(Numbers and Operations > Operations with Rationals > Multiplication and Division > Fractions)
To divide a fraction we must multiply the fraction by the reciprocal of the other factor. As teachers, this makes sense. To students, this can be a very confusing concept. The mastery of the algorithm for dividing fractions will almost guarantee a correct solution, but does nothing for the understanding of the concept.
Dividing Fractions Investigating Patterns with Multiplication introduces students to the relationship between multiplication and division and how this relationship is applied when dividing fractions. This document begins with a visual representation of both dividing whole numbers into fractional parts and multiplying whole numbers by a fractional part to arrive at the same answer.
Throughout the document students are guided through an explanation of why we multiply a fraction by the reciprocal of a factor when we are dividing fractions. Students will use a table to input information that is later used to match corresponding multiplication and division statements. They are also given numerous opportunities to practice dividing fractions and mixed numbers as the document progresses.