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Key to Geometry introduces students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Includes: Book 3 of Key to Geometry
Key to Geometry introduces students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Includes: Book 2 of Key to Geometry
Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
Put compasses into your students' hands and behold the results! Hands-On Geometry teaches students to draw accurate constructions of equilateral triangles, squares, and regular hexagons, octagons, and dodecagons; to construct kites and use their diagonals to construct altitudes, angle bisectors, perpendicular bisectors, and the inscribed and circumscribed circles of any triangle; to construct perpendicular lines and rectangles, parallel lines, and parallelograms; and to construct a regular pentagon and a golden rectangle. Students will enjoy fulfilling high standards of precision with these hands-on activities. Hands-On Geometry provides the background students need to become exceptionally well prepared for a formal geometry class. The book provides an easy way to differentiate instruction: Because the lessons are self-explanatory, students can proceed at their own pace, and the finished constructions can be assessed at a glance. Grades 4-6
Topics include: Segment Constructions; Angles Constructions; Constructions Based on Congruent Triangle Theorems; Special Segments in Triangles; Circle Constructions.
Key to Geometry introduces students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Includes: Book 8 of Key to Geometry
Key to Geometry introduces students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Includes: Book 6 of Key to Geometry
Key to Geometry introduces students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Includes: Book 1 of Key to Geometry