 ## Math Courses

### Mathematics I Year

Darrow's Math sequence begins with this course, taught non-traditionally. Topics include number sense, linear, absolute-value, and quadratic functions. This is the first year of an integrated, student-centered, and problem-based four-year Math program. In class, students utilize the Harkness method by presenting their solutions to problems and, with the teacher’s facilitation, identify key concepts and surprising connections between mathematical ideas as they emerge.

### Geometry Year

Geometry is essential as a means to giving students the quantitative skills to describe and measure the 2D and 3D world. It is a fundamental part of understanding such diverse applications as visual arts, navigation, construction, design and architecture, etc. It is also the classic manner of fostering the mathematical skill of logical reasoning and proof. And it provides a visual means of reinforcing and enhancing the algebraic skills that were stressed in Algebra I and will be expanded upon in Algebra II. Thus, at Darrow, Geometry is the second in the series of three required year-long courses. The primary topics in this course include: a review of the properties of points, lines, angles & polygons, an introduction to logical statements and proof, parallel and perpendicular lines, triangle congruence, ratios and proportions, right triangle trigonometry, properties of quadrilaterals, properties of circles, arcs and chords, two dimensional measurement involving perimeter, circumference and area, properties of three dimensional solids, as well as measurement of these solids involving surface area and volume. In addition to lectures, nightly homework assignments, quizzes and tests, students are assessed through lab exercises involving Geometer’s Sketchpad, a computer drawing program that can be used both analytically and creatively.

For students who have completed Algebra I of old Math sequence

### Algebra II Year

Algebra II is distinguished from Algebra I in two ways. First, it emphasizes an increased level of proficiency in the fundamental skill set of manipulating variables and equations, such as graphing, factoring and simplifying. Second, it stresses the central importance of functions in understanding any quantitative relationship. Each new unit covers a different “family” of functions and explores the overlapping ways of describing their properties, graphing their key points and end behavior, solving their roots and modeling their applications in real-world phenomena. The primary topics in this course include: a review of linear functions and inequalities; solving systems of linear equations graphically, algebraically, and with matrices; quadratic functions, higher degree polynomial functions, and rational exponent and radical functions. Depending on the class, time is spent on exponential and logarithmic functions, as well as an introduction to the unit circle and trigonometric functions. In each unit, the TI-84 graphing calculator is used extensively, both as a utility for calculations as well as a tool for exploring function properties. At Darrow, Algebra II is the last in the series of three required year-long courses, typically preceded by Algebra I and then Geometry. Most students continue on to our higher level elective courses, depending on the year they complete Algebra II, as well as their post-high school goals and interests. Students who successfully complete Algebra II are well-prepared for the mathematics portion of the SAT.

### Pre-Calculus Year

Pre-Calculus is an in-depth study of functions and ways in which they can be manipulated. Course topics include, but are not limited to, combinations and composition of functions, graphing transformations, exponential and logarithmic functions, trigonometry, rational functions, conic sections and an introduction to limits. Pre-Calculus prepares students for Calculus by providing them with greater understanding of fundamental concepts of Algebra.

Prerequisite: Algebra II

### Calculus Year

Calculus is an advanced mathematics topic that requires abstract thought. The first semester is devoted to the derivative as defined by the slope of a curve; students begin by investigating limits and use this concept through formal proofs to define derivative. As the semester continues, students look at increasingly complex ways in which to take derivatives of various common functions. During the second semester, students investigate the integral, as defined by area under a curve. This study begins with a look at Riemann sums and antiderivatives, and progresses to more complex ways in which to take integrals, including substitution, integration by parts, algebraic identities, and improper integrals. The second semester ends with the study of practical applications of the integral. Prerequisites: Pre-Calculus or permission of Math Department Chair.

Prerequisite: Pre-Calculus or permission of Math Department Chair.

### Advanced Topics in Calculus Year

In the year long course, Advanced Topics in Calculus (ATC) we will be studying many advanced topics. These may include: more advanced differential equations, parametric equations, polar equations, vectors, more advanced applications of derivatives and antiderivatives, more advanced series and sequences, and more that will be decided amongst the class.

Prerequisite: Calculus

### Advanced Geometry and Design Fall

Advanced Geometry is a one semester, upper level elective course that pushes students to express geometric and related mathematical ideas through visual and tactile means. Possible topics explored in depth include fractal art, tessellations and Islamic tile art, topology, map making, origami, knots & weaving, Bezier’s curves, optical illusions and anamorphic art, and non-Euclidean Geometry. Student-driven projects will be the primary means of demonstrating knowledge and success in the class, and will heavily depend on computer based drawing and modeling applications such as Geometer’s Sketchpad, GeoGebra and Google SketchUp. Three dimensional art and construction projects will complement the digital learning environment.

This course is open to those who have completed Algebra II.

### Matrix Algebra Fall

Matrix Algebra is an in-depth study of matrices and their properties. Course topics include, but are not limited to, adding, subtracting, and multiplying matrices, an introduction to vector algebra, solving matrix equations through inverse and Gauss Elimination methods, linear dependence and independence, linear transformations, subspaces, and calculating eigenvalues and eigenvectors. If time permits, the class will move on to cover powers of matrices, the Gram-Schmidt process, and/or QR factorization.

Th​is ​course is open to ​those who have completed Algebra II.