Focus in grade 5

Focus in Grade 5, one in a series of grade-level publications, is designed to support teachers, supervisors and coordinators as they begin the discussion of a more focused curriculum across and within prekindergarten through eighth grade, as presented in Curriculum Focal Points. Additionally, teacher educators should find it useful as a vehicle for exploring mathematical ideas and curriculum issues involving the grade 5 mathematics curriculum with their preservice teachers. This book describes and illustrates learning paths for the mathematical concepts and skills of each fifth-grade Focal Point, including problems for students and powerful representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about mathematical thinking and provide a foundation for fluency with the core ideas. Also discussed are common student errors and misconceptions, reasons the errors may arise and teaching methods or visual representations to address the errors. Because learning paths cut across grades, some discussion of related Focal Points at grades 3 and 4 have been included to describe and clarify prerequisite knowledge and show how the grade 5 understandings build on what went before. Teachers should find these discussions of the learning paths, representations, problems and lines of reasoning valuable as they plan activities and discussions for their students and strive to help students achieve the depth of understanding of important mathematical concepts necessary for their future success.