Mixed Numbers Made Easy: Building and Converting Mixed Numbers and Improper Fractions

Abstract

After several years of observing and interacting with children, I have noticed their struggles with converting mixed numbers and improper fractions. I have tried several types of manipulatives, computer programs, pictures, and algorithm-based activity sheets. Even after being exposed to all these teaching approaches, many students still struggle with these representations. The concept of a mixed number—a whole number paired with a fraction—really boggles students' minds. More so, the idea of an improper fraction—a fraction with a numerator that is greater than or equal to the denominator—is virtually impossible for some fifth graders to grasp. They cannot connect their written algorithms to the concept or explain how they derived their answers. The reason for rewriting their answer in a different form was too abstract for them. Through direct work with my fifth-grade classes over the years, I have developed a new approach that produces great results and a deeper understanding of mixed numbers, improper fractions, and their relationship to each other.