The Mathematics Department strives to provide a program in which each student is challenged according to his or her ability to develop facility in using mathematical skills. This program has two main goals: an immediate one of preparing each student for future courses in mathematics and related disciplines and a long-range one of bringing students to a level of mathematical knowledge and competence which will enable them to approach any problem they encounter through various problem solving strategies. Each level of mathematics focus on the following Common Core Standards for Mathematical Practice: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Construct viable arguments and critique the reasoning of others, Model with mathematics, Use appropriate tools strategically, Attend to precision, Look for and make use of structure, Look for and make use of structure in repeated reasoning.
In this course students explore numerical, graphical, verbal, and analytical relationships through linear, exponential, and quadratic equations. Students examine the relationships between numbers, learn how to solve one variable equations, and learn how to communicate using math notation. Students interpret verbal, graphical, tabular, and algebraic representations of linear and quadratic functions and apply them to problem solving. They demonstrate mastery by accurately identifying the best method to use in a given situation. In addition, students engage in data analysis by choosing how to represent data visually and by using mathematical tools to extract measures of central tendency and spread from histograms and other displays of data.
This course helps students use logical reasoning to understand and analyze geometric shapes and their spatial properties. Students learn to prove conjectures about the basic concepts of size and shape on the coordinate plane and in three-dimensional space within the framework of Euclidian geometry. Students use their knowledge of basic geometric properties in order to manipulate and evaluate multi-dimensional figures.
In this course students explore numerical, graphical, verbal, and analytical relationships through exponential, logarithmic, polynomial, rational, and radical functions. Throughout the course students explore the relationship between these functions and apply inverse functions accordingly. They build on their understanding of linear relationships in order to explore and understand exponential relationships, and by solving exponential functions learn the necessity of logarithmic functions. Students analyze polynomials to understand patterns and trends between graphs, solutions, and equations, they manipulate and solve rational and radical equations, and they learn how to graph and solve on their own and with graphing calculators. The year culminates in an analysis of data which requires students to choose which type of function best models the data sets given, make predictions, and draw conclusions.
In this course students use trigonometry and advanced algebra to progress from finite mathematics to an analysis of infinite relationships. Students extend their knowledge of polynomial, rational, exponential and logarithmic functions through examination of the numerical, graphical, verbal, and analytical representations. From the various representations, students develop a sophisticated analysis of each function and connect the representations to one another. They also learn to apply algebra skills and understanding of functions to trigonometric relationships while further developing their understanding of trigonometry. Through these extensions, students develop an understanding of how the behavior of both algebraic and trigonometric functions is modeled in various applications. The year culminates in an analysis of data which requires students to choose which type of function best models the data sets given, make predictions, and draw conclusions.
In this course students learn about the mathematics of motion and change by solving problems, numerically, graphically, verbally, and analytically. Students learn limits in order to draw conclusions based on end behavior. They also learn to differentiate so that they can determine instantaneous rates of change. Finally, they learn to integrate in order to find the area and volume of any shape. Mastery of these concepts allows students to express and interpret functions and their derivatives through multiple representations in order to make connections and solve a variety of problems.