The fifth edition of this user-friendly textbook helps mathematics educators explore and explain the complex world of rational numbers. It translates research into usable ideas for the classroom, including reasoning strategies, models, and questioning techniques that promote deep understanding that cannot be achieved by merely practicing fraction computation.Updated throughout with new examples and models from research, each chapter in the new edition incorporates samples of student work for teacher analysis, as well as activities for practicing each thinking strategy, designed to be solved without rules or algorithms, using reasoning alone. All content has been used with students and is presented with the learner in mind, acknowledging the brilliance of students' insights as well as the issues that challenge their understanding. It covers a broad range of topics in the progression from relative thinking to proportional reasoning, including fractions, ratios, rates, operators, measures, percents, and more.For over two decades, Teaching Fractions and Ratios for Understanding has helped elementary and middle school teachers expand their understanding and teaching strategies for rational number topics. The fifth edition is essential reading for mathematics courses, teacher preparation courses, graduate courses preparing researchers in mathematics education, and parents engaged in home schooling.