Mathematics at Pathways Academy of Technology and Design

The intent of the high school mathematics program is to prepare all students to use mathematics and problem-solving skills in further education or on the job. The program focuses on mastering the objectives of the Smarter Balanced Assessment, problem-solving, communicating mathematically, reasoning mathematically, applying mathematics to real-world situations, and using technology. Our mathematics program offers a wide range of courses to provide students with opportunities to actively participate in learning the structure and the nature of mathematics, while developing analytic skills that will help them apply basic principles to other areas of study and everyday living. Each course is based upon a program of studies aligned with the Connecticut Common Core State Standards. Students may begin their studies at various levels based on their middle school math experience. Many students enroll in higher-level mathematics courses after successful completion of Algebra II. All mathematics courses make use of Project-Based Learning, and technology in the form of computer software and/or graphing calculators. Technology allows students to visualize the mathematics that they are learning as well as lessening the burden of voluminous and complicated numerical computation. Students should check with their current mathematics teachers for recommendations about appropriate types of graphing calculators. The Mathematics Department suggests students purchase their own calculators (which will be used throughout their math program at the high school and beyond).

Advanced Placement (AP) Calculus - 1 credit

Prerequisite: Pre-Calculus

This course emphasizes a multi-representational approach to calculus. Concepts, results, and problems are expressed graphically, numerically, analytically, and verbally. Content includes concepts and applications of differential and integral calculus, limits, and elementary differential equations. This course prepares students for the Calculus AB Advanced Placement examination, for which placement and/or credit may be awarded at the college level, if a qualifying score is obtained. Content of this college level course corresponds to the syllabus of the College Board Calculus AB Advanced Placement Program. All students are required to take the Advanced Placement exam.

Algebra II - 1 credit

Prerequisite: Algebra I

Algebra II is a course that extends the content of Algebra I and provides further development of the concept of a function. Topics include: relations, functions, equations and inequalities; conic sections; polynomials; algebraic fractions; logarithmic and exponential functions; sequences and series; and counting principles and probability.

Algebra I - 1 credit

The Algebra I course builds on foundational mathematics content learned by students in previous grades by expanding mathematics understanding to provide students with a strong mathematics education. Content is designed to engage students in a variety of mathematical experiences that include the use of reasoning and problem-solving skills, which may be applied to life situations beyond the classroom setting. This course serves as the cornerstone for all high school mathematics courses; therefore, all subsequent mathematics courses require student mastery of the Algebra I content standards.

Geometry - 1 credit

Prerequisite: Algebra I

Geometry builds on a number of key geometric topics developed in the middle grades, namely relationships between angles, triangles, quadrilaterals, circles, and simple three-dimensional shapes. Students studying Geometry will further develop analytic and spatial reasoning and move towards formal mathematical arguments and constructions. They apply what they know about two-dimensional figures to three-dimensional figures in real-world contexts, building spatial visualization skills and deepening their understanding of shape and shape relationships.

Honors Algebra II - 1 credit

Prerequisite: Algebra I, and teacher recommendation

This course will enhance the higher level thinking skills developed in previous Math courses through a more in-depth study of those concepts and exploration of some pre-calculus concepts. Students will be challenged to increase their understanding of algebraic, graphical, and numerical methods in order to analyze, translate and solve polynomial, rational, exponential, and logarithmic functions. Sequences and series will be used to represent and analyze real world problems and mathematical situations.

Honors Geometry - 1 credit

Prerequisite: Algebra I, and teacher recommendation

This is an accelerated geometry course designed for students who have been successful in an Algebra I course. Topics include inductive reasoning to identify patterns and to make conjectures about real world situations, as well as apply deductive reasoning in order to confirm their conjectures. There is a strong emphasis on Proofs in this course with additional topics on congruent and similar triangles, mid-segments of triangles, properties of special right triangles, and trigonometry.

Mathematics for Engineering - 1 credit

This course builds on students’ basic knowledge of geometry, while developing skills on the engineering design process. Students will apply math, science, and engineering standards to hands-on projects. Some projects include reverse engineering of real world objects, creating objects that can actually be used, as well as technical drawing (isometric/perspective drawing). They will work both individually and in teams to design solutions to real problems through extensive use of 3D modeling/AutoCAD software. Students will develop skills in problem solving, design, and research, as well as technical skills.

Pre-Calculus or Pre-Calculus Honors - 1 credit

Prerequisite: Algebra II (Honors, by teacher recommendation)

Pre-Calculus will emphasize a study of trigonometric functions and identities as well as applications of right triangle trigonometry and circular functions. Students will use symbolic reasoning and analytical methods to represent mathematical situations, express generalizations, and study mathematical concepts and the relationships among them. Students will use functions and equations as tools for expressing generalizations.

Probability and Statistics with Infographics - 1 credit

Prerequisite: Algebra I

Probability and Statistics is an activity-based introduction to statistics that emphasizes working with data, graphs, and statistical ideas including the use of statistical software. Students are expected to develop and present professional quality statistical analyses. Course content includes theory of probability, description of statistical measurements, sampling and experimental design, probability distributions, and statistical inference. The second part of the class will involve Infographics. Students will collect or otherwise conduct research for their data acquisition and analyze using statistical methods that range from measure of central tendency to ANOVA. Students will see how the graphics are used to tell the story of descriptive analysis leading to inferential analysis and providing conclusions.


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