calculate total area. The students used their strategies in flexible combinations in response to the varying features of the composite shapes presented and developed justifications to support their emerging adaptive strategy choice.