Math Explorations with a Geoboard

The activities presented in this book are designed to be used with a geoboard or dot paper. Students in Grades 3-10, as well as adults in preservice and inservice programs, will enjoy this practical resource. Each page is a prelude to more formal activities and exercises in the textbook. Why Use a Geoboard? Geoboards are certainly not a new device on the commercial market, but we believe that they have an important contribution to make in helping more students learn mathematics. Using a geoboard in the math classroom can make a significant contribution in several ways: It is a flexible and versatile tool. This makes it possible to use the geoboard in a wide variety of ways without prohibitive cost or extensive preparation and training. It helps teachers provide students with mathematical experiences that proceed from concrete to pictorial to abstract so that retention is greater. It provides students with a stimulating medium that keeps them actively involved while they are learning mathematical concepts. Active involvement and variety increases their motivation, and motivated students learn better. Students can better identify relationships and properties by building figures. Building figures on a geoboard or dot paper often saves time. Many exercises feature problems where the figures can be constructed quickly because the examples chosen for vertices, midpoints, etc. use nail or dot paper points. Building or drawing is a distinctly higher-level task than many of the identify exercises found in some standard textbooks. What s in This Book? This 180-page, reproducible resource book allows students to explore standards-based problem solving activities. The motivating collection offers: 3 free exploration activities 11 problem solving puzzles and games 5 problem solving investigations 16 graphing activities 50 activities involving polygons and their properties 15 fractions, ratio and percent activities 9 logical reasoning and communication activities Bonus word problems on selected pages Masters for teachers Selected answers and comments Challenging opportunities are provided throughout the book. Students are frequently asked to make generalizations based on the results of their work and create their own problems. In addition, problems such as drawing a triangle with a given perimeter are quite challenging because they require a student to use square roots and the Pythagorean Theorem. Finally, some exercises also help students see the limitations of continuing to use geoboards or dot paper exclusively or forever!