Curriculum Detail

Math

Students are required to take a total of 7 credits in Science and Mathematics in a 4/3 combination of their choice. Within this requirement, each student must obtain a credit in both Algebra and Geometry.

The mission of Burr and Burton Academy’s Mathematics Department is to challenge all students with an appropriate and engaging curriculum that focuses on mathematical concepts, fluency, and application. The Mathematics Department works to develop students who:
  • make sense of problems and persevere in solving them;
  • reason abstractly and quantitatively;
  • construct viable arguments and critique the reasoning of others;
  • model with mathematics;
  • use appropriate tools strategically;
  • are precise;
  • look for and make use of structure;
  • look for and express regularity in repeated reasoning.
The Mathematics Department believes that the ability to create and explore with technology is valuable for both presentation and investigation, and that technology should be used responsibly in the teaching and learning of mathematics. However, technology cannot become a substitute for basic understanding. A graphing calculator is necessary for students who anticipate taking a standardized test (AP, SAT or ACT). Exam policies are subject to change; we encourage student to have a conversation with a member of the Mathematics Department for a recommendation on what particular device to buy.

Placement for incoming freshmen is based on prior class achievement, scores on standardized tests, the Burr and Burton Algebra 1 exam, and the recommendation of previous teachers. With sufficient motivation and achievement, students have access to a broad array of courses, regardless of starting point.
  • AP Calculus BC

    AP Calculus continuously builds on foundational knowledge to provide conceptual understanding and procedural fluency in the traditional topics of a first and second college course in calculus. The approach is multi-representational, with concepts, results and problems expressed graphically, numerically, analytically and verbally. Emphasis includes clear communication of methods, reasoning, and justifications. Technology is used throughout to reinforce understanding, facilitate processes, and to assist in finding and evaluating results. AP Calculus BC is a rigorous course that maintains a steady pace through demanding content. A strong interest in and curiosity for math is essential. Students opting to take the AP exam are responsible for the exam fee of approximately $110. (Fee reduction applications are available in the school counseling office.)

  • AP Calculus BC, Part 2

    2 credits

    In order to receive AP credit, students must complete the full 2 credits. Students who complete only the first semester receive honors credit.

    AP Calculus continuously builds on foundational knowledge to provide conceptual understanding and procedural fluency in the traditional topics of a first and second college course in calculus. The approach is multi-representational, with concepts, results and problems expressed graphically, numerically, analytically and verbally. Emphasis includes clear communication of methods, reasoning, and justifications. Technology is used throughout to reinforce understanding, facilitate processes, and to assist in finding and evaluating results. AP Calculus BC is a rigorous course that maintains a steady pace through demanding content. A strong interest in and curiosity for math is essential. Students opting to take the AP exam are responsible for the exam fee of approximately $100. (Fee reduction applications are available in the school counseling office.)
  • AP Statistics

    Statistics is a course that teaches the concepts and tools for collecting, analyzing, and drawing conclusions from data. College majors such as business, engineering, health sciences, mathematics, psychology, sociology, and science typically require some study in statistics. AP Statistics offers students the opportunity for a non-calculus based college-level course. This vigorous and engaging class asks students to explore data by observing patterns and deviations from patterns; design a study, including decisions about what and how to measure; create models using probability; and use simulations and statistical inferences to confirm models. Students successfully completing this course may advance to Honors Calculus or AP Calculus. Students opting to take the AP exam are responsible for the exam fee of approximately $110. (Fee reduction applications are available in the school counseling office.) PREREQUISITE: Successful completion of CP Algebra 2 (with a recommended B or higher and permission of the teacher), or students in the Honors/AP track.

  • AP Statistics

    Statistics is a course that teaches the concepts and tools for collecting, analyzing, and drawing conclusions from data. College majors such as business, engineering, health sciences, mathematics, psychology, sociology, and science typically require some study in statistics. AP Statistics offers students the opportunity for a non-calculus based college-level course. This vigorous and engaging class asks students to explore data by observing patterns and deviations from patterns; design a study, including decisions about what and how to measure; create models using probability; and use simulations and statistical inferences to confirm models. Students successfully completing this course may advance to Honors Calculus or AP Calculus. Students opting to take the AP exam are responsible for the exam fee of approximately $110. (Fee reduction applications are available in the school counseling office.) PREREQUISITE: Successful completion of CP Algebra 2 (with a recommended B or higher and permission of the teacher), or students in the Honors/AP track.

  • AP Statistics, Part 2

    Juniors who have completed CP Algebra 2 (with a recommended B or higher and permission of the teacher), and Seniors in the Honors/AP track.
    1.5 credits
    Statistics is a course that teaches the concepts and tools for collecting, analyzing, and drawing conclusions from data. College majors, including business, engineering, health sciences, mathematics, psychology, sociology, and science typically require some study in statistics. Advanced Placement Statistics offers students the opportunity for a (non-calculus based) college-level course. This vigorous and engaging class asks students to explore data by observing patterns and deviations from patterns; design a study, including decisions about what and how to measure; create models using probability; and use simulations and statistical inferences to confirm models. Students enrolled in this class are required to complete summer work as assigned by the teacher. Text: The Practice of Statistics for AP (W.H. Freeman and Company, 4th edition, 2012). Students successfully completing this course may advance to Honors Calculus or AP Calculus (AB or BC). The AP exam fee of approximately $100 is the responsibility of the student. (Fee reduction applications are available in the school counseling office.)
  • Conceptual Geometry

    Conceptual Geometry includes applications of geometry in everyday life, geometric constructions as a way to understand measurement and to see relationships, and deductive reasoning. Math construction tools (compass and straight edge), measurement tools (ruler and protractor), and dynamic geometry software are all used in various applications and explorations. Integrated projects challenge students to apply geometric principles creatively, fostering a deep understanding of fundamental concepts. Successful completion of this course fulfills the geometry requirement, allowing advancement to Personal Finance, CP Data Science, CP Small Business Start-Up, or another math elective.

  • CP Advanced Engineering: Simulation and Systems

    This project-based course focuses on rigorous engineering analysis, technical documentation, and complex systems design. Students apply mechanical and civil engineering principles to ensure designs are not only visually accurate but physically viable. The curriculum centers on the validation phase of engineering: using Computer-Aided Design (CAD) software to perform Finite Element Analysis (FEA), test material properties, and simulate structural loads under real-world conditions. Students work in teams to produce comprehensive technical data packages, mastering the creation of professional blueprint sets, assembly instructions, and tolerance reports. Projects involve designing large-scale structural elements and intricate mechanical assemblies, requiring students to justify their decisions through calculation and simulation data. The course culminates in a capstone challenge where teams deliver a fully analyzed, construction-ready design solution to a client. This course emphasizes precision, technical communication, and data-driven decision-making, preparing students for professional or collegiate engineering environments. PREREQUISITE: Successful completion of CP Engineering Through CAD. Co-enrollment or completion of a physics class is strongly recommended.

  • CP Algebra 1

    CP Algebra I is the foundational cornerstone for high school mathematics; it has a strong focus on collaboration and problem solving. This course builds on computational experiences with different number sets to extend an understanding of how to manipulate mathematical expressions, equations and functions. Various representations of linear functions and inequalities help students develop connections and deepen their understanding of mathematical structures. It is a skills-based course that includes functions and function notation, solving equations, graphing and writing equations of lines, inequalities, systems of equations, exponent properties, and an introduction to polynomials. Students utilize appropriate tools including mental math, pencil and paper, and technology. Students successfully completing this course advance to Conceptual, CP, or Honors Geometry.*

  • CP Algebra 2

    CP Algebra 2 is a course that moves students beyond concrete reasoning to focus on solving, graphing, and applying higher-level functions and relations. Linear, quadratic, cubic, and polynomial functions are studied. Various forms of technology are used to support analytic methods and to give students visual representations that nurture an intuitive understanding. Problem solving is an important component. PREREQUISITE: Successful completion of CP Algebra 1. Students successfully completing this course may advance to CP Pre-Calculus, CP Data Science or another math elective.

  • CP Engineering Through Computer-aided Design

    This project-based course provides a hands-on introduction to the engineering design process using Computer-Aided Design (CAD) software. Students develop valuable skills in digital modeling, simulation, and 3D printing while tackling increasingly complex design challenges. They master essential CAD tools, create physical prototypes using 3D printing technology, and work with clients to design, prototype, and refine in an authentic design environment. The course culminates in a team project where students address a real-world issue in the local community, applying their engineering skills to make a positive impact. This course emphasizes creativity, problem-solving, and teamwork, providing a solid foundation in engineering design principles and preparing students for future studies or careers in STEM fields. PREREQUISITE: Successful completion of a geometry class and CP Foundations of Science or Foundations of STEM is recommended but not required.

  • CP Geometry

    CP Geometry explores the intricacies of shapes, angles and spatial relationships, incorporating deductive reasoning and the use of logic in mathematical proofs. This course supports students in developing a deep understanding of geometric concepts essential for analytical thinking and problem solving. A variety of tools (both physical and technological) are utilized for student exploration and teacher-directed presentations. Communication and collaboration are important components of the course, and algebra is embedded throughout. Students successfully completing this course may advance to CP Algebra 2, Honors Algebra 2*, or CP Data Science.

  • CP Pre-Calculus

    CP Pre-Calculus focuses on the structure of math and the relationships between numerical, graphical, and algebraic forms. The exploration of trigonometry and logarithmic functions allows students to extend their knowledge and understanding of the concept of functions and their inverses. Work with trigonometry includes extensive study of graphs, equations, identities, and applications. Students also explore conic sections and rational functions. Graphing utilities are used to support analytic methods and to give students visual representations that nurture an intuitive understanding. Students successfully completing this course may advance to Honors Calculus, Honors/AP Statistics, or another math elective.

  • CP Programming 1: Software and Hardware Applications

    This introductory programming course provides a comprehensive foundation in the principles of software development and hardware interaction. Through the programming language Python, students gain proficiency in fundamental programming concepts, including variables, data structures, control flow, and algorithmic thinking. Students build functional software applications and utilize Raspberry Pi microcontrollers to program hardware systems. Students also begin to investigate collaborative coding with Artificial Intelligence (LLMs) and understand the uses and drawbacks of co-writing software with Artificial Intelligence. Through hands-on projects and collaborative learning, students develop essential programming skills applicable to diverse domains in the digital age. This course requires no prior programming experience and is suitable for individuals seeking to acquire a foundational understanding of computer programming and its applications in both software and hardware contexts.

  • CP Programming 2: Advanced Software Design and Architecture

    This intermediate programming course focuses on the engineering of high-performance software through the study of compiled languages and advanced system architecture. Students select a technical specialization track-utilizing languages such as C++ (systems), C# (interactive media), or Swift (mobile applications)-to apply strict data typing, manual memory management, and Object-Oriented Programming (OOP). Through the development of complex, self-directed projects, students prioritize the creation of efficient, optimized, and scalable code. The curriculum integrates professional industry workflows, including version control and debugging, requiring students to directly manage hardware resources and system memory. Through independent inquiry and a personalized project roadmap, students execute advanced concepts within their chosen technical domain. PREREQUISITE: Successful completion of Programming 1.

  • CP Small Business Start-Up, Management and Economics

    This course fulfills the integrative, immersive learning experience graduation requirement when paired with CP/Honors Entrepreneurship or a work-based learning internship. This course focuses on teaching students the practical knowledge, skills and methods for writing a business plan based on a business model. Local small business owners help students to learn basic microeconomic concepts, principles of accounting and finance, and strategies for managing customers, employees and resources. Students learn about business model generation and how to build/create a business through problem solving, researching potential target markets, and marketing. Students are expected to build and iterate a business model, develop a plan to bring their product to market, budget expenses, and develop financial documents (including income and cash flow statements). At the end of the course, students have a better understanding of how to create and build a viable small business. PREREQUISITE: Successful completion of the algebra and geometry math requirements.

  • CP Statistics

    Statistics is the creation, collection, and interpretation of the data that surrounds us. The goal is to develop the skills to analyze, create, and present data in order to gain a better understanding of it and to share that understanding with others. Students learn how to use statistical software to interpret large and complex sets of data. This course is also designed to enhance students’ understanding of the statistics they encounter in everyday life; students design and present statistics and learn the tools for analyzing data quickly and efficiently. CP Statistics includes readings and responses, and student-driven data sets. Honors Statistics includes a deeper look into the specific topics, additional assessments, and a focus on detailed use. PREREQUISITE: Successful completion of any Algebra 2 course.
  • CP/Honors Data Science

    The goal of this course is to help students find, analyze, and make sense of data in their everyday lives. Students learn how to ask statistical questions of data, collect data, and then appropriately analyze it using technology and statistical methods. Students make decisions and communicate stories and solutions to others, utilizing different technologies to help do this (Google Sheets, R, and Python). Students also learn how to create visuals that convey meaning to others. The course is taught using multiple units of overarching projects, and students end the course with a portfolio of their data analyses across a variety of situations. PREREQUISITE: Successful completion of the algebra and geometry math requirements.

  • CP/Honors Statistics

    Statistics is the creation, collection, and interpretation of the data that surrounds us. The goal is to develop the skills to analyze, create, and present data in order to gain a better understanding of it and to share that understanding with others. Students learn how to use statistical software to interpret large and complex sets of data. This course is also designed to enhance students' understanding of the statistics they encounter in everyday life; students design and present statistics and learn the tools for analyzing data quickly and efficiently. CP Statistics includes readings and responses, and student-driven data sets. Honors Statistics includes a deeper look into the specific topics, additional assessments, and a focus on detailed use. PREREQUISITE: Successful completion of CP Algebra 2.

  • Foundations of STEM

    2 credits (1 math, 1 science)

    This year-long entry level course provides 9th grade students with a solid foundation in applied mathematics and science. Students gain a holistic understanding of the interconnectedness of mathematics and science. Through a combination of hands-on labs, data collection, and analysis, students develop essential skills that bridge the gap between theoretical concepts and real-world applications. They build valuable skills in mathematical modeling of linear equations and scientific inquiry, setting a strong foundation for further studies in mathematics and science. Students successfully completing this course may advance to Conceptual Geometry or CP Algebra 1, and General or CP Chemistry.
  • Foundations of STEM

    2 credits (1 math, 1 science)

    This year-long entry level course provides 9th grade students with a solid foundation in applied mathematics and science. Students gain a holistic understanding of the interconnectedness of mathematics and science. Through a combination of hands-on labs, data collection, and analysis, students develop essential skills that bridge the gap between theoretical concepts and real-world applications. They build valuable skills in mathematical modeling of linear equations and scientific inquiry, setting a strong foundation for further studies in mathematics and science. Students successfully completing this course may advance to Conceptual Geometry or CP Algebra 1, and General or CP Chemistry.
  • Honors Algebra 1

    Honors Algebra 1 is presented through a problem-centered approach, where students utilize and extend their aptitude through engaging problems. The design allows students to be supported in a tailored manner, as class time offers opportunities to work with the teacher, and whole-class discussion unpacks different solutions. Like CP Algebra 1, content includes extensive work with variables, equations and inequalities, various forms of linear equations and inequalities, the use of tables and graphs, exponents and an introduction to polynomials. Appropriate computational tools (mental math, pencil and paper, and technology) are utilized throughout. Resources include the Exeter Academy Year 1 Problem Set. Students successfully completing this course advance to CP or Honors Geometry.

  • Honors Algebra 2

    The accelerated pace of Honors Algebra 2 is for students who have demonstrated both an aptitude for and a deep interest in mathematics. The focus of this rigorous course is helping students to move beyond concrete reasoning and on to abstract reasoning related to solving, graphing, analyzing, and applying higher-level functions and relations. Linear, quadratic, cubic, and polynomial functions are studied. Graphing utilities are used to support analytic methods and to give students visual representations that nurture an intuitive understanding. Students successfully completing this course may advance to CP Pre-Calculus, Honors Pre-Calculus, or another math elective.

  • Honors Calculus

    Honors Calculus furthers students' ability to work between graphical, numerical, analytical, verbal and written representations as they become familiar with differentiation and are introduced to the concept of the integral. Students study the behavior of functions and how calculus techniques are used to analyze and predict behavior of various functions, including algebraic, rational, exponential, logarithmic and trigonometric. Graphing utilities are used to support analytic methods and to give students visual representations that nurture an intuitive understanding. Students successfully completing this course may advance to AP Calculus, Honors/AP Statistics, or another math elective.

  • Honors Geometry

    Like Honors Algebra 1, Honors Geometry is presented through a problem-centered approach, where students utilize and extend their aptitude through engaging problems. This design allows students to be supported in a tailored manner, as class time offers an opportunity to work with the teacher, to work in small peer groups, and to engage in whole-class discussions that unpack strategies for solutions. Students are asked to apply their strengths in algebra throughout the course. Topics include coordinate and Euclidean geometry in two and three dimensions. Students successfully completing this course may advance to CP Algebra 2, Honors Algebra 2, or CP Data Science.

  • Honors Pre-Calculus

    Honors Pre-Calculus, designed for the most ambitious and capable math students, focuses on the structure of math and the relationships between numerical, graphical, and algebraic forms. The exploration of trigonometry and logarithmic functions allows students to extend their knowledge and understanding of the concept of functions and their inverses. Additional topics include conic sections and rational functions, as well as an extensive study of derivations with trigonometry and trigonometric expressions as algebraic objects. Graphing utilities are used to support analytic methods and to give students visual representations that nurture an intuitive understanding. An important focus is abstract reasoning, in addition to the skills of algebraic manipulation. Students successfully completing this course may advance to Honors Calculus, AP Calculus, Honors/AP Statistics, or another math elective.

  • IS AP Computer Science A

    AP Computer Science A introduces the Java programming language while emphasizing universal language techniques like syntax, semantics and readability. Students gain mastery in programming concepts by using a subset of Java features that are required for the AP Computer Science A exam, including abstraction, algorithms, data structures, and object-oriented programming. This allows the student to understand and master important concepts that apply to programming problems in many additional languages.The curriculum prepares students for advanced college coursework and careers in computer science. Because this class is comprised of 9 units of study, it is recommended that students pursue this independent study for a full school year. Students pursue this class independently, with the support of the computer science teacher; strong self-directed learning skills are necessary. PREREQUISITE: Successful completion of Algebra 1. Algebra 2 is recommended. Permission of the teacher is required.

  • IS AP Computer Science A

    AP Computer Science A introduces the Java programming language while emphasizing universal language techniques like syntax, semantics and readability. Students gain mastery in programming concepts by using a subset of Java features that are required for the AP Computer Science A exam, including abstraction, algorithms, data structures, and object-oriented programming. This allows the student to understand and master important concepts that apply to programming problems in many additional languages.The curriculum prepares students for advanced college coursework and careers in computer science. Because this class is comprised of 9 units of study, it is recommended that students pursue this independent study for a full school year. Students pursue this class independently, with the support of the computer science teacher; strong self-directed learning skills are necessary. PREREQUISITE: Successful completion of Algebra 1. Algebra 2 is recommended. Permission of the teacher is required.

  • IS AP Computer Science A - Amazon Future Engineers

    Students study how to use computers to solve human problems, using the programming language Java. This course is an Amazon Future Engineer (AFE) Pathway class offered in partnership with Amazon and Edhesive and is primarily delivered as an online course. Strong self-directed learners will find the greatest success with this format. This course fulfills the technology requirement for graduation. PREREQUISITE: Permission of the teacher.
  • IS AP Computer Science Principles - Amazon Future Engineers

    Students are introduced to and analyze a number of innovations in computing and digital media that form the backbone of online and offline interactions; throughout, students develop robust computational thinking skills. This course is an Amazon Future Engineer (AFE) Pathway class offered in partnership with Amazon and Edhesive and is primarily delivered as an online course. Strong self-directed learners will find the greatest success with this format. This course fulfills the technology requirement for graduation. PREREQUISITE: Permission of the teacher.
  • Personal Finance

    This course fulfills the integrative, immersive learning experience graduation requirement when paired with a work-based learning internship or Student Accessibility Youth Employment. Is it possible to retire with a million dollars? Is it better to lease or buy a car? What are the advantages and disadvantages of using a credit card? Personal Finance is a course designed to prepare students for a lifetime of financial responsibility and independence. From insurance, loans, and investments to maintaining a checkbook and understanding paycheck deductions, real-life applications are explored in order to provide students with useful knowledge that will help them in daily life. Students collaborate and work through various activities and simulations as they investigate and learn about topics of particular interest, all in the name of better understanding their finances. PREREQUISITE: Successful completion of the algebra and geometry math requirements.

  • Practical Algebra

    Practical Algebra: 
    Learning how algebra relates to life activities. The use of algebra in the real world through word problems, life activities such as shopping for groceries, the use, maintenance, and cost of vehicles and houses, and many other life long math processes. 
     
  • TG Conceptual Geometry

    * This course is offered to students who have applied and been accepted to Target. The course is personalized to meet the needs of each student participant, and the teacher modifies the instruction and assessment plans to promote learning.

    Conceptual Geometry includes applications of geometry in everyday life, geometric constructions as a way to understand measurement and to see relationships, and deductive reasoning. Math construction tools (compass and straight edge), measurement tools (ruler and protractor), and dynamic geometry software such as Desmos are all used in various applications and explorations. With specific emphasis on connecting math, art, and modeling engineering concepts, many assessments are project-based.

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Burr and Burton Academy does not discriminate against any person or group on the basis of race, color, religion (creed), ancestry, national origin, place of birth, sex, sexual orientation, gender identity, disability, age, political affiliation or marital status in admission or access to, or treatment or employment in, its programs and activities. Any person having inquiries concerning the school's compliance with the regulations implementing Title VI, Title IX, section 504 of the Rehabilitation Act of 1973 or other federal or state nondiscrimination laws or regulations is directed to The Headmaster's Office, Burr and Burton Academy, Manchester, VT 05254. Burr and Burton complies with all applicable state and federal nondiscrimination statutes, including the Vermont Public Accommodations Act (9 V.S.A. Chapter 139), the Vermont Fair Employment Practices Act (21 V.S.A. Chapter 5, Subchapter 6) and Vermont State Board of Education rules 2226.6 and 2229.1.