Dean's great discovery : multiplication, division and fractions

Multiplication, division and fractions are 'hotspots' for students in the middle years with many students experiencing difficulty with these concepts (Siemon, Virgona & Cornielle, 2001). Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts (Young-Loveridge, 2005). In this article we show how an open-ended array problem enabled a Grade 5/6 student to think about the relationship between multiplication, division and fractions. In the article we describe the project and 'hot spot' mathematical tasks that we used and provide some background on multiplicative thinking before presenting the case and a commentary (Western Melbourne Roundtable, 1997) of one student's exploration. This case was documented whilst we were working on a collaborative project with a team of upper primary teachers and a group of pre-service teachers at a local primary school.