 Introduction and Overview Geometry Connections Geometry Connections emphasizes several big ideas in an integrated algebra/geometry context. The key concepts addressed in this course are: • Transformations (reflection, rotation, translation, dilation) and symmetry • Relationships between figures (such as similarity and congruence) • Properties of plane figures (such as equal or perpendicular sides or diagonals) • Measurements of plane figures (such as area, perimeter, and angle measure) • Measurements of three-dimensional shapes (such as volume and surface area) • Tools for analyzing and measuring shapes (such as the Pythagorean Theorem, trigonometric ratios, the Laws of Sines and Cosines, and coordinate geometry) • Investigation and proof (having found patterns, students conjecture and prove) • Geometric construction (with compass and straightedge) • Algebra (with substantial review of writing and solving equations and graphing) • Probability The course is structured around problems and investigations that build spatial visualization skills, conceptual understanding of geometry topics, and an awareness of connections between different ideas. Students are encouraged to investigate, conjecture, and then prove to develop their reasoning skills. Lessons are structured for students to collaborate actively by working in study teams. During class time, students work in study teams on challenging problems that introduce new material. In several circumstances, an investigation or challenge will be presented with a Task Statement and Further Guidance structure. These activities are designed to provide teachers with the freedom of deciding how structured or open to leave a mathematical challenge. The homework in the “Review & Preview” section of each lesson reinforces previously-learned skills and concepts and prepares students for new ones. The homework problems also allow students to apply previously-learned concepts and skills in new contexts and deepen their understanding by solving the same type of problem in different ways. Geometry Goals for Students Upon completing this geometry course, students should be able to: • pose mathematical questions, such as “What if...?,” meaningfully and appropriately. • make conjectures and test their validity. • recognize and represent patterns mathematically or in prose. • appreciate geometry as a connected, systematic branch of mathematics. • apply geometry to solve problems in both mathematical and real-world contexts. • critique a logical argument. • communicate their mathematical understanding effectively and formulate complete, logical arguments to support their conclusions. • use algebra to formulate and solve equations arising from geometric situations both on and off a coordinate grid. • exhibit creativity and perseverance in mathematical problem solving, with the ability to determine when an approach is not working and a new direction is needed. |