Niskayuna Central School District > Academics > Niskayuna High School Program of Studies 2024-25 > NHS Program of Studies: Mathematics

NHS Program of Studies: Mathematics

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The program in mathematics offers preparation in the concepts and skills necessary for competence in mathematics, as well as preparation for further study. All courses in mathematics aim to increase understanding of the basic concepts of mathematics and problem solving.

Attention will be given to providing a deeper knowledge of our number system, experience with quantitative reasoning, study of the nature of proof and of the techniques of critical thinking, and knowledge of the contributions mathematics has made and is making to the progress of civilization.

All students should have some experience with technology and should understand the close relationship that exists between technology and mathematics. Three different computer courses are offered.

Graduation Requirements

All students are required to earn at least three credits of high school mathematics in order to graduate. Additionally, students must meet the New York State requirement by passing the Algebra I Regents examination. Students must be enrolled in a math course from grades 9-11. No student may drop a math course altogether (without enrolling in another) unless they have successfully completed the minimum graduation requirement of 3 years/3 credits.

Grouping

The mathematics courses are grouped according to ability and interest in mathematics. The Advanced or Honors levels courses are for students with high interest and ability. These courses are intended for students who demonstrate exceptional mathematics skills.

In all cases, teachers make recommendations for student placements. School counselors discuss these recommendations with students and the recommendations are sent home for parental approval. If a parent wishes to question a teacher’s recommendation, the parent should contact the teacher or school counselor immediately.

Calculators

Graphing calculators are required on the New York State Regents examinations in Algebra 1, Geometry, and Algebra 2 as well as all Advanced Placement examinations.

It is recommended that students purchase their own calculators. -Students wishing to own a graphing calculator are strongly encouraged to purchase the TI-84, as this is the model teachers will be using for demonstrations in classrooms.

Mathematics Courses

21107 INTEGRATED ALGEBRA A

1 year, 1 credit, Grades 9-10

This course is the first year of a year and a half sequence leading to the Common Core Algebra I Regents exam. The remaining part of the Integrated Algebra curriculum will be completed in the subsequent course, Integrated Algebra B / Geometry A . The main topics of this course are working with variables, solving equations, operations with integers, formulas, polynomials, factoring, graphing elementary relationships, two variable equations, squares and square roots, and statistics. A final examination is taken at the completion of this course in June. The Common Core Algebra I Regents exam will be taken in the Integrated Algebra B/Geometry A course in the next year.

21225 ALGEBRA 1

1 year, 1 credit, Grades 9-10

This course entails a comprehensive study of elementary algebra, linear and quadratic functions, inequalities and absolute value, coordinate geometry, probability and statistics. Additional emphasis is placed on problem solving and algebraic skills. The final examination will be the Algebra I Regents taken in June.

22345 GEOMETRY ACCELERATED

1 year, 1 credit, Grades 9-10

This course focuses on the study of geometry. Topics will include plane and solid figures, congruence, constructions, transformations, deductive proof, similarity, coordinate geometry, trigonometry related triangle laws, circles, and measurement. Since algebra is integrated throughout the course, a high level of proficiency in elementary algebra is expected. This course is intended for students who demonstrate exceptional mathematics skills. The final examination will be the Common Core Geometry Regents Exam, which is taken in June.

Prerequisite: Accelerated Algebra; 93% or better recommended

22107 INTEGRATED ALGEBRA B/GEOMETRY A

1 year, 1 credit, Grades 10-11

This course is second year of a year and a half sequence leading to the Algebra I Regents. The second semester will begin the Geometry curriculum. Topics include linear and quadratic equations; systems of equations and inequalities; probability and statistics; area, perimeter, and volume; polygons, angles, segments and lines; circles, and trigonometry. The Algebra 1 Regents will be taken in January.

Prerequisite: Integrated Algebra A

22225 GEOMETRY

1 year, 1 credit, Grades 9-11

This course focuses on the study of geometry with an integration of algebraic concepts. Topics will include plane and solid figures, congruence, constructions, transformations, deductive proof, similarity, coordinate geometry, trigonometry related triangle laws, circles, and measurement. Since algebra is integrated throughout the course, a proficient level in algebra is expected. This course is intended for students who have completed the Common Core Algebra 1 Course. Students will take a midterm exam in January and the NYS Common Core Geometry Regents Exam in June.

Prerequisite: Algebra 1; 80% or better recommended

23346 ALGEBRA 2 ACCELERATED

1 year, 1 credit, Grades 10-11

Students in this course will follow the Algebra 2 Common Core learning standards adopted by New York State. Units covered will include the exploration of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. Students will also study relationships involving sequences and series and drawing inferences and conclusions from data. It is designed for accelerated tenth-graders and will include enrichment beyond the Algebra 2 curriculum. There will be a local final examination for this course in June. Students wishing to receive an Advanced Regents Diploma must take and pass the Common Core Algebra 2 Regents Exam.

Prerequisite: Algebra Accelerated and Geometry Accelerated; 83% or better recommended

23466 ALGEBRA 2 HONORS

1 year, 1 credit, Grades 10-11

Students in this course will follow the Algebra 2 Common Core learning standards adopted by New York State. Units covered will include the exploration of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. Students will also study relationships involving sequences and series and drawing inferences and conclusions from data. It is designed for accelerated tenth-graders who demonstrate exceptional mathematical skills and will include enrichment beyond the Algebra II curriculum. The final examination is a compilation of the midterm exam given in January and the Algebra 2 Regents given in June. Students wishing to receive an Advanced Regents Diploma must take and pass the Common Core Algebra 2 Regents Exam.

Prerequisite: Algebra Accelerated and Geometry Accelerated; 93% or better recommended

23108 INTRODUCTION TO COLLEGE MATH

1 year, 1 credit, Grades 10-12

This course covers intermediate algebra and trigonometry topics. Course material includes the study of functions (linear, quadratic, square root, cubic/cube root, periodic, and exponential), inverses and compositions of functions, operations on real and complex numbers, statistical data analysis, right triangle trigonometry, and periodic functions. Units of study have a calculator and algebraic approach and have a focus on application questions. The final exam is a compilation of exams given in January and June. There is no Regents exam in this course.

Prerequisite: Integrated Algebra B/Geometry A or Geometry

23226 ALGEBRA 2

1 year, 1 credit, Grades 10-12

Students in this course will follow the Algebra 2 Common Core learning standards adopted by New York State. Units covered will include the exploration of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. Students will also study relationships involving sequences and series and drawing inferences and conclusions from data. Students will take a midterm exam in January and the NYS Common Core Algebra 2 Regents Exam in June.

Prerequisite: Algebra 1 and Geometry; 75% or better recommended

24345 PRECALCULUS ACCELERATED

1 year, 1 credit, Grades 10-11

This course covers the study of pre-calculus topics such as two-dimensional analytic geometry, vectors, mathematical induction, polar coordinates, polynomial, rational, exponential, logarithmic and trigonometric functions; sequences and series; complex numbers; DeMoivre’s Theorem; and conic sections. Students planning to take the AP Calculus AB course should elect this course. A final examination is taken at the completion of this course in June.

Prerequisite: Algebra 2 Accelerated; 83% or better recommended

24465 PRECALCULUS HONORS

1 year, 1 credit, Grades 10-11

This course provides in-depth coverage of the pre-calculus topics: polynomial, rational, exponential, logarithmic and trigonometric functions, polar coordinates, matrices, sequences and series, conics, parametric equations, two-dimensional analytic geometry, and mathematical induction. Students planning to take the AP Calculus BC course should elect this course. A final examination is taken at the completion of this course in June.

Prerequisite: Algebra 2 Honors; 83% or better recommended

24110 INTRODUCTION TO PRECALCULUS

1 semester, 1/2 credit, Grades 11-12

The main purpose for this course is to help prepare students for a college level math course. The curriculum will strengthen a student’s skills introduced in the Algebra 2 & Trigonometry curriculum and extend them into the traditional Pre Calculus domain. The mathematical investigations will take a graphing calculator approach with emphasis on mathematical applications. Topics to be investigated will include: Analytic Trigonometry, polynomial functions and their graphs, arithmetic and geometric sequences and series, and exponential and logarithmic functions.

Prerequisite: Algebra 2 or Intro to College Math

24115 ANALYTIC GEOMETRY

1 semester, 1/2 credit, Grades 11-12

The main purpose for this course is to help prepare students for a college level math course. The curriculum is set up to introduce a traditional Pre Calculus experience. The mathematical investigations will take a graphing calculator approach with an emphasis on mathematical applications. Topics to be investigated will include: conics, parent functions and their graphs, transformations, and rational and piecewise functions and their graphs.

Prerequisite: Algebra 2 or Intro to College Math

24050 INTRODUCTION TO STATISTICS

1 semester, 1/2 credit, Grades 11-12

This course is designed as an introduction to descriptive and inferential statistics. Topics for discussion during the first quarter will include: data sources and ways of representing data, measures of central tendency and their applications, normal distributions, and linear regression. During the second quarter we will discuss: probability concepts including binomial distributions and conditional probability, expected value, confidence intervals, and hypothesis testing. Handheld and appropriate computer technologies, such as Excel, will be utilized.

Prerequisite: Algebra 2 or Intro to College Math

24060 MATH FOR THE BUSINESS WORLD

1 semester, 1/2 credit, Grades 11-12

Business models using linear, quadratic, piecewise, and exponential models will be studied. Applications will include cost, revenue, and profit. Topics for discussion will include: compound interest, annuities, and other finance problems, linear programming and applications of matrices. Handheld and appropriate computer technologies will be utilized. The final exam is a compilation of two half-course exams. There is no Regents exam for this course.

Prerequisite: Algebra 2 or Intro to College Math

24225 PRECALCULUS

1 year, 1 credit, Grades 11-12

Topics to be studied include algebraic and transcendental functions, trigonometry and its applications, complex numbers, analytic geometry, parametric equations, polar coordinates, and sequences and series. This course is a must for students planning to take calculus in college or planning to continue in a mathematics or science-related field. The final examination is a compilation of exams given in January and June.

Prerequisite: Algebra 2; 73% or better recommended

26020 CALCULUS

1 year, 1 credit, Grade 12

This course covers the study of calculus topics such as functions, limits and continuity, differentiation and integration. It is designed to permit the student to take more advanced courses in college, both in mathematics and subject areas that require a background in mathematics. The final examination is a compilation of exams given in January and June. Prerequisite: Precalculus; 73% or better recommended

26100 AP CALCULUS AB

1 year, 1 credit, Grade 12

This is a calculus course that follows the Advanced Placement AB Calculus syllabus. This course is designed to permit the student to take more advanced courses in college, both in mathematics and in subject areas which require an extensive background in mathematics. There will be a final examination for this course. The AB Advanced Placement examination is offered in May.

Prerequisite: Precalculus Accelerated; 83% or better recommended

26120 AP CALCULUS BC

1 year, 1 credit, Grade 12

This course completes the topics of the Advanced Placement BC Calculus syllabus started in Precalculus Honors. It is designed to permit the student to take more advanced courses in college, both in mathematics and in subject areas which require an extensive background in mathematics. There will be a final examination for this course. The BC Advanced Placement examination is offered in May.

Prerequisite: Precalculus Honors; 83% or better recommended

26445 MULTIVARIABLE CALCULUS (CALCULUS 3)

1 Semester, 1/2 credit, Grade 12

This course is designed for students who have completed AP Calculus BC prior to their senior year. Topics include vectors and their applications, derivatives of multivariable functions, multivariable optimization, multiple integrals, vector fields and the theorems of Green, Gauss and Stokes.

Prerequisite: AP Calculus BC

26180 AP STATISTICS

1 year, 1 credit, Grades 11-12

This statistics course follows the Advanced Placement syllabus which introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. This course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics and is heavily dependent on graphing calculator and computer technology. This course will be useful for any student considering study in science, engineering, business, psychology or the social sciences. A final examination is taken at the completion of this course. Students will be prepared to take the AP Statistics Exam which is offered in May.

Recommended preparation: A or better in Algebra 2; 83% or better in Algebra 2 (A/H)

COMPUTER COURSES

27100 COMPUTER SCIENCE 1

1 semester, 1/2 credit, Grades 9-12

At Niskayuna we constantly are striving to introduce our students to the field of computer science. The course starts off utilizing HTML and CSS, so students can see the end result using an Internet Browser and design a website. The course then transitions into graphical programming environments known as Alice and Scratch, followed by an introduction to object-oriented programming using Python. These languages are a gentle approach to learning the structure and syntax of JAVA. Students will develop games starting with Alice and Scratch. Students utilize their computational thinking to design their games and programs. Computational thinking techniques include: problem decomposition, pattern recognition, pattern generalization to define abstractions or models, algorithm design, and data analysis and visualization.

Prerequisite: Algebra or Integrated Algebra A

27120 COMPUTER SCIENCE 2

1 semester, 1/2 credit, Grades 9-12

A continuation of computer science one with an emphasis on computational thinking with Java utilized as a vehicle for algorithm implementation. The class prepares students for latter computer science classes such as APCS A or introductory computer science in college. Depending on the availability of resources and classroom dynamics, programming using an Android device using AppInventor will be explored.

Prerequisite: Computer Science 1 or exemption test given by the instructor

27140 AP COMPUTER SCIENCE A

1 year, 1 credit, Grades 10-12

AP Computer Science goes beyond merely learning how to use applications like word processing, spread sheets, and internet browsers. It uses the Java language and focuses on the basic principles needed to design and build applications. It’s a college level course. At the course’s end, students will be asked to take the AP Computer Science A test. Students have the opportunity to receive college credit for one semester of computer science.

Recommended preparation: Computer Science 1 and Computer Science 2 or demonstration of a solid understanding of Java to the instructor