Mathematics Department

Essential Knowledge and Skills

Students in Geometry study Euclid’s postulates and theorems. Geometric properties for polygons, triangles and circles are studied as well as the reasoning and development of proofs. Students will explore geometric terminology and definitions. Students will also study the construction of geometric figures such as bisectors, perpendiculars, congruent angles, segments, and triangles. Topics of investigation include logic, angle and line relationships, triangle congruence and similarity, along with polygon and circle properties. Students will solve right triangles using the Pythagorean theorem and the trigonometric ratios of sine, cosine and tangent. Students will also 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 picture or diagram, looking for patterns, identifying counterexamples, choosing appropriate operations, and checking the reasonableness of results.

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

• Calculate perimeter, lateral face area, surface area, circumference, total area and volume.

• Solve a variety of multi-step, routine and non-routine problems verbally, numerically, graphically,geometrically, and algebraically.

Reasoning and Proof

• Understand properties, definitions, postulates, theorem and all aspects of the two- column 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 reasoning with properties from algebra 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 and notation 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 repetition, 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 discussions, visual presentations, written responses and multi-media presentations.

• Uses writing as a learning tool, e.g., journals, learning logs, paraphrasing, summarizing, research reports, and 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 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 creative works.

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

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 methods, 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 processes, presenting ideas and information in visual presentations, written responses, and multi-media presentations.

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