# Math Curriculum

The Mathematics Department at WHHS empowers students to appreciate mathematics, exhibit confidence in mathematical ability, and apply various mathematical algorithms in problem solving, number theory, operations, measurement, and discrete mathematics. An emphasis is placed on the cumulative nature of mathematics as it evolves in each course. Students are encouraged to identify and model mathematical connections, functions, and patterns to other subjects as well as the real world. Instruction methods enable students to design mathematical solutions using inductive and deductive reasoning, statistics, data analysis, logic, and critical thinking skills, communicate using the language of mathematics in oral and written form, and use technology to facilitate and enhance mathematics learning.

## Algebra I (9th Grade)

Algebra I focuses on topics such as the real number system, linear functions, linear algebra, linear systems, quadratic functions, quadratic algebra, rational algebra, right triangle trigonometry, measurement, statistics, probability, set theory, and counting theory. The goal of the course is to assess students’ conceptual understanding, procedural fluency, and problem-solving abilities rather than to assess knowledge of isolated skills and facts. Students learn how to use a graphing calculator as an effective problem-solving tool. While the course follows the New York State Regents syllabus, the course is designed to go beyond the content and process strands of New York State Mathematics curriculum. This course is offered for 9th grade students who have not yet taken the NYS Algebra I Regents Exam.

## Geometry (9th and 10th Grade)

Students learn to build their understanding of geometric properties and reasoning through investigations of figures and shapes. The curriculum includes topics covered on the New York State Regents exam as well as additional enrichment topics. Course topics include geometric relationships, informal and formal proofs, triangles, polygons, quadrilaterals, coordinate geometry, transformational geometry, circles, geometric relationships, constructions, and locus. Other topics covered include logic, proofs, parallel lines, congruent triangles and properties of polygons as well as an extension of algebra and probability. Sections of this course are offered to 9th and 10th grade students who have already passed the NYS Algebra I Regents Exam.

## Algebra II and Trigonometry (10th and 11th Grade)

In this course, students conduct an in-depth study of rational expressions, radicals and complex numbers, quadratics, relations and functions, trigonometry (functions, graphs, equations, identities and applications), exponents, logarithms, sequences and series, probability and statistics. Concepts are extended and advanced topics are presented. Sections of this course are offered to 10th and 11th grade students who have already passed the NYS Geometry Regents Exam.

## Pre-Calculus (11th and 12th Grade)

Students explore all topics and prerequisite skills necessary to ensure success in AP Calculus AB or a college calculus course. Students model real world phenomena, understand functions, explore exponential and logarithmic functions, learn applications of trigonometry, investigate sequences and series, discover conic sections, and be introduced to Calculus. Sections of this course are offered to 11th and 12th grade students who have already passed the NYS Algebra II Regents Exam

## Advanced Placement Calculus AB

This is an honors level course that follows a college syllabus and introduces students to the two fundamental concepts of the derivative and integral. Techniques for finding derivatives are explored and applications studied. Integration follows the fundamental question of finding the area under a curve. Volumes of irregular shapes are found. Students use graphing calculators to illuminate the abstract ideas they are studying. This course is offered to 11th & 12th grade students who have successfully completed the Pre-Calculus course. At the conclusion of the course, students take the AP Calculus Exam administered by the College Board, which may, depending upon their score and university, yield 3-4 college academic credits.

## Advanced Placement Statistics

AP Statistics is a college level course that provides an understanding of the main ideas of statistics and useful skills for working with data. Students use real data from sports, economics, psychology and biomedical research. Using a graphing calculator and other types of technology, students focus on concepts and problem-solving rather than on calculations that are now automated. The major units include organizing data, producing data, probability and the foundations of inference (conclusions with confidence). Special attention is also given to simulation and the imitation of chance behavior. This course is offered to 11th & 12th grade students, based on teacher recommendation. At the conclusion of the course, students take the AP Statistics Exam administered by the College Board, which may, depending upon their score and university, yield 3-4 college academic credits

## Math Electives

**Math and Modern Logic**

This course focuses on the development of sound reasoning abilities through the study and application of the tools of logical analysis, with the objective of enhancing students’ problem-solving skills as well as their reasoning skills. Students will learn the tools of logical argument analysis, how to mathematically model and evaluate syllogistic forms of arguments, and how to represent arguments in symbolic form. They will learn the tools necessary to establish the validity of an argument and the fundamentals of inductive analysis. Students will learn various strategies to solve problems, which they will be able to apply to mathematical proof, to logical argument validity testing, and to logical argument writing.

**Number Theory**

Number Theory began as a playground for a few mathematicians that were fascinated by the curious properties of numbers. Today, it has numerous applications from pencil and paper algorithms, to the solving of puzzles, to the design of computer software, to cryptanalysis (a science of code breaking). Number Theory uses the familiar operations of arithmetic, but more as the starting point of intriguing investigations than as topics of primary interest. Number Theory is more involved in finding relations, patterns, and the structure of numbers. This course will cover topics such as the Fundamental Theorem of Algebra, Euclid's Algorithm, Pascal's Triangle, Fermat's Last Theorem, and Pythagorean Triples. We will finish the course with a linkage of Number Theory to Cryptography. In today's world of high speed communication, banks, corporations, law enforcement agencies and so on need to transmit confidential information over public phone lines or airwaves to a large number of other similar institutions. Prime numbers and composite numbers play a crucial role in many cryptographic schemes.