Mathematics

MATHEMATICS COURSE SEQUENCE
3 credits required for graduation

MATHEMATICS COURSE DESCRIPTIONS

ALGEBRA I (1 credit)                                                                                                                
Based on a real-world application of algebra, students will develop an understanding of the symbolic language of mathematics. Algebraic skills and concepts are developed and applied in a wide variety of problem-solving situations. The application of mathematical concepts to trade experiences reinforces the course curriculum. Students will learn to simplify algebraic expressions, solve algebraic sentences, and to communicate their procedures as well as defend their results. The study and application of linear functions will be emphasized (graphing and writing linear equations).  Algebra I prepares students to take the Connecticut Academic Performance Test (CAPT) by teaching key skills throughout the curriculum, as well as within the Mathematics Lab. The use of a graphing calculator is incorporated.

HONORS ALGEBRA I (1 credit)                                                                                               
Prerequisite:  (Self-selection by student)
This is an accelerated course that focuses on an in-depth understanding of algebra.  The course contains an in-depth study of functions, linear and quadratic.  Topics include solving, graphing and interpreting linear models, simplifying expressions containing exponents, performing operations with polynomials, basic trigonometry and topics from discrete mathematics.  Students are prepared to take the Connecticut Academic Performance Test (CAPT) by practicing key skills throughout the curriculum, as well as within the mathematics lab.  Statistics, probability and geometry are integrated throughout this course.  The use of a graphing calculator is incorporated.

GEOMETRY (1 credit)                                                                                                               
Prerequisite: Successful completion of Algebra I
Based on the real-life application of geometry, a student will investigate the spatial relationships of polygons and solids. The course is based on understanding the basic relationships of congruence and similarity, the structures used to analyze them, and the language used to communicate these ideas. Students are taught basic geometric concepts, including applications of areas, perimeters, lengths, circles, parallel lines, angle measures and volumes of geometric figures to solve problems. Geometry prepares students to take the Connecticut Academic Performance Test (CAPT) by teaching key skills throughout the curriculum, as well as within the Mathematics Lab. The application of mathematical concepts to trade experiences reinforces the curriculum. The use of a graphing calculator is encouraged.

Honors GEOMETRY (1 credit)                                                                                              
Prerequisite: Successful completion of Algebra I (self-selection by student)
This is an accelerated course that focuses on an in-depth understanding of the relationships of congruence and similarity, the structures used to analyze them, and the language used to communicate these ideas. This course requires a greater degree of independence and competence in critical thinking and communicating mathematically. The application of mathematical concepts to technology experiences reinforces the curriculum. The use of a graphing calculator is encouraged.

ALGEBRA II (1 credit)                                                                                                               
Prerequisite:  Successful completion of Algebra I (70% or above is recommended)
In Algebra II, the student’s knowledge of algebra is reinforced and extended. Knowledge of functions is expanded to quadratics and polynomials. Topics include algebraic vocabulary, variations, solving systems of equations, understanding non-linear function and graphs, with as many applications as possible. The course sets the stage for a higher-level study of mathematics (Advanced Algebra). Students are expected to communicate their procedures, as well as defend their results. The application of mathematical concepts to trade experiences reinforces the curriculum. The use of a graphing calculator is encouraged.
*College Career Pathways – Students successfully completing this course and Advanced Algebra can receive advanced college credit.

ADVANCED ALGEBRA (1 credit)
Prerequisite:  Successful completion of Algebra II (70% or above is recommended)
In Advanced Algebra, the student’s knowledge of algebra is reinforced and extended.  Knowledge of functions is extended to include exponential, rational, trigonometric and logarithmic.  The purpose of this course is to prepare students for the transition to college level math and solidify their knowledge and skills in preparation to be successful in a pre-calculus course. Students are expected to communicate their procedures, as well as defend their results. The application of mathematical concepts to trade experiences reinforces the curriculum. The use of a graphing calculator is encouraged.
*College Career Pathways – Students successfully completing this course and Algebra II can receive advanced college credit.

 Honors ALGEBRA II (1 credit)                                                                                             
Prerequisite: Successful completions of Honors Algebra I (80% or above) (self-selection by student)
This is an accelerated course that focuses on an in-depth understanding of algebra. The course continues an in-depth study of functions, which is extended to quadratics, exponential, rational and trigonometric functions. Topics include algebraic vocabulary, variations and graphs, complex numbers, sequences, probability, and trigonometry, with as many applications as possible. The course sets the stage for a higher-level study of mathematics. This course requires a greater degree of independence and competence in critical thinking and communicating mathematically. The application of mathematical concepts to trade experiences reinforces the curriculum. The use of a graphing calculator is encouraged.
*College Career Pathways – Students successfully completing this course can receive advanced college credit.

Honors PRE-CALCULUS (1 credit)                                                                                       
Prerequisite: Successful completion of Algebra II Honors (80% or above is recommended) (self-selection by student)
This course will enable students to develop an in-depth understanding of graphs of relations, algebraic and trigonometric functions. Special focus is placed on the use of models to solve real-life problems. The course is taught as a preparation for the study of calculus. In addition, students convert real-world data into numerical or algebraic models. Students also use these models to analyze and predict behavior of data and effectively communicate those results. This demanding course requires a great deal of independence and competence in critical thinking and communicating mathematically.    The use of a graphing calculator is highly integrated into instruction and learning.
*College Career Pathways – Students successfully completing this course can receive advanced college credit.

HONORS CALCULUS (1 credit)                                                                                               
Prerequisite: Successful completion of Honors Pre-Calculus (85% or above is recommended)
This course includes the study of real numbers and the creation and use of graphs, relations, functions, trigonometric functions, limits, derivatives and integrals. These concepts will be used to model, solve problems and convert real-world data sets into limits, derivatives, and integrals as graphical, numerical and algebraic models. This demanding course requires a great deal of independence and competence in critical thinking and communicating mathematically.  The use of a graphing calculator is incorporated.

STATISTICS (1 credit)                                                                                                                
Prerequisite: Successful completion of Algebra II
This course will use the standard approaches to statistical analysis, exploratory data analysis, elementary probability, sampling distributions and estimation. The application of mathematical concepts to trade experiences reinforces the curriculum. The use of a graphing calculator is incorporated.

MATHEMATICAL APPLICATIONS I (1 credit)
Prerequisite:  Successful completion of Algebra I and Geometry
The purpose of this course is to explore new areas of mathematics and reinforce them through the application of algebraic and geometry concepts.  Areas of study include topics such as discrete math (graph theory, simulations and optimizations), simple statistics and data analysis, application of the Pythagorean Theorem and linear programming.  The application of mathematical concepts to trade experiences reinforces this curriculum.

MATHEMATICAL APPLICATIONS II (1 credit)
Prerequisite:  Successful completion of Algebra I and Geometry
The purpose of this course is to explore new areas of mathematics and reinforce them through the application of algebraic and geometry concepts.  Areas of study include topics such as the study of two-dimensional geometry, Tessellations, three-dimensional geometry, indirect variation, proportionality, three-dimensional coordinate and topographical maps, and systems of equations/inequalities.  The application of mathematical concepts to trade experiences reinforces this curriculum.
 
APPLIED TRIGONOMETRY (1 credit)
Pre-requisite:  Successful completion of Algebra II (70% or above is recommended) or more advanced course
Applied Trigonometry is designed for students wishing to take a fourth or fifth credit in math.  Students who successfully complete Algebra II and want a fourth year can select this course as senior math.  Some student may wish to take Applied Trigonometry concurrently with Advanced Algebra, Pre-calculus or Statistics.  This course is designed primarily as an application of trigonometry and the study of the unit circle.  A thorough examination will be conducted of the sine, cosine and tangent functions, including their inverses, with respect to a variety of application specific to the trades.  Both the right triangle and oblique triangle cases will be considered in detail.  Traditional methods of instruction and the examination of the unit circle in conjunction with the use of graphing calculator will be employed.  Topic in analytical trigonometry will also touched upon and certain students may delve deeper into the study of analytically trigonometry.