Written in a user-friendly, conversational style, the fourth edition of this groundbreaking text helps pre-service and in-service mathematics teachers build the comfort and confidence they need to begin talking to children about fractions and ratios, distilling complex ideas and translating research into usable ideas for the classroom. For two decades, Teaching Fractions and Ratios for Understanding has pushed readers beyond the limits of their current understanding of fractions and rational numbers, challenging them to refine and explain their thinking without falling back on rules and procedures they have relied on throughout their lives. All of the material offered in the book has been used with students, and is presented so that readers can see the brilliance of their insights as well as the issues that challenge their understanding. Each chapter includes children’s strategies and 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. The fourth edition of this popular text has been updated throughout and includes new examples of student work, updated artwork, and more. As with previous editions, an equally valuable component of this text is the companion book MORE! Teaching Fractions and Ratios for Understanding (2012), a supplement that is not merely an answer key but a resource that provides the scaffolding for the groundbreaking approach to fraction and ratio instruction explored here. MORE! includes in-depth discussions of selected problems in the main text, supplementary activities, Praxis preparation questions, more student work, and templates for key manipulatives.

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.