[b]Conceptual Objectives[/b] (Understanding Ideas)[br]Students will:[br][list=1][*]Understand what algebraic curves are and classify them by degree (linear, quadratic, cubic, quartic, etc.).[br][/*][*]Recognize the defining properties of conic sections (circle, ellipse, parabola, hyperbola) and their historical importance.[br][/*][*]Describe how symmetry, transformations, and parameters affect the geometry of curves.[br][/*][*]Explain the historical development of curves and their role in solving mathematical and scientific problems.[br][br][/*][/list][b]Skill-Based Objectives[/b] (Procedural & Analytical Skills)[br]Students will:[list=1][*]Derive and manipulate equations of conic sections, cubic curves, and quartic curves.[br][/*][*]Identify and compute key features such as centers, vertices, foci, asymptotes, and axes of symmetry.[br][/*][*]Apply transformations (translations, reflections, rotations, dilations) to curves algebraically and graphically.[br][/*][*]Use GeoGebra (or similar tools) to construct, visualize, and dynamically explore families of algebraic curves.[br][/*][*]Analyze calculus-related properties of curves (e.g., slope of tangents, critical points, and loci) at an introductory level.[br][/*][/list][br][b]Application Objectives[/b] (Real-World & Extended Uses)[br]Students will:[list=1][*]Interpret the role of conics in real-world contexts such as planetary motion, satellite orbits, optics, and architecture.[br][/*][*]Explore cubic and quartic curves to model complex geometric phenomena and patterns.[br][/*][*]Connect algebraic curves to modern applications in technology, design, and data visualization.[br][/*][*]Investigate and present historical and modern perspectives on algebraic curves to show their evolving significance.[br][/*][*]Integrate technology to simulate, test, and communicate findings about algebraic curves through interactive exploration.[br][/*][/list]