Algebra 1A (Not offered in 2024-2025)

Algebra 1A is the first year of the revised Common Core Mathematics curriculum.  This course is half of a two-year program that will culminate in the passing of the Algebra 1 regent’s exam.  Students will receive an introduction to the world of algebra.  The teacher will stress functions and their notation throughout the year.  Included in this course will be a review of all operations with polynomials, solving multi-step equations, with an emphasis on real world applications of the algebra, manipulating expressions and open sentences, and factoring binomials and trinomials.  The teacher will address solving quadratic equations by factoring and completing the square.  Students will perform graphing linear, exponential, absolute value, and quadratic functions.  The class will explore solving systems of inequalities and equations using several different methods.  The class will explore operations on algebraic fractions.  Students will produce stem and leaf, box-and-whisker, scatter plots, lines of best fit, and histograms for statistical data.  The class will explore quartiles, percentiles, and standard deviation calculations.  Problem solving and modeling will be the key strand, which will dominate all lessons.

• Grade: 9 – 10
• Prerequisites: Successful completion of Math 8
• Length: 40 weeks
• Final Evaluation: Local Final
• Credits: 1
• Next Course: Algebra 1B

Algebra 1B (Not offered 2024-2025)

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. This course deepens and extends understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The course prescribes that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Topics include; solving characteristic problems involving the analytic geometry of lines, adding/subtracting/multiplying polynomials, transforming expressions and chunking (seeing the parts of an expression as a single object) as used in factoring, completing the square, and other algebraic calculations.

• Grade: 10 – 11
• Prerequisites: Successful completion of Algebra 1A
• Length: 40 weeks
• Final Evaluation: Algebra Regents
• Credits: 1
• Next Course: Informal Geometry or Regents Geometry (with passing Algebra Regents exam grade and a 75 final course grade or better) or Math with Financial Applications

Algebra 1

Algebra 1 is the first year of the revised New York State Math curriculum.  This one-year course will introduce students to the world of algebra.  This includes a review of all operations with polynomials, solving multi-step equations with an emphasis on real world applications of algebra, manipulating expressions and open sentences, and factoring binomials and trinomials.  Students will explore graphing and solving systems of inequalities and equations using several different methods.  The class will explore linear, quadratic, absolute values, and exponential graphs.  Students will also examine and produce linear regressions, statistical data, and statistical graphs.  Problem solving will be a key strand and will dominate all lessons.

• Grade: 9
• Prerequisites: Successful completion of Math 8 or Algebra 1A
• Length: 40 weeks
• Final Evaluation: Algebra Regents
• Credits: 1
• Next Course: Informal Geometry or Regents Geometry (with passing Algebra Regents exam grade and a 75 final course grade or better)

Informal Geometry

Informal Geometry is a one year course that emphasizes a practical approach to the study of geometry and deemphasizes an abstract, formal approach. Topics include properties and operations of real numbers; evaluation of rational algebraic expressions; operations with and factoring of polynomials; simple quadratics; properties of plane and solid figures; rules of congruence and similarity; coordinate geometry including lines, segments, triangles and parallelograms in the coordinate plane; concepts of similarity, parallelism, perpendicularity, and proportions; and rules of angle measurement in triangles.

• Grade: 9-12
• Prerequisites: Successful completion of Algebra 1 or Algebra 1A  and Algebra 1B.
• Length: 40 weeks
• Final Evaluation: Final Exam
• Credits: 1
• Next Course: Regents Geometry (with a passing Algebra Regents exam grade), College Algebra  (with passing Algebra Regents exam grade), Elementary Statistics, or Math w/ Financial Applications

Regents Geometry

Geometry is a one-year course.  Students will have the opportunity to make conjectures about geometric situations and prove in a variety of ways, both formal and informal, that their conclusion follows logically from their hypothesis.  This course will employ an integrated approach to the study of geometric relationships.  Integrating synthetic, transformational, and coordinate approaches to geometry, students will justify geometric relationships and properties of geometric figures.  Congruence and similarity of triangles will be established using appropriate theorems.  The classroom teacher will use transformations including rotations, reflections, translations, and glide reflections and coordinate geometry to establish and verify geometric relationships.  A major emphasis of this course is to allow students to investigate geometric situations.  Properties of triangles, quadrilaterals, and circles should receive particular attention.  Students will use the traditional tools of compass and straightedge as well as dynamic geometry software that model these tools more efficiently and accurately, to assist in these investigations.  Geometry will lead students to an understanding that reasoning and proof are fundamental aspects of mathematics and something that sets it apart from the other sciences.

• Grade: 9-12
• Prerequisites: Successful completion of Algebra 1 or Algebra 1A/Algebra 1B with a 75 final course grade or better, and a passing grade on the Algebra 1 Regents Exam
• Length: 40 weeks
• Final Evaluation: Geometry Regents
• Credits: 1
• Next Course: Algebra 2 (only with a passing Geometry Regents exam grade), or SCCC Advanced Algebra, or Math w/ Financial Applications).

Algebra 2

Algebra 2 is the third Regents level course in the new mathematics sequence.  In order to obtain an advanced Regents diploma, students must successfully complete this course and Regents exam.  Topics covered will include solving rational, radical, quadratic, recognition of transformations, functions and relations, composition and inverse functions, Trigonometric functions and their graphs, exponential functions, logarithmic functions, complex numbers, statistics, sequences and series, regressions, and probability.  Students will use graphing calculators to enhance instruction.

• Grade: 10 –  12
• Prerequisite: Successful completion of Algebra I and Regents Geometry and passing grades on each Regents exam.
• Final Evaluation: Algebra 2 Regents
• Credits: 1
• Next Course: Pre-calculus (passing grade on Algebra, Geometry, and Algebra 2 Regents exams) and/or Elementary Statistics

Math with Financial Applications

Math with Financial Applications is a one-year math class taken upon completion of Algebra 1A and 1B.  This class offers a student one more year of math and prepares him or her for the dynamics of math outside of school.  The class deals with various consumer topics, such as banking and mortgages, budgeting, income taxes, types of loans and the result of borrowing, buying versus renting, insurance costs, payroll data, investments, and other real life applications of mathematics.

• Grade:  10 – 12
• Prerequisites:  Successful completion of Algebra 1A and 1B
• Length:  40 weeks
• Final Evaluation: Cumulative Test/Project
• Credits:  1

Elementary Statistics – SUNY Sullivan (SCCC)

The offering of the elementary statistics course at Liberty Central School is through Sullivan County Community College. Students learn about probability, frequency distributions, mean and standard deviation, the binomial distribution, the normal distribution, hypothesis testing, samples from a finite population, regression and correlation, confidence intervals, and chi-square tests.

• Grades: 11-12
• Prerequisites: Successful completion of Algebra 1 (or Algebra 1A and Algebra 1B) and Informal Geometry or and Regents Geometry. and a passing grade on one Regents exam
• Length: 40 weeks
• Final Evaluation: Project
• Credits: 1 high school and 3 college credits
• Next Course: College Algebra (with passing Algebra Regents exam grade) or Math with Financial Applications

College Algebra – SUNY Sullivan (SCCC)

The high school offers this course at Liberty Central School through Sullivan County Community College. Students will learn about polynomials, radicals, trigonometry of right triangles, Laws of Sine and Cosine, and the following types of functions: linear, quadratic, polynomial, rational, radical, exponential, and logarithmic.

• Grade: 11-12
• Prerequisites: Successful completion of Algebra 1 (or Algebra 1A and 1B) and Informal Geometry or Regents Geometry (with at least 1 passed Regents exam grade)
• Length: 40 weeks
• Final Evaluation: College Final
• Credits: 1 high school and 4 college credits
• Next Course: Regents Geometry (if not already taken), Algebra 2 (with passing grades on Algebra and Geometry Regents exams), or Elementary Statistics or Math with Financial Applications

Pre-Calculus – SUNY Sullivan (SCCC)

The offering of the pre-calculus course at Liberty Central School is through Sullivan County Community College.  Pre-Calculus consists of advanced algebra with a pre-calculus approach.  The class will explore all of the Trigonometric functions and students will transform their graphs in the coordinate plane.  Topics that will be covered are solving higher degree polynomials, mathematical modeling, applications in linear and angular velocities, linear programming, rational and exponential functions and their graphs, polar coordinates and equations, graphs of polar equations, powers and roots of complex numbers, conic sections, matrices, sequences and series, mathematical induction, and other topics as time permits.  Because of the explorative nature of this course, the teacher will introduce many areas of math.

• Grade: 11 and 12
• Prerequisites: Successful completion of Algebra 1, Geometry, and Algebra 2 and passing grades on all Math Regents exams
• Length:  40 weeks
• Final Evaluation:  Local final
• Credits: 1 high school and 4 college credits
• Next course:  Calculus and/or Elementary Statistics

Calculus – SUNY Sullivan (SCCC)

The high school offers the calculus course at Liberty Central School through Sullivan County Community College.  Upon successful completion of this class, the student will be able to:

• solve problems with limit
• demonstrate use of various rules of differentiation
• integrate expressions using appropriate integration rules
• solve problems involving rate of change
• solve optimization problems
• find areas between curves and volumes using integration
• demonstrate graphing with the help of techniques from calculus, and
• integrate and differentiate natural log functions and exponential functions.

• Grade: 12
• Prerequisites: Successful completion of Algebra 1, Geometry, and Algebra 2 and passing grades on all Math Regents exams. Also, successful completion of Pre-Calculus.
• Length:  40 weeks
• Final Evaluation:  Final Exam
• Credits: 1 high school and  4 college credits
• Next course: Classes at SCCC

General Math

General Math is a one year course created to meet the needs of students that would benefit from a stronger foundation of skills presented in 7th grade, 8th grade, and the Algebra 1 Next Generation Mathematics curriculum.  Students are recommended for this course based on 7th and 8th grade performance.  Students will review foundational topics essential for successful algebraic thinking.  Topics include the Real Number System, simplifying and evaluating variable expressions, solving and graphing linear equations and inequalities including systems of equations, ratios and proportions, functions, and statistics.

• Grade: 9
• Prerequisites: Recommendation by 8th grade teacher, failing grades in math in middle school (7th and/or 8th), or disrupted math education
• Length: 40 weeks
• Final Evaluation: Local Final
• Credits: 1
• Next Course: Algebra 1A or Algebra 1

Math AIS

Students receive Academic Intervention Services (AIS) if they will benefit from additional support outside of the regularly scheduled math courses.  Students’ placement in AIS occurs because students did not meet state mandated standards on the eighth grade math assessment or failed a required Regents exam.  Students may exit AIS after they have obtained an 80% on the school final or a passing grade on the Integrated Algebra Regents.

• Grade:  9 – 12
• Prerequisites:  Unsuccessful on math regents exam or teacher recommendation with approval of principal.
• Length:  40 weeks
• Final Evaluation:  None
• Credits:  0
• Next Course:  None