Geometry Problems: One Step Beyond

From Introduction: "'Geometry Problems: One Step Beyond" is a collection of 25 sets of problems for students in grade 10 through 12. Each set contains three related problems, including one main problem, a warm-up problem that eases students into the work of the main problem, with an extension problem that takes students into more difficult but related concepts. About the book: Each of the 75 problems - warm-ups, main problems, and extensions - appears in this book on a separate reproducible worksheet page, with space allowed for students to work out their solutions. You may duplicate the pages and distribute them as in-class assignments or as homework. On the back of each student worksheet page is a discussion of the problem for the teacher, including the answer to the problem, clues to assist students in completing the problem, a solutions (sometimes more than one) that shows where the answer came from, and teaching suggestions that warn about points of confusion, indicate ways to get started and follow-up, and provide interesting background for the problems. Using the Problem: Problems are arranged to follow the standard 10th grade curriculum, starting with logical thinking, then properties of triangles, and leading into work with circles, area, and volume. There is no required order for using the 25 sets of problems, however; simply choose those sets that best suit your students' learning situation. Within each set of problems, it is best to assign the warm-up problem first, then the main problem, and finally the extension problem." From Preface: "With this book I have tried to give a set of problems that supplement the standard first-year geometry course. I have tried to cover all the major topics in the course. I must confess that I have a particular liking for the Pythagorean Theorem and have included many problems that use it somewhere in their solutions. Since most students have seen this property before entering geometry, I have assumed a familiarity with the theorem even though some geometry courses don't get to it until later in the year. I've also scattered problems including area and volume concepts throughout the later portions of this book." - author, Reuben Schadler