## Mathematics

# Mathematics at Avon Old Farms School

Developing strong problem-solving and critical-thinking skills empowers students to find success not only in mathematics, but also in other disciplines.

Faculty help students develop the skills necessary to effectively utilize technology as a mathematical tool for exploration and analysis. We nurture an appreciation for mathematics as an exact science and the role it plays in the fields of physical science, art, philosophy, engineering, architecture, and industry.

## Mathematics Courses

- Algebra 1
- Geometry
- Geometry Honors
- Algebra 2
- Algebra 2 with Trigonometry
- Algebra 2 with Trigonometry Honors
- Advanced Functional Analysis
- Precalculus
- Precalculus Honors
- Probability and Statistics
- AP Statistics
- Calculus
- AP Calculus AB
- AP Calculus BC
- Differential Equations
- Multivariable Calculus
- Computer Science
- AP Computer Science A
- Advanced Topics in Computer Science
- Advanced Topics in Computer Science: Mobile Apps

## Algebra 1

## Algebra 1

Algebra 1 introduces the student to fundamental operations using signed numbers and their elementary applications. The goal of Algebra 1 is to develop fluency in working with expressions, equations and variables. Students will extend their experiences with tables, graphs, and learn to solve linear equations, inequalities and systems of linear equations. Students will generate equivalent expressions and begin to apply formulas to methodically solve questions involving motion, speed and distance. Students will simplify polynomials and begin to study and apply strategies to solve quadratic relationships.

Students will use technology to learn, investigate, and develop strategies for analyzing complex situations and mathematical relationships. Topics covered in the course include grouping techniques, exponents, algebraic fractions, linear and quadratic equations, radicals, graphing, inequalities, and the solution of verbal problems.

## Geometry

Geometry

Geometry’s primary objective is the study of Euclidean Geometry as a formal, logical system. Where possible, excursions are made into three-dimensional figures and elementary analytic geometry. Some review of algebraic materials may be included. This course begins with developing visualization and some drawing skills. Both algebraic and geometric models are introduced and are further enhanced throughout the course. Proofs are developed slowly in the first half of the course. Various proof formats, including paragraph, flow-chart, and two-column proofs are presented. Students are expected to be actively involved in their own learning. The use of manipulatives is integrated into this course.

## Geometry Honors

Geometry Honors

The Geometry Honors course begins with a strong development of visualization and drawing skills. Both algebraic and geometric models are introduced and are used throughout the course. Proofs are developed slowly in the first half of the year. Various proof formats, including paragraph, flow chart, and two column proofs, are presented. Students are expected to be actively involved in their own learning. Manipulatives, constructions, and the computer program Geometer's Sketchpad are also integrated into this course.

## Algebra 2

## Algebra 2

**Pre-requisites: Algebra 1 and Geometry**

This course expands and reinforces the concepts learned in Algebra 1 before being introduced to more advanced concepts in Algebra. Students will spend extensive time in the Cartesian plane to begin the year. A review of slopes, rates of change, and linear equations will be followed by solving systems of linear equations and piecewise functions. Students will then focus on quadratic functions. From graphing to solving by factoring and the quadratic formula, students will be well prepared to study polynomial functions before exploring the idea of vertical and horizontal asymptotes when studying rational functions. The course will conclude with the study of special functions, such as root functions, logarithmic and exponential functions. This course will also have a standardized test preparation component as students prepare for the the SAT and ACT. Students from this course will matriculate to Advanced Functional Analysis and the study of Trigonometry.

## Algebra 2 with Trigonometry

Algebra 2 with Trigonometry

This course is a more intensive and extensive study of topics introduced in Algebra 1. The primary objective of the Algebra 2 curriculum is to prepare students for Precalculus or Precalculus Honors. The course is designed to prepare students for college level mathematics and is beneficial for those who will pursue further study in mathematics or related fields. Extensive work is included with equalities, inequalities, absolute value, fractional and negative exponents, radicals, systems of quadratics, logarithms and trigonometric properties. The content of the course is organized around families of functions, including linear, quadratic, exponential, logarithmic, radical and rational functions. Students will learn to represent functions in multiple ways, including verbal descriptions, equations, tables, and graphs. Students will also learn to model real-world situations using functions. To help students prepare for standardized tests, this course provides instruction and practice in a variety of formats. Graphing calculator skills will be taught and used extensively in this course. Throughout this course, students will develop learning strategies, critical thinking skills, and problem solving techniques to prepare for future math courses and college entrance exams.

## Algebra 2 with Trigonometry Honors

## Algebra 2 with Trigonometry Honors

This course is an extensive, fast-moving study of the fundamental principles of algebra and trigonometry. Topics covered in Algebra 2 with Trigonometry Honors include linear equations and inequalities, functions, polynomials, complex numbers, quadratic equations and inequalities. Solving word problems and graphing (polynomial functions, exponential functions, logarithmic functions and trigonometric functions) are all major points of emphasis. Honors students will learn how to write programs on the TI-84 Calculator.

Students who earn a high “B” range grade or better in this class usually pursue Honors Precalculus the following year while all students who satisfactorily complete this course will be thoroughly prepared for precalculus.

Algebra is the language of calculus. Understanding this, there will be special emphasis early in the year on developing a solid working understanding of the algebraic skills and procedures necessary for success in more advanced math courses. Students will learn to define the major concepts in a second-year algebra course including polynomials, rational expressions, radical expressions, and complex numbers and then learn how to simplify, add, subtract, multiply and divide these expressions. Other major themes include: solving various types of equations and inequalities, factoring, understanding the concept of a function, and graphing functions on the coordinate plane. Linear and quadratic functions are studied in great detail. Later in the year, students will be introduced to higher degree polynomial functions and associated theorems. Students are introduced to exponents and logarithms, right triangle and circular trigonometry, and, if time permits, sequences and series.

## Advanced Functional Analysis

This course consists of a more thorough treatment of Trigonometry and other selected topics in Algebra 2 with Trigonometry to prepare students for further study in mathematics. Algebra 2 with Trigonometry is a prerequisite. The primary objective of the curriculum is to prepare students for Precalculus. Integral to the learning process is the systematic review of earlier concepts learned in Algebra 2 with Trigonometry and procedures in which students use previously learned skills to develop proficiency with more advanced concepts. The course includes organizational skills, communication, mathematical tools, calculators, hands-on activities and group work.

## Precalculus

Precalculus

The primary objective of the Precalculus curriculum is to prepare students for Calculus. Integral to the learning process is the systematic review of earlier concepts learned in Algebra 2 and/or Advanced Math and procedures in which students use previously learned skills to develop proficiency with more advanced concepts, especially Trigonometry. The Precalculus course includes exploration, communication, mathematical tools, manipulatives, calculators, hands on activities and group work.

## Precalculus Honors

Precalculus Honors

Designed to prepare the more advanced student for Advanced Placement Calculus, this course provides students an honors level study of trigonometry, advanced functions, analytic geometry, and data analysis. A faster pace also allows for the introduction of topics from calculus earlier in the second semester. Limits, continuity, the definition of the derivative, techniques of differentiation, and applications of the derivative are all explored. Applications and modeling are included throughout the course. Appropriate technology is used regularly for instruction and assessment.

## Probability and Statistics

Probability and Statistics

The primary objective of Probability and Statistics is to offer students an opportunity to continue their mathematical studies in a new area. This course begins with an overview of statistics and includes an investigation of the fundamental laws of probability. It also includes such topics as distributions, sampling, regression, estimation, and hypothesis testing.

## AP Statistics

## AP Statistics

AP Statistics is the high school equivalent of a one semester, introductory college statistics course. In this rigorous course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance behavior. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-84 graphing calculator, Fathom and Minitab statistical software, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.

## Calculus

Calculus

This advanced course is an introduction to the fundamental topics comprising calculus. Algebraic, trigonometric, and transcendental functions are studied in the context of differentiation and integration. The Calculus curriculum includes exploration, communication, mathematical tools, manipulatives, calculators, hands on activities and group work. At the conclusion of this course, students should be able to use calculus methods in a variety of applications and problem solving situations.

## AP Calculus AB

## AP Calculus AB

This is a rigorous Advanced Placement course designed to prepare students for the AP Calculus AB exam in the spring. The course seeks to develop students’ understanding of the concepts of calculus, while providing experience with its methods and applications. A multi-representational approach to calculus is employed with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections between these representations are also explored.

## AP Calculus BC

## AP Calculus BC

This is a rigorous Advanced Placement course that prepares students to take the AP Calculus BC exam in the spring. The course seeks to develop advanced problem solving skills by stressing the application of the concepts covered in the problem solving process. The class requires some vacation assignments that are to reinforce the concepts that have been taught. The class moves quickly and covers all the material outlined by the College Board and is intended for students that have had success in Precalculus or lower levels of Calculus and want to challenge themselves at the highest level.

## Differential Equations

## Differential Equations

The main objective of the course is to teach techniques to solve first and second order linear differential equations. Throughout the course differential equations will be used to model problems with real applications such as the motion of an object, population growth, heating & cooling, and mixing problems. The techniques developed will then be applied to these models to find solutions.

*Note: This course runs in alternate years with Multivariable Calculus.*

## Multivariable Calculus

## Multivariable Calculus

This course covers differential, integral and vector Calculus for functions of more than one variable. Topics include vectors and matrices, partial derivatives, double and triple integrals and vector calculus in 2 and 3-dimensional space. Though full year, this course covers the same topics taught in a typical college semester. Multivariable Calculus is well suited for students who have previously completed AP BC Calculus.

*Note: This course runs in alternate years with Differential Equations.*

## Computer Science

## Computer Science

Using JavaScript and Python, this course aims to develop computational thinking and generate excitement about computing using professional tools that foster creativity and collaboration. Introduction to Computer Science helps students develop programming expertise and explore the workings of devices and the internet. Projects and problems include console-based games, simulations, and cybersecurity. After completing this course, students will have established an excellent foundation for more advanced courses in Computer Science, such as Mobile App Development or AP® Computer Science A.

## AP Computer Science A

## AP Computer Science A

This is a rigorous Advanced Placement course that prepares students to take the AP Computer Science exam in the spring. The course seeks to teach students to think critically and develop carefully thought out algorithms to solve problems. Students will learn how to utilize object-oriented programming in Java throughout the course and will develop a thorough understanding of the language and concepts such as inheritance, hierarchy, polymorphism, as well as basic programming concepts such as conditional and looping statements. Upon successful completion of the class, students will be well prepared to take the AP Computer Science exam in the spring.

## Advanced Topics in Computer Science

This course is intended as an introduction to data structures, algorithms, and more advanced programming techniques. Students will be able to solve real-world problems by reasoning about data structure choices, choose appropriate implementations, and analyze the costs associated with those choices. Students will learn to write, debug, and test large programs systematically. The major topics within the course include: Recursion, Abstraction, Problem Solving, Software Design, Sets, Linked Lists, Stacks, Queues, Trees, Heaps, Sorting Algorithms, Graphs, and Hashing, with exposure to complexity and algorithm analysis.

## Advanced Topics in Computer Science: Mobile Apps

**Advanced Topics in Computer Science: Mobile Apps**

This course will introduce students to common software engineering practices in the context of designing and building mobile applications. Students will use the Dart programming language to create native apps for Android and iOS. Students will learn to design responsive user interfaces, utilize public APIs, and manage large projects using GitHub. The major topics within the course include: Responsive Design, Abstraction, Version Control, APIs, Efficiency, Agile Development, and the Google Play and Apple App Stores.