Mathematics

The Dana Hall Mathematics Department cultivates mathematical thinkers who are prepared for the challenges they will face in a dynamic world.

Students succeed when they are appropriately challenged; thus, we provide differentiated instruction. Collaboration, the utilization of technology, and investigative tasks are some of the tools used to encourage students to be resourceful, questioning, curious, independent, and confident mathematical thinkers. We seek to inspire students to build connections between mathematical topics, across other disciplines, and to the world around them.

We encourage perseverance, problem-solving, and logical and creative thinking as students investigate patterns, data, geometric figures, graphs, numbers, functions, and applications. Dana Hall fosters a rigorous program of study, but also ensures that every student has the support needed to succeed by providing the time, space, and resources to enhance their understanding.
Preparation for continued mathematics study at the college level is a goal of Dana Hall’s Upper School Math Department.

MATHEMATICS CLASSES

Algebra I

This course covers traditional first-year algebra topics and further builds on an ability to utilize these skills in solving application problems. Topics include properties of real numbers, exponents, linear equations and inequalities, linear systems, functions, graphing, factoring, polynomials, and solving quadratic equations. (Open to students who have completed Pre-Algebra or the equivalent. Full year. 1 credit.)

Geometry

This course covers traditional topics in geometry emphasizing discovery along with the development and application of data analysis, probability, and algebraic skills. Topics include the Pythagorean Theorem, parallel lines, similar triangles, congruent triangles, special right triangles, an introduction to trigonometry, circles, parallelograms, polygons, area, and volume. (Open to students who have completed Algebra I, and with permission of the Department Head. Full year. 1 credit.)

Geometry Honors

This rigorous course focuses on the discovery and comprehension of traditional Euclidean geometry. The detailed structure of logic and mathematical argument is emphasized. This course covers traditional topics in geometry emphasizing discovery along with the development and application of data analysis, probability, and algebraic skills. Topics include the Pythagorean Theorem, parallel lines, similar triangles, congruent triangles, special right triangles, an introduction to trigonometry, circles, parallelograms, polygons, area, and volume. This course includes an in-depth look at introductory topics covered in an Algebra II course. (Open to students who have completed Algebra I, and with permission of the Department Head. Full year. 1 credit.)

Algebra II

This course continues to develop the students’ algebraic skills and introduces elementary functions. Linear, absolute value, quadratic, polynomial, and rational functions are explored both with and without the use of a graphing calculator. Additional topics include complex numbers, powers, radicals, inequalities, and systems of equations. (Open to students who have completed Algebra I and Geometry, and with permission of the Department Head. Full year. 1 credit.)

Algebra II with Applications

This course continues to develop the students’ algebraic skills and introduces elementary functions with attention to graphing, evaluating, simplifying, solving, and modeling. Linear, absolute value, piecewise, quadratic, polynomial, rational, radical, exponential, and logarithmic functions are explored both with and without the use of a graphing calculator. Other topics include inequalities, inverse functions, complex numbers, and systems of equations. (Open to students who have completed Algebra I and Geometry with a minimum grade of B, and with permission of the Department Head. Full year. 1 credit.)

Algebra II Honors

This course covers all of the topics of Algebra II, as well as a great deal of material from Precalculus. Topics such as quadratic, polynomial, rational, exponential and logarithmic functions, sequences and series, combinations, permutations, probability, and conics are studied in detail. These functions are explored with attention to graphing, evaluating, simplifying, solving, and modeling, both with and without the use of technology. In addition to the mathematical concepts
themselves, this course incorporates their theoretical underpinnings as well as their applications. (Open to students who have completed Geometry Honors with a minimum grade of B+, and with permission of the Department Head. Full year. 1 credit.)

Precalculus

Precalculus with Applications

This course includes a detailed study of trigonometry. Other topics include sequences and series, combinations, permutations, probability, and exponential, logarithmic, polynomial, and rational functions with and without the use of technology. The application of these topics to real-world problems is emphasized and developed throughout the course. (Open to students who have completed Algebra II with Applications with a minimum grade of B, and with permission of the Department Head. Full year. 1 credit.)

Precalculus Honors

During the first half of the year, this course completes the study of precalculus topics by building on our knowledge of functions, with an emphasis on trigonometry. Topics include the unit circle, trigonometric functions, their inverses, and polar coordinates. During the second half of the year, it covers the differential calculus topics taught in AP Calculus AB. The goal is to prepare students to take AP Calculus the following year. Students use a graphing calculator. (Open to students who have completed Algebra II Honors with a minimum grade of B, and with permission of the Department Head. Full year. 1 credit.)

Introduction to Calculus and Statistics

This course will introduce students to the study of calculus, where it focuses on the fundamental concepts of differential calculus, including limits, derivatives, derivative applications, and an introduction to indefinite and definite integrals. Additionally, this course will introduce students to statistics, covering the mathematics of gathering and analyzing data and drawing inferences from data. Statistics topics include sampling techniques, the Normal distribution, linear correlation, confidence intervals, and hypothesis testing. (Open to seniors who have completed Precalculus or are taking Precalculus concurrently, and have finished Algebra II with a minimum grade of B, and with permission of the Department Head. Full year. 1 credit.)

Calculus

This course focuses on the fundamental concepts of differential calculus, including limits, derivatives, and derivative applications. It introduces the concept of integration with applications that includes finding the area under a curve and investigating rectilinear motion. The application of these topics to real-world problems is emphasized and developed throughout the course. This course includes projects surrounding diversity, equity, and inclusion. (Open to students who have completed Precalculus with Applications with a minimum grade of B or Precalculus with a minimum grade of A, and with permission of the Department Head. Full year. 1 credit.)

Advanced Placement (AP) Calculus AB

This course covers the differential and integral calculus of real functions, including algebraic, trigonometric, and transcendental functions. Application problems include maxima/minima, rectilinear motion with velocity and acceleration, related rates, area between curves, volumes of solids of revolution, volumes by cross-sectional slicing, slope fields, and separable differentiable equations. AP examination in May is strongly encouraged for seniors and required for all other students in this course. (Open to students who have completed Precalculus Honors, Precalculus with Applications with a minimum grade of A-, and with permission of the Department Head. Full year. 1 credit.)

Advanced Placement (AP) Calculus BC

In addition to the topics of AP Calculus AB, this course covers lengths of curves, surface area, applications for physics, parametric equations, polar equations, vectors, further methods of integration, infinite series, and first-order differential equations. AP examination in May is strongly encouraged for seniors and required for all other students in this course. (Open to students who have completed Precalculus Honors or Calculus AB with a minimum grade of B+, and with permission of the Department Head. Full year. 1 credit.)

Advanced Placement (AP) Statistics

This course covers the mathematics of gathering and analyzing data and drawing inferences from data. Topics include sampling techniques, the Normal distribution, probability, linear correlation, confidence intervals, and hypothesis testing. Throughout the year, students work on investigative tasks that utilize real world data and allow them to apply the theoretical concepts learned in class. Students use a graphing calculator. AP examination in May is strongly encouraged for seniors and required for all other students in this course. (Open to students who have completed Precalculus with Applications with a minimum grade of B, or are taking Precalculus with Applications concurrently and have completed Algebra II with Applications with at least a B+, and with permission of the Department Head. Full year. 1 credit.)

Advanced Topics in Math (Honors)

This honors-level course is intended for the student who wants to further her study of mathematics outside of Calculus. The list of topics taught in this course changes on a year-to-year basis and may include compass and straightedge constructions, proof techniques and strategies, complex variables, number theory, group theory, abstract algebra, probability and combinatorics, topology, and linear algebra. (Open to students who have completed or are concurrently enrolled in AP Calculus AB or AP Calculus BC, and with permission of the Department Head. Full year. 1 credit.)

Mathematics

Upper School Departments