The third edition of this book offers a unique approach to making mathematics education research on the teaching and learning of fraction concepts readily accessible and understandable to pre-service and in-service K-8 mathematics teachers. Revealing students' thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers' experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features: Two new chapters dedicated to understanding the OGAP Fraction Framework and Progression - based on research conducted with hundreds of teachers - to gather and interpret evidence of student learning along a learning progression, referenced throughout the book so readers can apply the concepts to their instruction; A close focus on student work, including 180+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students' errors and misconceptions, as well as their developing conceptual understanding; A discussion of decimal fractions, also new to the third edition; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter Looking Back questions to allow teachers to analyze student thinking and consider instructional strategies for their own students; Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs; Accompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression. A Focus on Fractions is part of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and multiplication and division, this updated new edition bridges the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions. Marjorie M. Petit has provided leadership in the development and ongoing implementation of the Ongoing Assessment Project (OGAP) and is a partner in OGAPMath LLC. Robert E. Laird is Co-director of Teaching, Learning, and Research for the Vermont Mathematics Institute (VMI), USA. Bob is a OGAP National Facilitator and a partner in OGAPMath LLC. Caroline B. Ebby is Senior Researcher at the Consortium for Policy Research in Education (CPRE) and an Adjunct Associate Professor at the Graduate School of Education at the University of Pennsylvania, USA. Caroline is a National OGAP Facilitator. Edwin L. Marsden was a Professor of Mathematics and former chair of the Department of Mathematics at Norwich University, USA.