Mathematics

Academic Intervention Services is a non-credit course designed for students who have not passed or are in jeopardy of not passing the New York State Algebra I Regents assessment.  Students can be assigned on recommendation from school counselors or teachers, or at the request of students or parents.  Classes are typically smaller in size than a regular math class which allows for more individualized instruction and additional practice on current and previously taught topics.  While students in other courses besides those preparing for the Algebra I assessment are also eligible for this course – priority is given to students preparing for the Algebra I Regents examination.

Algebra I is the first mathematics course in high school and the focal point is functions; specifically linear, quadratic, and exponential functions.  By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. In Algebra I, students analyze and explain precisely the process of solving an equation. Students, through reasoning, develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They reason abstractly and quantitatively by choosing and interpreting units in the context of creating equations in two variables to represent relationships between quantities. They master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations.  

Students learn the terminology specific to polynomials and understand that polynomials form a system analogous to that of integers. Students learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions represented graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students build on their understanding of integer exponents to consider exponential functions with integer domains. They compare and contrast linear and exponential functions, looking for structure in each and distinguishing between additive and multiplicative change. Students explore systems of linear and quadratic equations and linear inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions focusing on the explicit forms of sequences written in subscript notation. In building models of relationships between two quantities, students analyze the key features of a graph or table of a function.  

Students strengthen their ability to discern structure in polynomial expressions. They create and solve equations involving quadratic and cubic expressions. Students reason abstractly and quantitatively in interpreting parts of an expression that represent a quantity in terms of its context; they also learn to make sense of problems and persevere in solving them by choosing or producing equivalent forms of an expression. Students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They learn through repeated reasoning to anticipate the graph of a quadratic function by interpreting the structure of various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function, which may require students to write solutions in simplest radical form. 

Students expand their experience with functions to include more specialized functions—linear, exponential, quadratic, square, and those that are piecewise-defined, including absolute value and step. Students select from among these functions to model phenomena using the modeling cycle. 

Students build upon prior experiences with data, and are introduced to working with more formal means of assessing how a model fits data. Students display and interpret graphical representations of data, and if appropriate, choose regression techniques when building a model that approximates a linear relationship between quantities. They analyze their knowledge of the context of a situation to justify their choice of a linear model, compute and interpret the correlation coefficient, and distinguish between situations of correlation and causation.  

Students will sit for the Algebra 1 Regents assessment in June.

Algebra I with Lab uses the same curriculum as Algebra 1 but includes an additional 40 minutes of instructional time every other day. This course is ideal for students who may benefit from re-teaching and extra practice.

Algebra I is the first mathematics course in high school and the focal point is functions; specifically linear, quadratic, and exponential functions.  By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. In Algebra I, students analyze and explain precisely the process of solving an equation. Students, through reasoning, develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They reason abstractly and quantitatively by choosing and interpreting units in the context of creating equations in two variables to represent relationships between quantities. They master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations.  

Students learn the terminology specific to polynomials and understand that polynomials form a system analogous to that of integers. Students learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions represented graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students build on their understanding of integer exponents to consider exponential functions with integer domains. They compare and contrast linear and exponential functions, looking for structure in each and distinguishing between additive and multiplicative change. Students explore systems of linear and quadratic equations and linear inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions focusing on the explicit forms of sequences written in subscript notation. In building models of relationships between two quantities, students analyze the key features of a graph or table of a function.  

Students strengthen their ability to discern structure in polynomial expressions. They create and solve equations involving quadratic and cubic expressions. Students reason abstractly and quantitatively in interpreting parts of an expression that represent a quantity in terms of its context; they also learn to make sense of problems and persevere in solving them by choosing or producing equivalent forms of an expression. Students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They learn through repeated reasoning to anticipate the graph of a quadratic function by interpreting the structure of various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function, which may require students to write solutions in simplest radical form. 

Students expand their experience with functions to include more specialized functions—linear, exponential, quadratic, square, and those that are piecewise-defined, including absolute value and step. Students select from among these functions to model phenomena using the modeling cycle. 

Students build upon prior experiences with data, and are introduced to working with more formal means of assessing how a model fits data. Students display and interpret graphical representations of data, and if appropriate, choose regression techniques when building a model that approximates a linear relationship between quantities. They analyze their knowledge of the context of a situation to justify their choice of a linear model, compute and interpret the correlation coefficient, and distinguish between situations of correlation and causation.  

Students will sit for the Algebra I Regents assessment in June.

This is a non-Regents course designed as the follow-on for students who have taken Algebra 1A and 1B courses and prepares students for a local assessment in June.  Properties of polygons (focusing on triangles and quadrilaterals) and circles will receive particular attention.  Students will identify relationships of geometric figures; formulate conjecture and hypothesis about geometric situations; practice and identify how geometric transformations are used in the workplace; and, gain an understanding of geometric measurements to include linear, area and volume and their respective uses outside of the school environment.

Note: the Geometry and Geometric Applications course outlines are similar but students in Geometric Applications may not delve as deep into topics or cover all topics as Geometry students.  This course does not prepare students to sit for a Regents examination and is not recommended for the student who is working towards an Advanced Regents Diploma. 

Students will sit for a locally prepared final examination in June.

Geometry is intended to be the second course in mathematics for high school students who have successfully completed Algebra I. During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions to establish the validity of geometric conjectures through deduction, proof, or mathematical arguments.  Over the years, students develop an understanding of the attributes and relationships of two- and three-dimensional geometric shapes that can be applied in diverse contexts.

The concepts of congruence, similarity, and symmetry can be understood from the perspective of geometric transformations. Fundamental are the rigid motions: translations, rotations, reflections, and sequences of these, all of which are here assumed to preserve distance and angle measure reflections and rotations each explain a particular type of symmetry leading to insight into a figure’s attributes.  Two geometric figures are defined to be congruent if there is a sequence of rigid motions that maps one figure onto the other. For triangles, congruence means that all corresponding pairs of sides and all corresponding pairs of angles are congruent. This leads to the triangle congruence criteria ASA, SAS, SSS, AAS and Hypotenuse-Leg (HL). Once these criteria are established using rigid motions, they can be used to prove theorems about triangles, quadrilaterals, and other geometric figures.

Similarity transformations define similarity as a sequence of dilations and/or rigid motions that maps one figure onto another. Students formalize the similarity ideas of "same shape" and "scale factor" developed in the middle grades by establishing that similar triangles have all pairs of corresponding angles congruent and all corresponding pairs of sides proportional. These transformations lead to the criteria AA, SSS similarity, and SAS similarity for similar triangles. 

The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and similarity, along with the Pythagorean Theorem and are fundamental in many mathematical situations. Radian measure will be introduced in Algebra II, along with the unit circle.  

Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area, and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line. They reason abstractly and quantitatively to model problems using volume formulas. 

Students prove and apply basic theorems about circles and study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students explain the correspondence between the definition of a circle and the equation of a circle written in terms of the distance formula, its radius, and coordinates of its center. Given an equation of a circle, students graph the circle in the coordinate plane and apply techniques for solving quadratic equations. 

Students will sit for the Geometry Regents assessment in June.

Algebra II is the capstone course of the three high school Regents mathematics courses and is a continuation and extension of the two courses that precede it.  Building on their work with linear, quadratic, and exponential functions in Algebra I, students in Algebra II extend their repertoire of functions to include polynomial, rational, radical, and trigonometric functions. Students work closely with the expressions that define the functions and continue to expand and hone their abilities to model situations and solve equations, including solving quadratic equations over a set of complex numbers and solving exponential equations using the properties of logarithms.

Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect the structure inherent in multi-digit whole number multiplication with the multiplication of polynomials and similarly connect the division of polynomials with the long division of integers. Students identify zeros of polynomials, including complex zeros of quadratic polynomials. Through regularity in repeated reasoning, they make connections between zeros of polynomials and solutions of polynomial equations. Students analyze the key features of a graph or table of a polynomial function and relate those features to the two quantities the function is modeling.

Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students extend trigonometric functions to all (or most) real numbers. To reinforce their understanding of these functions, students begin building fluency with the values of sine, cosine, and tangent at π/6, π/4, π/3, π/2, etc. Students make sense of periodic phenomena as they model with trigonometric functions.  Students synthesize and generalize what they have learned about a variety of function families. They extend their work with exponential functions to include solving exponential equations with logarithms as well as understanding the inverse relationship between exponential and logarithmic functions. They explore (with appropriate tools) the effects of transformations on graphs of diverse functions, including functions arising in an application. Students identify appropriate types of functions to model a situation. They adjust parameters to improve the model, and they compare models by analyzing the appropriateness of fit and making judgments about the domain over which a model is a good fit. With repeated opportunities to work through the modeling cycle, students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations. 

Students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify different ways of collecting data, including sample surveys, observational studies, and experiments. Using simulation, randomization, and careful design, students make inferences, justify conclusions, and critique statistical claims. Students create theoretical and experimental probability models following the modeling cycle. They compute and interpret probabilities from those models for compound events, attending to mutually exclusive events, independent events, and conditional probability.

Students will sit for the Algebra II Regents assessment in June.

This full-year course is designed for students who want or need a refresher in algebra concepts to prepare them for Regents Algebra 2 or a college-level math course.  This course will review and expand on topics presented in the Algebra 1 curriculum and provide the necessary algebra skills to prepare students for at least a 100-level college math course.

Students will sit for a locally prepared final examination.

Note: Students not doing well on a college math placement test may not be eligible to take credit-bearing courses at college but instead be enrolled in non-credit refresher courses.  Taking this high school course will lessen the chance of a student being required to take a year of math at college for no credit but at a cost to the student.  This course is not available for students who have passed Algebra 2. 

Topics include:

• Language of Statistical Decision Making

• Sampling and Bias

• Observational Studies and Experiments

• Summarizing Data Graphically and Numerically

• Basic Probability Rules

• Normal and Uniform Distributions and Density Curves

• Sampling Distributions

• Significance Testing and Confidence Intervals for Means and Proportions

• Correlation and Regression

Students will sit for a locally prepared final exam in June.

Note: This is an accredited SUNY Adirondack course and students meeting requirements are eligible for four college credits.  Cost for college credit will be based on SUNY Adirondack rates for the current school year.

This course covers topics that will prepare students for our AP Calculus or College Calculus courses, or future mathematics courses at college. This course takes an in depth look at  polynomials, rational functions, radical functions, absolute value functions, logarithmic functions, exponential functions and trigonometric functions. The emphasis will be on preparation for developing a sound foundation of topics that will be needed to go further in mathematics, in particular an introduction to Calculus.

Students will sit for a locally prepared final exam in June.

Note: This is an accredited SUNY Adirondack course and students meeting prerequisites are eligible for college credit. Those students have the opportunity to earn six college credits. Cost for college credit will be based on SUNY Adirondack rates for the current school year.

This course is designed for students who have completed Pre-Calculus and includes such topics as differential calculus and integral calculus of algebraic functions.  Concepts will be applied to real world situations with solutions being explored both analytically and graphically. 

Students will sit for a locally prepared final exam in June (not the AP Calculus examination).

Note: This is an accredited SUNY Adirondack course and students meeting requirements are eligible for four college credits.  Cost for college credit will be based on SUNY Adirondack rates for the current school year.

Topics include differential calculus of algebraic functions and their applications, integral calculus of algebraic functions, geometric and physical applications of integration, and calculus of elementary transcendental functions.  Students are required to take the Advanced Placement exam offered by the College Board in May.  The results determine college course placement and/or academic credit granted in accordance with individual college guidelines.

This course is a broad introduction to a variety of fundamental topics in computer science through contemporary themes such as robotics, the web, graphics, or gaming. Students will consider problems in the application area that can be solved with software.  Using the theme of the course, students will be introduced to important areas of computer science including abstraction, computer organization, representation of information, history of computing, ethics, and the development and evaluation of algorithmic solutions using an appropriate programming environment. 

Students will sit for a final exam prepared by Siena College in June.

Note: this is an elective Siena College course and students meeting requirements are eligible for three college credits.  Cost for college-credit will be based on Siena rates for the current school year.

Students will complete projects solving real world problems using number theory, graph theory, analytical geometry, statistics and probability, programming and financial analysis. This is a non-Regents course designed as the follow-on for students who have taken Algebra 1A and 1B courses.

 Students will sit for a locally prepared assessment in June. 

This course is designed as an introduction to computer science for high school students who want to express themselves creatively and solve problems that are interesting to them using computational devices. This course is designed for students that have little or no experience studying computer science. Through a series of engaging, hands-on labs and projects, students learn the fundamentals of computer programming using the block-based language NetsBlox. Students will also study the world wide web, designing and creating their own websites by writing their own HTML, CSS, and JavaScript. Finally, students will explore drawing, animation, and problem solving using Python. Throughout the course, computing history and current events in computer science will be incorporated. Special topics in computer science such as encryption, data representation, assistive technologies, and others will be explored.

This course is a good introduction to Siena’s dual enrollment course, College Introduction to Computer Science.