Honors Geometry / Geometry 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); and 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.
Honors Algebra 2 / Algebra 2 aims to apply and extend what students have learned in previous courses by focusing on finding connections between multiple representations of functions, transformations of different function families, finding zeros of polynomials and connecting them to graphs and equations of polynomials, modeling periodic phenomena with trigonometric, and understanding the role of randomness and the normal distribution in making statistical conclusions. On a daily basis, students will use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. The course is well balanced between procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem-solving), and adaptive reasoning (extension and transference).
Honors Precalculus / Precalculus is designed for students who have successfully completed Honors Algebra 2. Students will use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study mathematical concepts and the relationships among them. Students will use functions and equations as tools for expressing generalizations. Precalculus combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Facility with these topics is especially important for students intending to study calculus, physics, and other sciences, and/or engineering in college.
AP Calculus AB / BC This course will be the equivalent of first semester college calculus; all students taking calculus will be encouraged to take the Advanced Placement exam. Though equivalent, we have an opportunity with our small class size to build a more solid foundation of calculus concepts than is possible in a college course given their larger class size and intense pace. As a result, the intent here will be to establish an intuitive understanding of change and the way calculus can quantify change. Graphic calculators and computer algebra systems will be an integral part of the program leading to a deeper understanding of applications and an expertise with current technology. Applications will be presented analytically, numerically, graphically, and verbally and students are expected to communicate their solutions and justifications verbally and in written form. Special attention is given to helping students use correct justification of answers using specific theorems and correct units as part of their analysis.
Honors Statistics / Statistics is the study of the collection, organization, analysis, interpretation, and presentation of data. In today’s technological age, we are surrounded with an abundance of data and, in turn, statistics are used to aid in the decision-making process in many societal issues. This course will introduce students to major statistical concepts allowing them to effectively collect and analyze data. Successful completion of this course will allow students to walk away with the ability to critically think about statistical methods, and the validity of conclusions drawn from the statistics they see in their everyday lives.
AP Statistics is a college-level course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes — exploring data: describing patterns and departures from patterns; sampling and experimentation: planning and conducting a study; anticipating patterns: exploring random phenomena using probability and simulation; and statistical inference: estimating population parameters and testing hypotheses. The course is heavily centered on active participation both in a traditional classroom lecture setting as well as in a more hands-on project-oriented learning environment (both group and individual). Students who successfully complete the course and exam may receive credit, advanced placement or both for a one-semester introductory college statistics course.