Dividing Fractions

Summary of "Dividing Fractions and Problem Solving" from Mathematics teaching in the Middle School

This article outlines how teachers helped a class of sixth graders comprehend the algorithm for dividing fractions (invert and multiply). In most textbooks, the article states, fraction division is explained with one or maybe two pictures showing why the problem turns out a larger answer than the whole (1/2 divided by 6 equals 12). Some students may gain a superficial understanding of dividing fractions from these pictures, but most of the time, the vague examples go over their heads as the teacher dives directly into teaching the algorithm. Unfortunately, many students are detached from any problems dealing with fractional division because it makes no sense to them - memorizing the algorithm becomes their crutch. In this lesson, however, students solve problems using their own pictorial representations. Not only do they solve one or two problems, they solve many problems and explain their answers verbally. After sharing together as a class, the students begin to see patterns in their math processes. They naturally find the common denominators between the numbers they are working with, and naturally note correlations between the written symbols and their pictorial representations.

At first, I wondered how students could really comprehend fractional division. It seems like such an abstract concept, and looking back on my own education, memorizing the algorithm worked great for me. I never struggled with dividing fractions. It was easy - just invert and multiply! But as I continued reading and computing the problems pictorially as the children in the article did, I began to notice patterns that I had never realized before. In addition, for the first time I felt like I understood why we invert and multiply. Working through the problems definitely assisted my own comprehension. I can only imagine how helpful it must be for a sixth grader to build understanding of fractional division through personally created representations. Indeed, I will keep this article and use it in my future classroom. Not only will I use the problems given to work on, I will use the method of teaching fractional division presented in this article. In so doing, I will be addressing many of the mathematical process standards: the students will create, use, and translate representations; they will communicate mathematically in both written and verbal contexts; they will problem solve by determining what the part and the whole is and what they are searching for; and they will reason and prove their answers with their representations and their words.