# Mathematics

### a focus om problem solving

The Salisbury Mathematics Department aims to help students build a solid foundation in mathematics. We accomplish this goal by offering a challenging and diverse curriculum that focuses on perseverance, collaboration and problem solving. We help our students improve their skills by providing constant feedback and by fostering a growth mindset that capitalizes on mistakes and challenges. We pride ourselves on meeting students where they are and guiding them towards success and mastery. Fluency with data, computer competency and financial literacy imbue our curriculum at all levels.

The Rule of Four is a focus whenever it is applicable. Mathematical ideas can be communicated in many ways. These Rule of Four leads to a deeper understanding of the mathematics and gives students a variety of modalities to express their understanding.

Placement is based largely on recommendations from prior teachers and, when necessary, on Mathematics placement tests. Our core requirements of Algebra I, Geometry and Algebra II are taught at multiple levels to ensure you are appropriately challenged and supported. Virtually all students study beyond Algebra II, through Precalculus and Calculus.

Economics courses are offered through the Salisbury Mathematics Department. In addition, we offer Advanced Placement courses in Calculus, Computer Science, Economics, and Statistics. We also offer a year-long course in Multivariable Calculus. By permission of the department and the Director of Studies, we also arrange for and enable students to receive academic credit for independent studies or online courses in advanced topics such as Abstract Linear Algebra.

The Salisbury Mathematics Department uses the TI-84 Plus CE Graphing Calculator.

## Mathematics Offerings At Salisbury:

- Mathematics
- Computer Science
- Economics
- Entrepreneurial Studies
- Mathematics Department Requirements for Honors and Advanced Placement Study

## Mathematics

### M112 ALGEBRA I

This course will provide students with a deeper knowledge and understanding of the real number system and its properties through the study of variables, expressions, equations, inequalities, and analysis of data derived from real-world applications. Emphasis is placed on the relationships between numerical, graphical and symbolic approaches, drawing connections to real-world applications and models. Topics include linear equations and inequalities, linear systems, relations, functions, polynomials and factoring, graphical transformations, graphing applications, as well as data display and analysis. The skills emphasized in Algebra I provide a formal development of the algebraic skills and concepts necessary for students to succeed in advanced courses.

### M113 ALGEBRA I

This course is based on M112 but moves at a slower pace to accommodate different learning styles. It is expected that students in this course will continue to M223, which incorporates algebra topics into the study of geometry.

### M222 GEOMETRY

This course will provide students with a base in the concepts of geometry. Emphasis is placed on the geometric proof and logical thinking. Properties of parallel lines, circles and polygons will be fully explored. Translations in the coordinate plane as well as measurements will be studied. Algebra will be heavily used throughout the course and a review will be done in preparation for M322.

Prerequisite: Successful completion of Algebra I

### M223 GEOMETRY

This course covers the same topics as M222 with a lesser emphasis on formal proof and greater emphasis on application. The course also provides further exploration and application of algebra concepts with a review at the end of the year in preparation for M333.

Prerequisite: Algebra I

### M331 ALGEBRA II and TRIGONOMETRY HONORS

Through the Rule of Four, this honors course focuses on functions and their properties. Linear, quadratic, polynomial, exponential, logarithmic, trigonometric, rational and inverse functions will be fully explored. This course involves extensive use of the TI-84Plus CE graphing calculator.

Prerequisite: Algebra I and Geometry with permission of the Mathematics Department Chair and the Director of Studies.

### M332 ALGEBRA II

This course will focus on functions and the Rule of Four. Linear, quadratic, polynomial, exponential, logarithmic and inverse functions will be fully explored. This course involves extensive use of the TI-84Plus CE graphing calculator.

Prerequisite: Algebra I and Geometry

### M333 ALGEBRA II

This course covers the same topics as M332 but at a slower pace. The TI-84 Plus CE will be used.

Prerequisite: Algebra I and Geometry

### M441 PRECALCULUS HONORS

This course is a springboard to AP Calculus BC or AB. Functions are reviewed, and probability, vectors, sequences, series and deductive reasoning are explored. Limits and continuity are introduced so that derivatives and integrals can be explored along with the two Fundamental Theorems of Calculus. This course involves extensive use of the TI-84Plus CE graphing calculator.

Prerequisite: Algebra II and Trigonometry Honors with permission of the Mathematics Department Chair and the Director of Studies.

### M442 PRECALCULUS

This course provides preparation for the study of calculus. Students will solidify their foundation by going deeper into the study of functions and adding trigonometric functions to their knowledge base. The Rule of Four is still a focus and probability along with conics will be introduced. This course involves extensive use of the TI-84Plus CE graphing calculator.

###### Prerequisite: Algebra II

### M440 INTRODUCTION TO PRE-CALCULUS

This course is designed to solidify students’ algebraic foundation in preparation for precalculus. Topics include an in-depth review of the functions that were studied in algebra and additional topics include rational expressions, inequalities, complex numbers, parent functions, higher degree polynomial, zeros of polynomial functions and inverse functions. This course is designed for V Formers to prepare them for M441. This course involves extensive use of the TI-84Plus CE graphing calculator.

###### Prerequisite: Algebra II

### M422P PROBABILITY AND STATISTICS

This course provides an introduction to probability modeling and statistical inference. It is focused around five major ideas: 1. Data consists of structure and variance 2. Distribution describes variability 3. Hypothesis tests answer the question, “Could this have happened by chance?” 4. The way in which data is collected matters and 5. Evaluating an estimator involves considering bias, precision and the sampling method.

###### Prerequisite: Algebra II. Open to VI Formers

### M442D DISCRETE MATHEMATICS

This course will use problem solving and reasoning skills to explore areas of mathematics not traditionally covered in earlier courses of study. It is the study of mathematics dealing with objects that have some distinct separate values that lends itself to a wide variety of real world applications. Topics will include counting and sorting techniques, the exploration of combinations, game strategies, the appropriate use of the building tree diagrams and the applications of networking. Several calculus concepts, including the first derivative, are employed to study business systems and investment trends. This course involves extensive use of the TI-84Plus CE graphing calculator.

###### Prerequisite: Algebra II. Open to VI Formers

### M552 CALCULUS

This is a non-advanced placement course that introduces students to the two main ideas of Calculus: differentiation and integration. An emphasis is placed on application of the techniques taught in Calculus to solving business and scientific problems. This course involves extensive use of the TI-84Plus CE graphing calculator.

###### Prerequisite: Precalculus

### M551 ADVANCED PLACEMENT CALCULUS AB

This course follows the national curriculum for AP Calculus AB and prepares students for the Advanced Placement test in May. In addition to the national curriculum, this course emphasizes problem solving, collaboration and alternative assessments. This course involves extensive use of the TI-84Plus CE graphing calculator.

###### Prerequisite: Precalculus Honors or Precalculus with permission of the Mathematics Department Chair and the Director of Studies.

### M661 ADVANCED PLACEMENT CALCUUS BC

This course follows the national curriculum for AP Calculus BC and prepares students for the Advanced Placement test in May. In addition to the national curriculum, this course emphasizes problem solving, collaboration and alternative assessments. This course involves extensive use of the TI-84 Plus CE graphing calculator.

###### Prerequisite: Precalculus Honors with permission of the Mathematics Department Chair and the Director of Studies.

### M771 ADVANCED PLACEMENT STATISTICS

This course follows the national curriculum for AP Statistics and prepares students for the Advanced Placement test in May. In addition to the national curriculum, this course emphasizes problem solving, collaboration and alternative assessments. This course requires extensive use of the TI-84 Plus CE graphing calculator.

###### Prerequisite: Precalculus with permission of the Mathematics Department Chair and the Director of Studies.

### M881 MULTIVARIABLE CALCULUS

This course is a thorough introduction to multivariable calculus and mathematical methods used to solve problems in three dimensions. Topics include limits, continuity and differentiability in several variables, Lagrange’s multipliers, Taylor theorem, multiple integrals as well as integration on curves and surfaces. Green’s, Stokes’ and divergence theorems are also explored. While the course emphasizes concrete computations over proof, it demands that students move beyond thinking of mathematics as a set of rules and algorithms to memorize and encourages students to approach problems with greater independence and maturity. This course involves extensive use of the TI-84 Plus CE Graphing Calculator.

###### Prerequisite: AP Calculus BC

## Computer Science

### M991 Advanced Placement COMPUTER SCIENCE A

The course emphasizes object-oriented programming methodology with a concentration on problem solving and algorithmic development and is meant to be the equivalent of a first-semester college-level course in computer science. It also includes the study of data structures, design, and abstraction and follows the proscribed curriculum for the AP.

### M992 Advanced Placement COMPUTER SCIENCE PRINCIPLES

The course introduces students to the central ideas of computer science, instilling the ideas and practices of computational thinking and inviting students to understand how computing changes the world. The rigorous course promotes deep learning of computational content, develops computational thinking skills, and engages student in creative aspects of the field.

## Economics

### E442P ECONOMICS

This year long course introduces students to fundamental economic concepts and emphasizes how the principles of economics relate to each other and the overall structure of economic systems. Students will use economic concepts to better analyze, comprehend and explain personal, community, national and global economic issues. Though not a math course, students will use measurement concepts and methods such as the tables, charts, graphs, ratios, percentages and index numbers to understand and interpret relevant data. Where applicable, Excel skills will be developed and strengthened as spreadsheets are utilized in the investigation of economic concepts. From time to time, guest speakers and field trips may be incorporated into the curriculum.

### ES441 ADVANCED PLACEMENT MICROECONOMICS

This course covers the national curriculum for AP Microeconomics and prepares students for the Advanced Placement test in May.

###### Prerequisite: Overall GPA requirement of 3.6.

## Entrepreneurial Studies

### EE440 ENTREPRENEURIAL STUDIES

**Trimesters I and II: **

Entrepreneurship in History – Students will gain an appreciation of the role of entrepreneurs in history through investigation of entrepreneurship in different sectors and time periods. The interrelationship between scientific and technological discoveries and entrepreneurial development will also be examined. Students explore a myriad of applications of algebra in the world of business. Topics include and introduction to accounting, microeconomic theory, corporate evaluation and the many implications of the time value of money. The spreadsheet is taught and used extensively as a learning presentation medium.

Business Ethics – Interspersed throughout the course and interwoven within projects, the topics of business ethics will be addressed, debated and acted upon over the first two trimesters and put into practice in developing and executing the business plan.

__Trimester III: __

The Business Plan -Over the course of the final trimester, students apply many of the concepts learned in the previous two trimesters to determine the viability of their business idea and then draft and finalize a business plan that they will present to members of the school administration. If they are successful in presentencing and defending their business plan, then they are provided funding to execute their business plans in their sixth form year.

###### Prerequisite: Open to V Formers

## Mathematics Department Requirements for Honors and Advanced Placement Study

__ NOTE: __ Placement in all levels of mathematics is determined by performance in previous courses and recommendations from teachers and is finalized by the Mathematics Department Chair and the Director of Studies. A placement test may be given if needed. If a student wishes to take more than one mathematics course, they too will need the permission of the Department Chair and the Director of Studies.

The academic life at Salisbury is motivating. The teachers, coaches, and mentors at Salisbury are exceptional. They bring passion and expertise into their intimate classroom settings. Collaboration, innovation, problem solving, creativity, and civic responsibility are just some of the principles that guide Salisbury School’s educational model. Most importantly, these men and women partner with you each day and always with the highest expectations.

*Dean of Academic Life Sarah Mulrooney*

## A Glimpse At Three Of Our Math Offerings:

**MULTIVARIABLE CALCULUS**

A thorough introduction to multivariable calculus and mathematical methods used to solve problems in three dimensions. Topics include limits, continuity and differentiability in several variables, Lagrange multipliers, Taylor's theorem, multiple integrals, integration on curves and surfaces, Green's, Stokes' and divergence theorems. While the course emphasizes concrete computations over proof, it demands that students move beyond thinking of mathematics as a set of rules and algorithms to memorize, approaching problems with greater independence and maturity.

**AP COMPUTER SCIENCE A**

The course emphasizes object-oriented programming methodology with a concentration on problem solving and algorithm development, and is meant to be the equivalent of a first-semester college-level course in computer science. It also includes the study of data structures, design, and abstraction and follows the proscribed curriculum for the AP.

**AP COMPUTER SCIENCE PRINCIPLES**

The course introduces students to the central ideas of computer science, instilling the ideas and practices of computational thinking and inviting students to understand how computing changes the world. The rigorous course promotes deep learning of computational content, develops computational thinking skills, and engages students in the creative aspects of the field.