Supporting students to develop efficient procedures for fraction division, although important, should not be the only goal.
Instruction should also support the development of number and operation sense.
Fraction magnitude is a prerequisite for developing such number sense and operation sense (Behr et al. 1984). With fractions, number sense includes understanding magnitude or the size of an individual fraction in relation to a whole and in relation to other fractions. With fraction division, understanding what a reasonable quotient might be involves being able to compare the magnitude of the dividend with the magnitude of the divisor when the operation of division is carried out. This article will explore both modeling and equivalence as reasoning tools to support students’ developing number sense and understanding of the measurement interpretation of fraction division.