# Mathematics

The mathematics department prepares students to think logically and creatively about patterns, figures, numbers, functions, and applications and teaches skills necessary for success in an increasingly technical world. The department believes each student learns best and feels most successful and confident when she covers the material at an appropriately challenging pace.

Mathematics is a required subject for all students in Classes I through VII. All students in Class I and Class II have math class in heterogeneously mixed groups. Starting in Class III, students are grouped homogeneously. Algebra 1 is also offered to qualifying Class III Students. The offered math courses for Class VIII satisfy the quantitative course requirement.

## Mathematics Courses

- Classes I and II
- Class III
- Class IV
- Algebra II
- Geometry
- Precalculus
- AP Calculus
- Calculus
- AP Statistics
- Statistics & Data Analysis (1st Semester))
- Topics in Post-Calculus Mathematics
- Computer Science Electives (Class VII and VIII)

## Classes I and II

**Class I**

Students study arithmetic using whole numbers, fractions, and decimals to understand concepts and
strengthen skills. Manipulatives are used to help illustrate some concepts. Other topics include
measurement, geometry, and estimation. Mental and written computation is emphasized, but calculators
or computers are used for appropriate activities. Students work individually as well as in groups when
appropriate.

Throughout the year, students move away from rote arithmetic to applications and problem solving.
Learning how to apply skills, both in and out of the context in which they were taught, provides students
with a deeper understanding of how and why they will use mathematics as a valuable tool in their lives.

**Class II**

The mathematics curriculum includes fractions, decimals, percents, number theory, order of operations, measurement, two-dimensional geometry, data analysis, and an introduction to negative numbers. Students develop basic financial literacy through a computer simulation project. All topics involve individual and group activities and solving a variety of problems. Scientific calculators are introduced. Computer spreadsheets are also introduced and used during the study of financial literacy and data analysis. Students participate in the Elementary School Math Olympiads.

## Class III

### Introduction to Algebra

The course includes writing algebraic expressions and solving equations, three-dimensional geometry, ratio and proportion, and probability. Application of these topics is built-in throughout the course. Students also learn creative problem solving by participating in the Middle School Math Olympiad.

### Algebra 1

The course includes solving and graphing linear equations and inequalities, exponents, polynomials, solving and graphing quadratic equations and solving systems of equations. During the year students develop and refine their problem-solving and critical thinking skills, and a variety of word problems and applications are introduced. Graphing calculators are introduced. Students participate in the Math Olympiad

## Class IV

### Algebra 1

The course includes solving and graphing linear equations and inequalities, exponents, polynomials, solving and graphing quadratic equations and solving systems of equations. During the year students develop and refine their problem-solving and critical thinking skills, and a variety of word problems and applications are introduced. Graphing calculators are introduced. Students participate in the Math Olympiad.

### Algebra 2

All students will study the core topics of Algebra 2: linear, quadratic, radical, rational, exponential, and logarithmic expressions, and the equations and functions that involve them. Complex numbers, systems of equations, and inverse functions will also be studied. The algebraic and graphical aspects of each topic will be emphasized. Additional topics such as analytic geometry and data analysis will be included if time permits. The applications of the TI-Nspire CX graphing calculator will be introduced. This course is open to students who have completed a full year of Algebra 1 at Winsor.

## Algebra II

All students will study the core topics of Algebra 2: linear, quadratic, radical, rational, exponential, and logarithmic expressions, and the equations and functions that involve them. Complex numbers, systems of equations, and inverse functions will also be studied. The algebraic and graphical aspects of each topic will be emphasized. Additional topics such as analytic geometry and data analysis will be included if time permits. The applications of the TI-Nspire CX graphing calculator will be introduced. This course is open to students who have completed a full year of Algebra 1 at Winsor or at their previous school.

## Geometry

*This course is open to students who have completed a full year of Algebra 2 at Winsor or at their previous school.*

## Precalculus

In this course students continue to study functions, including polynomial, rational, exponential, logarithmic, and trigonometric, and their applications. Graphing calculators are used throughout the course to build understanding and to solve problems. More traditional analytic and algebraic problem-solving methods are also emphasized so that students will understand multiple approaches and techniques. Other topics covered include transformations of graphs, inverses of functions, solving equations and inequalities, trigonometric identities, and the laws of sines and cosines. In addition, polar coordinates, sequences and series, combinatorics, limits, and introductory calculus concepts are introduced if time permits. *This course is open to Class VI or VII students who have completed Geometry at Winsor.*

## AP Calculus

## Calculus

Students will primarily study the concepts of the derivative and the integral, including their meaning in relation to both graphs and formulas. They will also study applications of both concepts in a variety of situations. The emphasis of the course will be on studying these topics with polynomial, logarithmic, and exponential functions; trigonometric functions will be introduced in the second semester. Additional topics will be added if time allows. *This course is open to Class VIII students who have completed Precalculus at Winsor.*

## AP Statistics

This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Topics fall into 4 themes: Exploring Data (Describing patterns and departures from patterns); Sampling and Experimentation (Planning and conducting a study); Anticipating Patterns (Exploring random phenomena using probability and simulation); Statistical Inference (Estimating population parameters and testing hypotheses). While understanding formulas is important, memorizing formulas is kept to a minimum. The TI-84 or TI-Nspire will be used regularly to facilitate computation and to display data. The emphasis of the course is on understanding and communicating with statistical concepts and language. Students are required to take the AP Statistics test in May. *This course is open to Class VIII students.*

## Statistics & Data Analysis (1st Semester))

Students in this one semester course will have class with the AP Statistics course during the 1st semester. First semester topics come from all 4 themes mentioned above: Exploring Data, Sampling and Experimentation, Anticipating Patterns, and Statistical Inference. All students will be equally involved in the class. (AP students will be expected to do some additional reading and will have some additional homework problems and test questions.) This course is open to Class VIII students. (0.5 credits)

## Topics in Post-Calculus Mathematics

This year long course is for students who have completed an AP calculus class. Students will be introduced both to the rigors of higher mathematics beyond calculus and to some of the intriguing mathematical concepts that have been developed over the past 2000 years. Particular attention will be paid to the formality of mathematical notation and writing. Topics to be investigated may include but are not limited to formal logic, set theory, proof techniques, number theory, counting and induction, and cardinality. *Enrollment is by permission of the department only.*

## Computer Science Electives (Class VII and VIII)

### Introduction to Computer Programming (Spring Semester)

*This is a half-credit course that meets for 2x60 and 1x75 minute periods per week. It is meant to be taken in addition to your five major academic subjects. *

This course provides the student a strong foundation in the basics of computer programming and introduces her to algorithmic processes. Through a series of exercise sets and programming projects, the student will learn to code mathematical statements, variable assignments, lists, selection and iteration statements, subprocedures and functions, as well as other programming constructs. The programming language used for this course is Python. This class is open to classes VII, and VIII. No programming experience is required or expected of students. (0.25 credits)

### Java Programming (Fall Semester)

*This is a full-credit course that meets for 4x60 and 1x75-minute periods per week. It is meant to be taken as one of your five major academic subjects. *

This course provides students with the conceptual background in Computer Science necessary to gain insight into the nature of computing. After briefly discussing machine architecture and its effects on software design, the class will spend the semester discussing object-oriented programming, data structures, and algorithm analysis. A major theme of the course will be creating strategies for managing programs of increased complexity and scope. This class is open to classes VII and VIII. (0.5 credits)