Deepening students' understanding of multiplication and division by exploring divisibility by nine

Abstract

This paper explores how a focus on understanding divisibility rules can be used to help deepen students’ understanding of multiplication and division with whole numbers. It is based on research with seven Year 7–8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a way of proving why the divisibility rule for nine works, using materials grouped in tens and hundreds. After the lesson, students’ understanding of multiplication and division was considerably deepened.