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US Mathematics


The Mathematics Department strives to develop logical and creative problem solving skills in all students while providing them with the background to thrive in college mathematics and related courses. Students learn mathematics from numeric, algebraic, graphical and contextual approaches, . All Upper School students will take Algebra 1, if necessary, and some level of Geometry and Algebra II. All geometry courses contain a quarter’s worth of introductory statistics and probability, so all students have exposure to this important branch of mathematics. Most students take math every year, and many students take some level of calculus and/or a full year of statistics by the time they graduate. Students will need a TI-83 or 84 graphing calculator in a variety of courses over their time at Severn. The Mathematics Department recommends that students taking Geometry, Algebra II or Precalculus in the following year do approximately five hours of review on Khan Academy over the summer.
 
Computer Science courses at Severn likewise introduce students to logical and algorithmic thinking, prompting students to solve novel problems and model innovative solutions. Severn offers CS courses as stand-alone units, but individual courses can be combined to provide a more structured and in-depth sequence. Courses cover programming, robotics, and cybersecurity with a number of pioneer courses, two Advanced Placement level courses, and one course offered through the Malone Schools Online Network. Computer courses require a full featured computer running Windows, OS X, or Linux.

  • Integrated Math II

    Integrated Math II

    Integrated Math II is a math course which continues the study of algebra, geometry and data analysis begun in Integrated Math I.  By the end of the course, students will have covered all the material in Algebra 1, such as graphing lines and quadratics and applying the rules of exponents.  Geometry topics will include similar triangles and special right triangles, which form the basis for trigonometry in future math courses.  In data analysis, students will move on to analyzing and graphing two-variable data with linear regressions and also computing classical probability.  Students will progress to Algebra 2 or Intermediate Algebra 2 in the junior year. 

    This course will not run after the 2025-2026 school year.

  • Algebra I

    Algebra I

    This course begins with a review of operations on real numbers and techniques for solving linear equations in one variable. The course covers linear equations and inequalities in two variables, including the characteristics of their graphs and techniques for finding their equations. Students solve absolute value equations and systems of equations and inequalities in two variables. They learn to add, subtract, multiply, and divide monomial and polynomial expressions. Students are introduced to properties of exponents and exponential functions. Students also learn various techniques for solving quadratic equations and are introduced to the basic characteristics of the parabola. Multiple representations (verbal, graphic, algebraic, and numeric) and application problems are stressed throughout the course. The course concludes with a study of techniques for simplifying radical expressions as time permits.
    Prerequisite: mastery of pre-algebra skills

  • Intermediate Algebra II

    Intermediate Algebra II

    Intermediate Algebra II follows the standard Algebra II curriculum with an emphasis on strengthening the core concepts of Algebra I, beginning with a review and deeper study of topics from Algebra I, and then proceeding to new units on quadratic functions, relations and functions, powers and roots, exponential functions, radical functions and polynomial and rational functions. Throughout the course, students learn algebraic, numeric and graphic methods to solve problems that model real-life applications.
    Summer work on algebra skills is strongly encouraged.
    Prerequisite: departmental approval and a C- or better in Geometry

  • Algebra II

    Algebra II

    In this course students expand their investigation into the theories of Algebra with an emphasis on functions and relations. After a brief review of the topics covered in Algebra I, students study linear functions, linear systems, absolute value functions, quadratic functions, polynomial functions, radical functions, rational functions, exponential functions, function transformations, arithmetic and geometric sequences as time permits, and an introduction to trigonometry as time permits. Students will learn to solve problems using a variety of methods including with graphical software or a graphing calculator.

    Summer work on Algebra skills is strongly encouraged.

    Prerequisite: department approval and a B- or better in Geometry

  • Honors Algebra II

    Honors Algebra II

    This course addresses the same topics covered in Algebra II on a more intense level and at a faster pace.For example, students will do non-routine problems in addition to skill-builder exercises. Because the class moves at a faster pace, the course includes certain extensions, especially in the area of trigonometry, not covered in Algebra II.
    Summer work on algebra skills is strongly encouraged.
    Prerequisite: Departmental approval, strong algebra skills and (a) an A or better in Geometry or (b) a B or better in Honors Geometry.


  • Geometry

    Geometry

    Students study traditional Euclidean geometric topics, including parallel lines, congruence, similarity, polygons, right triangles, circles, and area and volume of 2D and 3D figures. Particular emphasis is placed on discovery, inductive and deductive reasoning, logic, proof, and problem solving. Concepts of Algebra I, including linear expressions and equations, are reinforced in applications of geometric concepts. The last part of the course is devoted to the study of data analysis and probability topics, including measures of central tendency, measures of dispersion, displaying and interpreting data in various forms, classical probability, and an introduction to samples and populations.
    Prerequisite: C- or better in Algebra I

  • Honors Geometry

    Honors Geometry

    Honors Geometry addresses the topics studied in Geometry in greater depth and at a faster pace. The overarching themes are problem solving and reasoning. As this course is different from previous algebra-based courses and more rigorous than the Geometry course, students must regularly engage in independent learning, demonstrate initiative, and exhibit a high level of numeracy.
    Prerequisite: Departmental approval and an A or better in Algebra I

  • Precalculus

    Precalculus

    Precalculus expands upon topics introduced in Algebra II with emphasis on domain, range, zeros, end behavior, symmetry, and inverses for polynomial, rational, exponential, and logarithmic functions. All functions are taught from verbal, symbolic, numerical and graphical perspectives. Approximately one quarter of the year is devoted to an in-depth study of trigonometry.

    Prerequisite: departmental approval, strong algebra skills, and (a) an A or better in Intermediate Algebra II or (b) a B- or better in Algebra II or (c) a B+ or better in Data Science or Statistics & Production.

  • Honors Precalculus

    Honors Precalculus

    This course, which prepares students for AP Calculus AB, addresses the topics of Precalculus in greater depth and at a faster pace. For example, students will do non-routine problems in addition to skill-builder exercises. Because the class moves at a faster pace, the course includes certain extensions, especially in the area of trigonometry, not covered in Precalculus. In addition, sequences and series are also covered as time permits.
     
    Prerequisite: Departmental approval, strong algebra skills, and (a) an A or better in Algebra II* or (b) a B or better in Honors Algebra II
    *Students who enroll in Honors Precalculus after completing Algebra II should be aware that trigonometry is studied more deeply in Honors Algebra II than in Algebra II.

  • Honors Functions / Calculus A

    Honors Functions/Calculus A

    The first semester of this fast-paced course investigates the characteristics of polynomial, rational, exponential, logarithmic and trigonometric functions. Domain, range, zeros, end behavior, symmetry and inverses are emphasized. The second semester covers the A portion of AP Calculus AB with the following topics: limits and continuity, differentiation, applications of derivatives, optimization and modeling rates of change. Throughout the year all topics are approached from verbal, graphic, numeric and symbolic perspectives. This course prepares students for the study of AP Calculus BC the following year. Due to the fast-paced nature of the course, students are expected to do substantial work outside the classroom including one or two textbook sections of homework problems per assignment.
    Prerequisite: Departmental approval, strong algebra skills, and an A or better in Honors Algebra II

  • Honors Calculus

    Honors Calculus

    The course starts with a quick review of precalculus topics most often used in calculus and then covers the following differential calculus topics: continuity and limits; derivatives from verbal, graphic, numeric and algebraic perspectives; applications of derivatives including optimization; modeling rates of change; and exponential growth. Integral calculus topics follow.
    Prerequisite: Departmental approval, strong algebra skills, and (a) a B+ or better in Precalculus or (b) a B- or better in Honors Precalculus.

  • AP Calculus AB

    AP Calculus AB

    The course begins with the following differential calculus topics: continuity and limits; derivatives from verbal, graphic, numeric and algebraic perspectives; applications of derivatives including optimization; modeling rates of change; slope fields; and exponential growth. Integral calculus topics follow with Riemann Sums, the definite integral, area, volumes of solids with known cross sections, volumes of solids of revolution, indefinite integrals, techniques of antidifferentiation and numerical approximations to definite integrals. Students are required to take the AP Calculus AB exam at the completion of the course. Because this course involves college-level study in content, rigor, pacing and assessment, students must regularly engage in a high level of independent learning, demonstrate initiative and study course materials outside of class. They should understand that there is potential for a dip in the grades they typically earn in math courses.

    Prerequisite: Departmental approval, strong algebra skills, and (a) a B+ or better in Honors Precalculus or (b) a B- or better in Honors Functions/Calculus A or ( c) a B or better in Honors Calculus.

    **On rare occasions, a student who earns an A or better in Precalculus and who performs well on a Severn-designed assessment during the week after final exams may take AP Calculus AB. Students interested in this opportunity must meet with the math department chair before final exams.

  • AP Calculus BC

    AP Calculus BC

    This course begins with a brief review of differential calculus. Integral calculus topics follow with Riemann Sums, the definite integral, area, volumes of solids with known cross sections, volumes of solids of revolution, indefinite integrals, techniques of antidifferentiation and numerical approximations to definite integrals. Other topics include calculus of parametric, polar, and vector functions, integration by parts and partial fractions, improper integrals, L’Hopital’s Rule, differential equations, analysis of slope fields, Euler’s Method and systems of ordinary differential equations, series, limits of a sequence of numbers, power series and Taylor Series including error analysis. Students are required to take the AP Calculus BC examination at the completion of the course.

    Prerequisite: Departmental approval and (a) a B or better in Honors Functions/Calculus A, or (b) 3 or better on the AP Calculus AB exam upon completion of AB Calc, or (c) an A or better in Honors Calculus and a 3 or better on the AP Calculus AB exam.

    **On rare occasions, a student who earns an A or better in Honors Precalculus and who successfully completes (in the opinion of the math department) an approved non-Severn Calculus I course may take AB Calculus BC. A Severn-designed assessment after such course may be required. Students interested in this opportunity must meet with the math department chair before final exams.

  • Linear Algebra and Advanced Calculus Topics

    Linear Algebra and Advanced Calculus Topics

    This course is designed for students who want to pursue the study of higher level mathematics during high school. Linear Algebra is the study of solving systems of equations with multiple variables. Topics studied in Linear Algebra include matrices, determinants, lines and planes in space, vector spaces, linear mappings between such spaces, and Eigenvalues. The applications of Linear Algebra will include: analytic geometry, calculus, engineering, physics, computer science, computer animation, and the social sciences as well as the connections between linear algebra and abstract algebra. 
     
    Prerequisite: Students concurrently enrolled in or who have completed AP Calculus BC are eligible.

  • Data Science

    Data Science

    This year-long course introduces students to the main ideas in data science through tools such as Google Sheets, Python, Data Commons, and Tableau. Students will learn to be data explorers in project-based units, through which they will develop their understanding of data analysis, sampling, correlation/causation, bias and uncertainty, probability, modeling with data, data-based arguments, the power of data in society, and more. At the end of the course, students will have a portfolio of their data science work to showcase their newly developed abilities. 
    Open to juniors and seniors
    Prerequisite: successful completion of Algebra II.

  • Statistical Reasoning in Sports

    Statistical Reasoning in Sports

    Statistical Reasoning in Sports is a semester-long math elective that utilizes professional and collegiate athletics data sets, as well as data within Severn’s athletics program, as source material for rigorous statistical analysis. Students will explore and compare categorical and quantitative data, investigate independence, and explore variability.  They will be introduced to standardized scores and the Normal distribution to estimate athletic ability from real performances. Students will have time in class to complete investigations where they will be evaluated on the strength of their statistical reasoning and skills as well as their ability to communicate their findings in various formats.  Some data analysis work product might feature on Admiral TV broadcasts. If this course is the student’s only math course, it would typically be paired with another math or computer elective in  the other semester

    Prerequisite: Successful completion of Algebra I or Integrated Math 1

  • Honors Statistics

    Honors Statistics

    This yearlong course covers descriptive statistics (such as graphical display of data, calculation of measures of central tendency and measures of dispersion), probability, discrete probability distributions, normal probability distributions, confidence intervals, estimates and sample sizes, and hypothesis testing. Students relate practical probability and statistical methods to real-life problems and develop skills in writing about mathematics. Students will use a TI-graphing calculator and perform numerous investigations and application projects to gain a deeper appreciation of data analysis.  The course is meant to prepare students for AP Statistics the following year.  
     
    Open to juniors and seniors.
    Prerequisite: Departmental approval and (a) a B+ or better in Algebra II or (b) a B or better in Precalculus or higher math.

  • AP Statistics

    AP Statistics

    In this course, students learn to interpret the center, shape, and spread of data through observation of patterns when the data is displayed graphically or numerically. Students learn how to plan a study, including the process of clarifying the question and deciding on a data-collection method. They use probability and simulation to anticipate patterns, and learn to use statistical inference, including confidence intervals and hypothesis testing, to get information from data. The course is designed to provide skills needed for effective decision-making for the student who plans to major in a field that does not require Calculus, such as sociology or psychology. It is also ideal for the student who wishes to take as much advanced mathematics as possible. Students are required to take the AP Statistics exam at the completion of this course. Because this course involves college-level study in content, rigor, pacing, and assessment, students must regularly engage in a high level of independent learning, demonstrate initiative, study course material outside of class, and should understand that there is a potential for a dip in the grades they typically earn in math courses.

    Open to juniors and seniors

    Prerequisite: Departmental approval and (a) an A or better in Algebra II or (b)  B or better in Honors Statistics or (c) A or better in Statistics & Production or Data Science or (d) a B+ or better in Precalculus or higher math.

  • Financial Algebra I

    Financial Algebra I (Fall)

    High school and college students, as well as young adults, make financial and life decisions, such as spending, saving, budgeting, planning, working, schooling, investing, paying taxes and renting all the time. Wouldn’t it be nice to get some practice before the real thing? This semester-elective will use a game-based simulation to teach budgeting and life skills and content. Your avatar will have the opportunity to engage in monetary and life decisions over the course of many simulated years. Most of the game will be played during class time with periodic lectures and other supporting activities. Students will also learn how to use spreadsheets. Homework will consist of reading, watching videos and completing some worksheets. There will also be traditional assessments such as tests and quizzes. The course is not a substitute for a student’s primary math course. A laptop is highly recommended over a tablet.
    Open to freshmen and sophomores
    Prerequisite: successful completion of Algebra I or Integrated Math I or experience with spreadsheets

  • Financial Algebra II

    Financial Algebra II (Spring)

    This one-semester course provides students with a mathematical framework to make important personal financial decisions using algebraic and statistical skills. Students will investigate the time value of money; the characteristics and risk/reward tradeoff of different financial instruments, such as stocks and bonds; and taxes and tax deferred vehicles such as 401k plans. The course will stress use of the calculator and Excel spreadsheets. This course can be a student's primary math course for the second semester and paired with a computer science course or other math elective in the first semester. It can also be taken as an elective second math course. Since some students will be taking it as their primary math course, there will be multiple assessments and work outside the classroom.
    Open to sophomores, juniors and seniors 
    Prerequisite: successful completion of Algebra II or concurrent enrollment in Honors Algebra II

  • Cybersecurity

    Cybersecurity (Fall)

    Starting with an introduction to computing and networking, students will use online resources and virtual image exercises to learn cybersecurity tools, defensive measures, and attack vectors. Students will incorporate safe computing practices and understand the history and trends that have led to our current cybersecurity landscape. Spreading out from individual PCs and personal security up to larger networks, the course will teach students about past and current threats, tools and techniques, and how to defend and keep networks safe. Students will use a number of competitions and online resources to understand how to safely work on cybersecurity problems.

  • Introduction to Computer Science

    Introduction to Computer Science (Spring)

    This one-semester course for students interested in computer science utilizes a modular approach covering web design, programming, networking, and cybersecurity. Much of computer science involves working with symbolic languages and using tools to manipulate code. To this end, students will learn two scripting languages and at least two programming languages, while learning to use text editors and integrated development environments as well as other software tools. This course introduces students and prepares them for continued studies in computer science including our AP courses, Introduction to Robotics, and Cybersecurity.

    Prerequisite: Successful completion of or concurrent registration in Algebra I or Integrated Math  plus  solid logic and abstract thinking skills.

  • AP Computer Science Principles

    AP Computer Science Principles

    AP Computer Science Principles helps students understand how computing and technology influence the world around them. This course focuses on seven big ideas in computer science: creativity, abstraction, data and information, algorithms, programming, the Internet, and the global impact of computing. With a unique focus on creative problem solving and applications, students create digital artifacts, such as videos and mobile apps, to address real world issues. A part of the class will address coding, but prior coding knowledge is not necessary. These aspects of the course make up a rigorous and rich curriculum that aims to broaden participation in computer science. This course is somewhat unique among AP courses in that students will submit two projects to the College Board as part of their AP portfolio. Students are also required to take the AP exam at the completion of this course. Because this course
    involves college level study in content, rigor, pacing, and assessment, students must regularly engage in a high level of independent learning, demonstrate initiative and study course material outside of class.
    Open to sophomores, juniors and seniors
    Prerequisites: Completion of Algebra I or Integrated Math I.

  • AP Computer Science A

    AP Computer Science A

    This course prepares students to take the A level AP Computer Science exam. Students will learn about the Java programming language, including the tools of the language and common implementation strategies. Emphasis is placed on creating working solutions to novel topics and developing strategies and habits for troubleshooting problems that arise. Topics include mathematical reasoning, 1 D and 2 D arrays, class hierarchy design, and recursion. Students are required to take the AP Computer Science A examination at the completion of the course.
    Prerequisite: Departmental approval and (a) an A- or better in Introduction to Computer Science or (b) recommendation by their AP Computer Science Principles teacher or (c) successful completion of an approved non-Severn introductory programming course in which the student learns about object-oriented design and development and uses design tools such as pseudocode to declare variables, develop classes and objects, and implement object-oriented designs in a high level language.

Lower School

Chesapeake Campus—PS-Grade 5
1185 Baltimore Annapolis Blvd
Arnold, MD  21012
410-647-7700

Upper School

Teel Campus—Grade 6-12
201 Water Street
Severna Park, MD  21146
410-647-7700