For years, students have been taught to cross multiply when presented with proportion problems. Few understood what they were doing or why they were doing it. Rarely were students invited to think about various representations to determine the relationship between the two ratios being compared. The ideas and activities in this guide will help you provide students with the conceptual understanding of ratios and proportional thinking that is essential for solving real-world problems and achieving success in higher-level mathematics.
It's All Relative includes thirty modules, which are aligned to specific Common Core State Standards. Each module in this accessible, spiral-bound flipchart addresses specific mathematical practices and common misconceptions; features timely classroom examples; includes proven, ready-to-use activities; and provides ideas for adapting activities to meet the needs of individual learners. The authors particularly emphasize how to use visual models--tables, tape diagrams, graphs, and double number lines--to represent ratios and proportional thinking. These visual models, which may be new to many teachers, enhance students' conceptual understanding and improve their ability to solve a wide range of proportional reasoning problems.
Collins, Anne: -
Anne Collins has thirty years of teaching experience having taught all grade levels K-12 including undergraduate and graduate level courses. She has been providing mathematics content professional development institutes and courses for teachers for the past fourteen years.
She was inducted into the Massachusetts Mathematics Educators Hall of Fame in 2005. She earned the ETACuisenaire Distinguished Service Award in 2011. Anne is the past president of the Association of Teachers of Mathematics in New England and the Association of Teachers of Mathematics in Massachusetts. She is an active member in the Association of Statewide Supervisors of Mathematics, the National Council of Teachers of Mathematics, and the National Council of Supervisors of Mathematics.
She is the series editor of NCTM's publication, Assessment Sampler: Tasks Aligned with Principles and Standards of School Mathematics andUsing Classroom Assessment to Improve Student Learning. She is or has served as a mathematics content author for on-line mathematics projects with CISCO, Raytheon, the Jason Foundation for Education and Math Resources. She was also a reviewer for NCTM's Focal Points, and Middle School Mathematics Journal. Anne is an elected member of the NCTM Board of Directors.
Dacey, Linda: - Linda Dacey, professor of mathematics and education at Lesley University, began her career teaching at the elementary level and early in her career, received an NSF grant to develop a model program for preparing middle school teachers. She works with pre-service and in-service teachers, helping them to develop both their content knowledge and their practice. Her commitment to the quality of mathematics education was noted when she was inducted into the Massachusetts Mathematics Educators Hall of Fame. She is a reviewer for NCTM's Teaching Children Mathematics, was guest editor for the recent issue of the New England Mathematics Journal's issue on equity, and a prolific writer of books and resource materials for both teachers and writers. Her research focuses on problem solving, number sense, and strategies for differentiation.
