Mathematics Department

Essential Knowledge and Skills

Pre-Calculus Honors encompasses and extends topics and concepts of intermediate algebra. General topics included are: properties of functions, piecewise-defined functions, theory of polynomial equations, vectors, matrices and determinants, circular functions, trigonometric functions and their inverses, applications of trigonometry, sequences and series, polar co-ordinates and complex numbers, exponential and logarithmic functions, analytical geometry of the conic sections, and probability theory.

Indicators of Student Learning

Upon the completion of this course, students will describe and explain the concepts learned utilizing mathematical vocabulary and symbols in the following ways:

Problem Solving

• Select and describe appropriate problem solving strategies.

• 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.

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

• Use mathematical models to translate real world problems into algebraic form.

• Select and use appropriate methods for computing, e.g., mental computation, estimation, paper and pencil, and calculator.

Reasoning and Proof

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

• Collect data, graph the data points, derive an equation representing the data, graphing the equation, and comparing the two graphs.

Communication

• Express algebraic concepts using correct terminology and symbols in oral and written form.

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

• Build algebraic 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, paraphrasing, summarizing, research reports, notebooks.

• Discuss, explain, and justify their thoughts and ideas.

Technology

• 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 algebraically or graphically.

• Select and apply technology tools such as online resources and information for problem-solving.

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

• Use a graphing calculator to organize and analyze data.

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 algebraic proofs.

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

• Demonstrate competency in technology by using graphing calculators and computers in an appropriate manner.