# Mathematics

The mathematics program strives to empower students with analytical and problem-solving skills while providing them with a strong foundation for future college mathematics courses. All Middle and Upper School classes balance drills involving fundamental mathematical skills with the application of such skills in solving complex problems. As a result, they emerge from the program possessing a broad knowledge of mathematical tools and techniques, as well as a deep understanding of abstract concepts. In the Middle School, students are placed in class groupings based on their exposure to, and their level of mastery of, various math concepts. A test is given to aid in the placement process. |

## Middle School

In the Middle School, students are placed in class groupings based on their exposure to, and their level of mastery of, various math concepts. A test is given to aid in the placement process.

- Mathematics 5
- Mathematics 5 (accelerated level)
- Mathematics 6 (standard level)
- Mathematics 6 Pre-Algebra I (accelerated level)
- Mathematics 7 Pre-Algebra (standard level)
- Mathematics 7 Pre-Algebra II (accelerated level)
- Mathematics 8 Algebra
- Math 8 Algebra (accelerated level)

## Mathematics 5

Students practice and develop the essentials of mathematics. Topics include whole number concepts; addition, subtraction, multiplication and division of whole numbers; decimals and fractions; prime and composite numbers; and an introduction to percent, integers, and topics in geometry. Students may be placed in an accelerated class if they have demonstrated mastery of the topics covered in Math 5.

## Mathematics 5 (accelerated level)

This course is designed to solidify students’ mathematical skills with practice in all four operations: addition, subtraction, multiplication, and division, with fractions and decimals. Students reinforce their knowledge of the order of operations (PEMDAS) and begin work on pre-algebra with variables, expressions, and equations. Students learn about percentages, estimation and rounding, and how to set up the solution to a word problem. This course also engages girls in the study of geometry, specifically area and perimeter of circles, squares, rectangles and triangles. Students start to work with integers – positive and negative numbers.

## Mathematics 6 (standard level)

## Mathematics 6 Pre-Algebra I (accelerated level)

Pre-Algebra I and II represent an integrated two-year program designed as a rigorous preparation for Upper School mathematics. Topics in Pre-Algebra I include operations with integers, fractions, decimals, and rational numbers with applications to graphing, geometric and algebraic contexts, introduction to probability and statistics, sets, and operations on sets. The curriculum emphasizes problem solving, reading skills, communication of mathematics, independent and small group work, and appropriate use of a calculator.

## Mathematics 7 Pre-Algebra (standard level)

Students continue to practice and develop the essentials of mathematics while being introduced to algebraic concepts. Topics include integers, solving equations, decimals and equations, number theory, rational numbers and expressions, ratios, proportions and percents, equations and inequalities, graphing in the coordinate plane, geometry and measurement, area and volume, statistics and probability, and polynomials.

## Mathematics 7 Pre-Algebra II (accelerated level)

Students enrolled in Pre-Algebra II study positive and negative numbers, rational numbers, equations and inequalities, polynomials, fractions, decimals, percents, and probability. Elements of algebra, geometry, number theory, and trigonometry are integrated, and deductive reasoning is emphasized. Students work independently in small groups under close guidance and supervision

## Mathematics 8 Algebra

The goal of Math 8 is to develop students’ confidence and perfecting skills while solving basic algebraic problems. The year begins with a review of the summer work and a diagnostic exam, following which students will begin the exploration of topics including: expressions, operations with negative numbers, distributing, axioms and other properties, equations both linear and quadratic, operations with polynomials and radicals, expressions ad equations with two variables, properties of exponents, operations with polynomials, rational algebraic expressions, radical algebraic expressions, inequalities, and functions.

## Math 8 Algebra (accelerated level)

## Upper School

In the Upper School, three years of mathematics are required and four are recommended. The goals of the department are to help students think clearly, to develop the ability to use inductive and deductive reasoning, and to strengthen the use of mathematics and technology in solving problems. Computer Science is a graduation requirement. |

- Algebra I
- Algebra II
- Honors Algebra II
- Principles of Geometry
- Geometry
- Honors Geometry
- PreCalculus
- Honors PreCalculus
- Calculus
- Advanced Placement Calculus AB
- Advanced Placement Calculus BC and Advanced Topics
- Advanced Placement Statistics
- Statistics and Financial Algebra

## Algebra I

This course provides a comprehensive study of first-year Algebra concepts. It is designed to prepare students for subsequent course work in geometry and second-year algebra. Topics include numbers and equations, solving multi-layered linear equations and inequalities, solving absolute value equations and inequalities, graphing and writing linear functions, systems of equations, properties of exponents, polynomial operations, factoring, solving polynomial equations by factoring, completing the square and the quadratic formula, graphing and writing quadratic functions, operations with rational and radical expressions, and solving rational and radical equations. By the end of the year, students are able to apply algebraic skills to a myriad of both linear and quadratic word problems. Emphasis is placed on developing a strong foundation upon which future mathematics can be built. Prerequisite: Pre-Algebra

## Algebra II

## Honors Algebra II

This course continues students’ comprehensive study of algebraic concepts. Students engage in problem solving, small group work, and lectures to solidify their comprehension of Algebra I concepts including linear equations and inequalities, solving and graphing systems of equations, and quadratics. Students explore functions extensively, namely piecewise, polynomial, rational, exponential, polynomial, radical and logarithmic functions. Inverse functions are introduced along with complex numbers. When time allows, students may also explore probability and statistics. All concepts are applied to a variety of real-life situations through word problems and the use of interactive technology tools. Students emerge from this course with proficiency in graphing functions and solving a host of equations. Conic sections are explored. At the honors level, students are expected to engage in a deeper level of abstraction at a significantly faster pace. Assessments include multiple unfamiliar problems to which students must apply innovative thinking in order to solve. Departmental approval required

## Principles of Geometry

This course in Euclidean Geometry provides students with the ability to explore the mathematical concepts of two and three dimensional space and shapes through reasoning, analyzing, classifying, and synthesizing. Students first become familiar with geometric building blocks and geometric constructions. They continue with the study of triangle congruence, quadrilaterals, similarity, transformation, Pythagorean Theorem, trigonometry, area, volume, and circles. Students apply algebraic skills in problem solving and employ the principles of logic by writing formal deductive geometric proofs. Students experience a variety of learning styles including direct instruction, independent learning, and group work. To develop logic and critical thinking skills, students are exposed to technological tools and manipulatives as they discern geometric relationships. This course places less emphasis on proofs than other geometry courses and takes more time to review algebraic skills as they are applied to geometric problems. Student-centered learning is emphasized. Departmental approval required

## Geometry

This course in Euclidean Geometry provides students with the ability to explore the mathematical concepts of two and three dimensional space and shapes through reasoning, analyzing, classifying, and synthesizing. Students first become familiar with geometric building blocks and geometric constructions. They continue with the study of triangle congruence, quadrilaterals, similarity, transformation, Pythagorean Theorem, trigonometry, area, volume, and circles. Students apply algebraic skills in problem solving and employ the principles of logic by writing formal deductive geometric proofs. Students experience a variety of learning styles including direct instruction, flipped instruction, independent learning, and group work. To develop logic and critical thinking skills, students are exposed to technological tools and manipulatives as they discern geometric relationships. Prerequisite: Algebra I

## Honors Geometry

This course in Euclidean Geometry provides students with the ability to explore the mathematical concepts of two and three dimensional space and shapes through reasoning, analyzing, classifying, and synthesizing. Students first become familiar with geometric building blocks and geometric constructions. They continue with the study of triangle congruence, quadrilaterals, similarity, transformation, Pythagorean Theorem, trigonometry, area, volume, and circles. Students apply algebraic skills in problem solving and employ the principles of logic by writing formal deductive geometric proofs. Students experience a variety of learning styles including direct instruction, independent learning, and group work. To develop logic and critical thinking skills, students are exposed to technological tools and manipulatives as they discern geometric relationships. At the honors level, proofs are studied more extensively than they are at other levels. Students are expected to engage in a deeper level of abstraction at a significantly faster pace. Assessments include multiple unfamiliar problems to which students must apply innovative thinking in order to solve. Departmental approval required

## PreCalculus

In this course, students continue to study polynomial, exponential and logarithmic functions in greater depth. Additionally, a full semester of trigonometry is examined. Students explore the laws of sine and cosine, solve a full complement of trigonometric equations, graph trigonometric functions, prove trigonometric identities, and apply these skills to modeling problems. Following this, limits are introduced. Graphing calculators are used throughout the course to reinforce comprehension and to solve real-world problems. More traditional analytic and algebraic problem solving methods are emphasized so that students understand multiple approaches to problems from different vantage points. The course equips students with the necessary skills and knowledge to pursue advanced mathematics. Prerequisites: Algebra II and Geometry

## Honors PreCalculus

In this course, students continue to study polynomial, exponential and logarithmic functions in greater depth. Additionally, a full semester of trigonometry is examined. Students explore the laws of sine and cosine, solve a full complement of trigonometric equations, graph trigonometric functions, prove trigonometric identities, and apply these skills to modeling problems. Following this, limits are introduced. Graphing calculators are used throughout the course to reinforce comprehension and to solve real-world problems. More traditional analytic and algebraic problem-solving methods are emphasized so that students understand multiple approaches to problems from different vantage points. The course equips students with the necessary skills and knowledge to pursue advanced mathematics. The honors level covers additional trigonometric topics as well as sequences and series. Students are expected to engage in a deeper level of abstraction at a significantly faster pace. Assessments include multiple unfamiliar problems to which students must apply innovative thinking in order to solve. Departmental recommendation required

## Calculus

This is a foundational course, playing an important role in the understanding of science, engineering, economics, and computer science, among other disciplines. Students in Calculus begin by studying limits, and then couple that learning with their understanding of slope and area to develop the concepts of derivatives and integrals. Study of these concepts includes learning to differentiate and integrate functions introduced in previous courses. Topics covered include continuity, tangent lines, the limit definition of derivative and derivative rules, implicit differentiation, related rate applications, curve sketching and graph analysis, anti-derivative and integration techniques, and area and volume of solids of revolution. Students emerge from the course prepared to pursue a more in-depth study of calculus in college. Prerequisite: PreCalculus

## Advanced Placement Calculus AB

This is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions. Topics include limits and continuity, differentiation rules, application to graphing, related rates, approximations, extremum problems, definite and indefinite integration, the Fundamental Theorem of Calculus, area, volume, techniques of integration, and L’Hôspital’s Rule. Throughout the course, graphing calculators are used as a tool to enhance understanding of concepts and to facilitate problem solving. Students are expected to take the AP exam in May. Departmental approval required

## Advanced Placement Calculus BC and Advanced Topics

This course continues the study of AP Calculus AB. Additional topics in the AP curriculum encompass integration by parts, integration using partial fractions, Euler's method and logistic models with differential equations, arc length, distance traveled along a smooth curve, parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series. Moreover, the course explores concepts taught in traditional college courses that do not appear in the AP curriculum. These include, but are not limited to: integration by trigonometric substitution, powers of sine, cosine, tangent, and secant, the epsilon-delta definition of a limit, proofs of numerous theorems including the product and quotient rules, volume using shells, Simpson’s rule, Newton’s method, and logarithmic differentiation. Students are expected to take the AP exam in May. Departmental approval required

## Advanced Placement Statistics

This is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore four main areas of study: quantitative and categorical data analysis, designing studies, probability, and statistical inference. Students are asked to both analyze and infer about applicable data sets from many sources. Topics include graphing, density curves, linear regression, analyzing and comparing distributions, observational studies, experiments, probability, random variables, binomial and geometric distributions, sampling distributions, confidence intervals, significance tests, and linearizing nonlinear data. Students are expected to take the AP exam in May. Departmental approval required

## Statistics and Financial Algebra

This course provides students with an opportunity to learn and use Statistics and Algebra in solving real-world problems with a financial focus. The course explores algebraic patterns and functions in a financial context and the application of these skills to relevant research topics of interest. Concepts covered include function analysis and systems of equations, graphing, statistics, linear regressions, variables, and modeling. This course is project-based; financial applications are a primary emphasis of the course. Project topics explore loans, investments, credit, insurance, taxes, and budgeting. By the end of the school year, students possess a significant degree of financial literacy. Armed with this knowledge, they enter college as financially responsible and educated individuals. Open to students in grade 12