# Mathematics

Through the study of Mathematics students cultivate their capacity for solving problems and harness the power of numbers to describe and model the world effectively. The curriculum aims to have students experience satisfaction and joy in working with numbers as they engage in critical thinking and analysis.

In the Nursery Division, students gain insight into the arithmetic properties of numbers. They discover how numbers help structure our perception of the world, working with manipulative tools that make numbers and mathematical concepts visible. Nursery students build number sense through the use of pattern blocks and Cuisenaire rods, which offer a visual representation of numbers and mathematical concepts. Students learn to recognize written numbers, understand and identify patterns in the world around them, and measure and compare quantities using various manipulative tools.

Lower Division students acquire the numerical reasoning skills necessary to grasp the properties of numbers as well as of algebraic relationships between numbers. In kindergarten, first, and second grade, students build algebraic reasoning skills by analyzing number patterns, estimating, and mastering addition and subtraction facts. In third, fourth, and fifth grade, these skills are used to solve multi-step word problems, analyze ratios, and master multiplication and division facts. In all grades, students strengthen their grasp of measurement and data analysis through hands-on work with manipulative tools and graphing projects. Throughout, students form a deep and nuanced appreciation of the properties of numbers, the significance of place-value, as well as a strong understanding of the application of mathematical concepts in the world.

Middle Division students learn to read the phrasing of patterns between numbers and relationships between variables, and discover the quadratic formula as a tool of analysis. Working with formulas, students solve for x in word problems, which are at the heart of understanding abstraction, and in analogies, which challenge students to derive relationships between the known and the unknown. Instruction is differentiated: in sixth and seventh grade, Math is taught at two distinct levels of competency, in eighth grade Math is taught at three distinct levels of competency. Sixth grade Math is comprised of a review of the decimal system, factors, fractions, and operations, as well as ratio, proportion, percent, integers, and coordinate graphing. Fundamental concepts of Geometry (area and perimeter of polygons and circles) and Statistics round out the year. At each stage, students strengthen their problem-solving skills and articulate and demonstrate their understanding of the material. Seventh and eighth grade Math combined form the equivalent of a traditional Algebra I course. Seventh graders explore variable expressions, order of operations, properties of real numbers, multi-step equations, formulas, and set theory. Eighth graders learn to work with factors, quadratic equations, algebraic fractions, systems of equations, inequalities, irrational numbers, and the quadratic formula. At all levels, we strive to cultivate active and independent problem solvers eager to engage with mathematical concepts. Students hone the requisite skills and build a solid foundation in arithmetic, algebra, geometry, statistics, probability, data analysis, and mathematical modeling.

The core of the Upper Division Mathematics curriculum follows a traditional independent school sequence: Geometry in ninth grade, Algebra II in tenth grade, Pre-Calculus in eleventh grade, and Calculus in twelfth grade. Instruction is differentiated: Geometry and Algebra are each taught at two distinct levels of competency; both Pre-Calculus and Calculus are taught at three distinct levels of competency. In Geometry, students discover properties of shape and space through deductive reasoning as they explore the creation of axiomatic structures through theorems and proofs. In Algebra II and Trigonometry, students solve complex problems, using algorithms to interpret a range of functions -- exponential, logarithmic, quadratic, linear, sine, and cosine -- algebraically and graphically. Calculus covers the concepts of differentiation and integration with applications to rates of change, optimization, area, and volume.

This core curriculum is complemented by a broad range of elective courses with topics including vector analysis, group and field theory, analytic geometry, modeling with parametric equations, combinatorics, probability, statistics, data mining, sequences and series, recursion, polar coordinates, and an introduction to differential calculus. Some of the most far-reaching and compelling ideas in Mathematics are broached in advanced Math seminars, a problem set-based course for students with serious interests in pursuing higher mathematics. Topics are explored with analytical rigor in logic and proof while allowing for intuition and approximation. Fields of inquiry include number theory, inversive geometry, linear algebra, multivariable calculus, finite calculus, continued fractions, game theory, and advanced problem solving.