# 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. 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. |

## 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. |

- Algebra I
- Geometry
- Algebra II and Trigonometry
- Pre-Calculus
- Statistics/Advanced Placement Statistics
- Calculus
- Advanced Placement Calculus AB
- Advanced Placement Calculus BC
- Introduction To Programming

## Algebra I

This course provides a comprehensive study of first-year concepts. It is designed to prepare students for subsequent course work in geometry and second-year algebra. Topics include numbers and equations, linear equations and inequalities, polynomials and factoring, quadratic equations, lines and their graphs, systems of linear equations, properties of exponents, rational and radical expressions, and probability and statistics.

## Geometry

This course provides students with training in the analytical approach to problem solving and with practice in deductive reasoning. Students first become familiar with the geometric building blocks and geometric constructions and continue with the study of angles, triangles, quadrilaterals, congruence, circles, Pythagorean Theorem, volume, similarity, trigonometry, and geometric proof. Students use algebraic methods in problem solving. Students who qualify may take this course at the honors level. The honors level moves at a faster pace and goes into more depth.

## Algebra II and Trigonometry

## Pre-Calculus

This course is designed to enable students to synthesize the concepts learned in Algebra and Geometry while preparing for higher study in abstract mathematics. Topics include coordinate geometry, polynomials, inequalities, functions, exponents, logarithms, trigonometric functions, triangle trigonometry, trigonometric addition formulae, advanced graphing, data analysis, sequences and series, limits, and an introduction to the concepts of calculus. Students who qualify may take this course at the honors level. The honors level moves at a faster pace and goes into more depth.

## Statistics/Advanced Placement Statistics

This course introduces students to the major concepts and tools for collecting, analyzing, and interpreting numerical information from our data. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns, and making statistical inferences. The Advanced Placement course prepares students for the Advanced Placement exam.

## Calculus

Students build on their knowledge of algebra, geometry, and trigonometry and gain an intuitive understanding of the principles of integral and differential calculus. They learn to apply these concepts through the presentation of the following topics: Cartesian plane, functions, limits, continuity, differentiation and applications, and integration and applications.

## Advanced Placement Calculus AB

## Advanced Placement Calculus BC

This course is open to students who successfully complete Advanced Placement Calculus AB. They perfect their calculus skills and cover advanced topics such as L'Hopital's Rule, the calculus of sequences and series, polar coordinates, and advanced integration techniques. They are prepared to take the Advanced Placement Examination in BC Calculus.

## Introduction To Programming

This course is a hybrid with two class periods per cycle as well as online lectures and activities. The class is project-based and students primarily demonstrate their knowledge with hands-on projects. It covers a variety of programming concepts and tools and looks at current day computer science issues in an effort to excite students about learning how to program.

It starts with a brief overview of Computational Thinking then into Scratch, from the MIT Media Lab. Scratch is great way to learn a variety of computer programming basics. The course then transitions into a unit focusing on Android App Development with MIT’s AppInventor. The girls will learn how to create apps and design some of their own. Some students may even be interested in participating in Technovations’s app contest. While working on apps, time is spent on current day issues surrounding computer programming, specifically those relating to recent studies on girls, women, and computer science.

The final part of the class incorporates the application, Processing. Students use the Processing language to learn some of the basics of programming that involves a line-by-line textual environment similar to JAVA. Girls may work with the application, Alice, It aims to teach the basics of object-oriented programming through the use of 3D graphics and a drag-and- drop interface. We would revisit some topics that we first saw in Scratch and will move on to methods, functions, parameters, arguments, if-else statements, and loops through this three dimensional animated environment. These new skills will prepare students to transition into a variety introductory course either at NCDS or in college.