Mathematics Department

Essential Knowledge and Skills

Students in Advanced Geometry Honors study Euclid’s postulates and theorems. Geometric properties for polygons, triangles and circles are studied as well as the development of formal proof. Students will explore geometric terminology and definitions. Students also study the construction of geometric figures such as bisectors, perpendiculars, congruent angles, segments, polygons and circles. Topics of investigation include logic, angle and line relationships, triangle congruence and similarity. Students will solve right triangles using the trigonometric ratios of sine, cosine and tangent. The Law of Sine and the Law of Cosine will be used to solve non-right triangles. Students will find the volume, surface area and total area of geometric solids.

Indicators of Student Learning

Upon the completion of this course, students will:

Problem Solving

• Select appropriate method for problem solving.

• Utilize different problem solving strategies including; drawing and labeling a diagram, looking for patterns, identifying counterexamples, choosing appropriate operations and checking the reasonableness of results.

• Use analytical process to organize information, establish problem-solving strategies, solve the problem and analyze the results.

• Calculate perimeter, lateral area, total area and volume.

• Represent and solve routine and non-routine problems verbally, numerically graphically, geometrically and algebraically.

Reasoning and Proof

• Understand properties, definitions, postulates, theorems and all aspects of the two columns proof including drawing, planning and writing proofs.

• Present a logical argument in the form of a geometric proof using appropriate properties and theorems.

• Demonstrate the use of inductive and deductive reasoning to arrive at logical conclusions.

• Use definitions, postulates and theorems to prove angle congruency, triangle congruency and similarity.

Communication

• Express geometric concepts using correct terminology and geometric symbols in oral, pictorial and written form.

• Identify and classify various geometric figures such as triangles, polygons, and circles.

• Use the language of mathematics to clearly express mathematical ideas.

• Build geometric vocabulary by adding concepts and understanding

• Use communication strategies to facilitate retention of information such as repeating information, constructing mnemonics and taking notes.

• Synthesize information to answer questions, solve problems, and communicate ideas.

• Connect prior knowledge and new information to expand understanding of topics.

• Share ideas and information in small and whole class discussion, visual presentations, written response and multi-media presentations.

• Use writing as a learning tool, e.g., journals, learning logs, paraphrasing, summarizing, research reports, lab reports, notebooks.

Technology • Construct geometric figures using Geometric software.

• Use a graphing calculator efficiently and accurately for computation, graphing, and modeling a wide variety of mathematical concepts.

• Select and use appropriate technology to solve problems geometrically.

• Select and apply technology tools such as fractal generators, tessellation generators, construction software, online resources and information for problem-solving and real-world simulations.

• Collaborate with peers to use technology to compile and produce projects, models, and other creative works.

• Create and give multi-media presentations, e.g., Salt Palace project, Fractal web quest.

Assessment Upon the completion of this course, students will:

• Demonstrate competency in problem solving including; drawing and labeling a diagram, looking for patterns, identifying counterexamples, choosing appropriate operations, calculating results and checking the reasonableness of those results.

• Demonstrate competency in reasoning and proof by using appropriate properties and theorems in geometric proofs.

• Demonstrate competency in communication by using correct terminology, expressing ideas clearly, explaining analytical process, presenting ideas and information in visual presentations, written response, and multi-media presentations.

• Demonstrate competency in technology by creating and constructing geometric figures, projects, models and multi-media presentations.