Consider this research-based intervention approach to ratio using concrete, semiconcrete, and abstract representations to help students who struggle with this concept.
Amy E. Hunter, email@example.com, is the mathematics specialist for LEAD Public Schools in Nashville, Tennessee. Hunter works in classrooms to support teachers as they implement the Common Core State Standards for Mathematics. She is the former secretary of the Kentucky Council of Teachers of Mathematics (KCTM) and a frequent presenter at NCTM's annual and regional conferences.
Sarah B. Bush, firstname.lastname@example.org, is an assistant professor of mathematics education at Bellarmine University in Louisville, Kentucky. She is a former middle-grades mathematics teacher who is interested in relevant and engaging middle-grades math activities.
Karen Karp, email@example.com, is a professor of mathematics education at the University of Louisville in Kentucky. She is a former member of the NCTM Board of Directors and a former president of the Association of Mathematics Teacher Educators (AMTE). Karp continues to work in classrooms to support teachers, particularly those who work with students with disabilities.