Academics
Academics
Berwick Academy Math Departmental Vision
Grades 5-12
 
Berwick Academy math faculty are committed to preparing students for successful roles in an ever-changing society through curriculum, instruction, and assessment that is dynamic, intellectually challenging, and attentive to the diverse needs of students. Students use problem solving, reasoning skills, creativity, and collaborative skills to be critical thinkers able to make sense of the world.
 
Upper School  

The math and computer science programs continue to build on the foundational work of the Middle School courses. We offer traditional math courses including Honors level at the Algebra 2 level and higher, and Advanced Placement offerings, as well as elective courses and Computer Programming. Additional course work is also offered for students who excel in mathematics beyond a traditional secondary program. Our options within the subject give students appropriate choices for college preparatory coursework.

Technology is integrated into math classes to enhance instruction and the learning of concepts. Students looking for ways to use their skills and explore beyond the classroom are encouraged to participate in the Upper School Math or Robotics Teams, and/or apply their specialized interests to a Berwick Innovation Project.

Faculty are committed to growth and self-reflection and model these for students, who in turn, are able to reflect on their own learning and growth.  While we are committed to preparing students for mathematical success in college, we are equally committed to preparing our students to problem solve, take mathematical risks and think critically through every endeavor they encounter. We believe the study of mathematics fosters the development of logical reasoning, attention to detail, and ability to make abstractions, skills that apply to multiple disciplines and life skills.
 

Offered Courses

List of 19 items.

  • Advanced Placement Calculus BC and Multivariate Analysis

    This course continues past the AB Calculus course into advanced topics which include: delta-epsilon proofs, Simpson’s Rule, advanced methods of integration, logistic differential equations, improper integrals, infinite sequences and series, Taylor and Maclaurin Series as polynomial approximations of transcendental functions, and polar and parametric equations.  Students are also introduced to 3-space, the calculus of vector valued functions, partial derivatives, and double integrals.  Students will be required to do summer work in preparation for this class.  Students who take AP Calculus are required to take the College Board Advanced Placement exam.
  • Advanced Placement Calculus: AB

     
    A rigorous Calculus course that covers limits and continuity, differentiation, applications of differentiation, integration, applications of integration, and (separable and linear) first order differential equations (including numerical and graphical approximation techniques).
  • Advanced Placement Computer Science A

    This course is an in-depth, theoretical approach to computer science emphasizing object-oriented methodology. The content of the course will include: object-oriented design (class specifications and relationships, class hierarchies); program implementation (appropriate distinctions between public and private data, data abstractions, interfaces, methods and parameters, problem solving); program analysis (efficiency, working with case studies); standard data structures (primitive data types, arrays, Array Lists); standard algorithms (searching, sorting); and computing in context. It will use the Java language to teach the concepts. Students will need access to a computer outside of class in order to complete homework. Students who take AP Computer Science A are required to take the College Board Advanced Placement exam.
  • Advanced Placement Statistics

    AP Statistics is a rigorous statistics course culminating in the Advanced Placement exam. The course weaves descriptive analysis, data collection and probability together to establish a conceptual understanding of inference. Though not a requirement, students should have taken Pre-Calculus or take it concurrently. Also this course can benefit juniors wishing to take an AP level science course in their senior year. Students who take AP Statistics are required to take the College Board Advanced Placement exam. 
  • Algebra I

    The topics covered will include: operations on integers; solutions of first degree equations; elementary word problems; factoring; percentages; simple number line graphs; operations on rational numbers, polynomials and radicals; properties of exponents; graphing linear equations and inequalities, systems of linear equations, and graphing and solving quadratics. 
     
  • Algebra II

    Topics include: data and linear representations, functions, systems of linear equations and inequalities, quadratic functions, exponential and logarithmic functions, polynomial functions, rational functions and radical functions, descriptive data analysis, and trigonometric functions. The TI-84+ calculator is strongly recommended.            
  • Algebra II Honors

    The topics covered in this honors level course will be the same core topics as in the regular course but in much greater depth and with much more detail and complexity.  
  • Business Mathematics

    Understanding mathematics is a critical component of adult life. How do you develop a budget? How do banks make money when they loan it out? What are the financial aspects of purchasing a car? Why should you pay more than just the minimum balance on your credit card? What is involved in starting your own business? Students will examine these daily uses of mathematics through problems and activities. 
  • Calculus I - Functions & Limits

    This course will review and build upon geometric and algebraic skills from previous math courses, focusing on those skills required for success in calculus.  Topics will include sketching the graphs of multi-term functions by adding (graphically) the graphs of the terms, factoring, simplifying complex fractions, and sign analysis of functions.  Rational, radical, composite, trigonometric, logarithmic, and exponential functions will all be included.  This course will define and begin to explore the process of finding limits.
  • Calculus II; Differentiation

    This course will begin where Calculus 1 ends, finding limits and examining the continuity of functions.  Then the derivative function will be defined, conceptually and algebraically.  Topics will include differentiation of all elementary functions as well as implicit and logarithmic differentiation as separate techniques.  Students will write equations of tangent lines and may begin to explore some applications of the derivative as time permits.
     
  • Calculus III; Application of Differentiation

    This course completes the differential calculus series of courses.  Applications of differentiation will include related rates, analysis of curves, optimization, Newton’s Method, motion on a line, and the Mean Value Theorem.  This course will include both the traditional physics based applications and those from business, biology, etc.
  • Explorations in Making: Arduinos

    This course will explore the relationship between hardware and software in solving problems.  Arduinos are miniature computers that can be configured to accept a variety of sensors and inputs; results can be physical displays of movement, or a recording of data. Arduinos can be used to work with robotics, light, sound, air, water-the possibilities are endless.  Students will be exposed to basic computer science principles as well as basic electronics.  This course will be project based; some work will be guided explorations as a class, some will be projects suggested by the instructor, and at least one project will be student designed.  
  • Geometry

    Geometry is designed to transition students into the Upper School through its emphasis on problem-solving, mathematical thinking and communication. As the entry level course, we acknowledge that students are coming from a myriad of different math experiences. We will incorporate fundamental algebraic skills when examining the geometric shapes of lines, angles, triangles, polygons, and circles. This emphasis on algebra and coordinate geometry will establish a firm foundation and prepare students to be successful in this course, and as they move onto Algebra II. Proofs will be used throughout to enhance the students understanding of these shapes. We will also cover the traditional geometry concepts of Pythagorean Theorem, similarity, trigonometry, transformations and spatial reasoning. These skills are developed through a collaborative classroom experience. 
  • Global Problem Solving

    This problem-based course will ask students to use mathematical modeling to solve global issues. Students, working collaboratively, will be expected to research the issue and then develop a logical argument `with supporting mathematical reasoning. There will be four or five questions over the trimester with each taking about two to three weeks. Students will be assessed by the thoughtfulness of their answer and their understanding of the complex issue through a paper and presentation. Students will examine how economic reasoning is used to analyze global issues, how statistical skills can be applied to the decision-making process, and how historical and social forces impact the possible solutions in the future.
  • Introductory Programming Concepts

    This is an introductory programming course and no previous experience is necessary.  Lab work is the primary component of the class.  Students will experience the theory and practice of programming through hands-on work with a variety of software tools which will include Lego Robotics and phone app development using MIT App Inventor.  Topics will include: input and output procedures; control statements and logic; looping; subprograms; and graphics. Several projects will be based on simple logic games, and many will involve group work.  Students will need access to a computer outside of class to complete work.  
  • JAVA Graphics

    Explore a new programming language while concentrating on graphics. This class will focus heavily on object oriented design while exploring graphics, applets and event handling. Standard CS topics, such as classes, input/output, decision making and logic, and looping will also be emphasized. This is a project based course; many of the assignments will be game oriented. Students will need access to a computer outside of class to complete work. 
  • Pre-Calculus

    The topics covered will include: continuing work with trigonometric, polynomial, rational, logarithmic and exponential functions; an introduction to analytic geometry; sequences and series; and matrices.  
  • Pre-Calculus Honors

    The topics covered will include the same material as regular Pre-Calculus, but each will be explored in greater depth.  Problem solving is an important component of this course along with extensive graphing calculator work.  Students who complete this course with exemplary work will be considered for the Advanced Placement Calculus courses the next year. 
     
  • Statistics

    Data is all around us. How do we make sense of it and use it to make decisions? How can we take a sample of 1000 people and know about 300 million people? Statistics, as a mathematical tool, helps us understand our world. This one-trimester course will use activities and problems to introduce the fundamental concepts of statistics, such as data analysis, data collection, and inferential procedures. 

Serving Maine, The Seacoast of New Hampshire, and the North Shore of Massachusetts

Berwick Academy is Maine's oldest, independent Pre-K through Post Graduate private school. Our community is dynamic, offering challenging academics, competitive athletics, and creative arts programs. Members of the community operate within a context of caring and respect as we pursue our quest for "useful knowledge" as "one school with three divisions." Students and faculty are encouraged to expand their horizons by balancing academics with athletic, dramatic, and musical options.