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Essentials of Mathematics

 

 

 

Credits: 5

Grades Offered: 11

Grade Weight: 1.0


This course, Essentials of Mathematics, is designed to prepare eleventh grade students for the state mandated PSSA, as well as review basic math concepts that all students need to be familiar with. The course will focus on the review of a wide variety of topics in all areas of mathematics, including algebra, geometry, and number sense. The course also serves as an introduction to other areas of elective mathematics, such as probability, statistics, trigonometry and calculus. The main focus of the class is to familiarize students with material eligible to be placed on the PSSA and therefore an emphasis on test taking skills is also incorporated.

Students will be exposed to PSSA type questions, as they broaden and deepen their knowledge in the mentioned areas. Students will participate in various sample multiple-choice formatted questions, as well as open-ended questions similar to those in the statewide test. Scoring of the PSSAs will also be addressed in class.

 

Algebra I

 

Credit: 1

Grades Offered: 8th – 12th

Weight: 1.0


This course focuses on mastery of the Pennsylvania Academic Standards for Mathematics incorporating Pennsylvania Assessment Anchors to prepare students for the applicable PSSA and /or Keystone Exams. The content of Algebra I is organized around families of functions, with special emphasis on linear and quadratic functions. As students study each family of functions, they will learn to represent them in multiple ways-as verbal descriptions, equations, tables and graphs. Students will also learn to model real-world situations using functions in order to solve problems arising from those situations. In addition to its Algebra content, Algebra I includes lessons on percents, probability and data analysis, as well as numerous examples and exercises involving geometry. These math topics often appear on standardized test, so maintaining the students’ familiarity with them is important.

Algebra I includes the introduction of variables, constants, expressions, equations, and functions. The language of numbers is examined. Topics include solving equations and inequalities, simplifying expressions, understanding order of operations, performing operations with positive and negative numbers, exploring polynomials, working with exponents, factoring, graphing (linear equations & inequalities), working with radicals and rational expressions, and expanding arithmetic knowledge. This class is a prerequisite for all other math classes in the math sequence. Students will be required to complete Algebra I level keystone application problems with the goal of passing the Keystone Exams.

 

Advanced Algebra I

 

Credit: 1

Grades Offered: 9th – 12th

Weight: 1.0


Advanced Algebra I will cover the same topics as Algebra I, but in a more in depth and faster pace. This is a challenging course meant for students who have successfully completed 8th grade Math with at least a 93% overall average.

Algebra II

Credit: 1

Grades Offered: 10th – 12th

Weight: 1.0


Algebra II is a course designed to prepare a student for further study in mathematics. Topics that were studied in Algebra I are reviewed and extended such as graphing, fractions, solving equations, and inequalities operations with polynomials and rational expressions. The new concepts studied in Algebra II include matrices, complex numbers, the quadratic formula, systems of equations, and absolute equations and inequalities.

This course focuses on the study of families of functions.  Specifically, linear, quadratic. exponential, logarithmic, radical and rational functions are explored.  Students will learn to represent the functions in various ways including graphically through a table, verbal models and equations.  Furthermore, students will learn how to manipulate functions and equations in order to solve more complex problems.  Advanced Algebra II explores a greater depth of knowledge, emphasizing real world scenarios and applications.

Advanced Algebra II

Credit: 1

Grades Offered: 10th – 12th

Weight: 1.04


The content of Advanced Algebra II is organized around families of functions including linear, quadratic, exponential, logarithmic, radical, and rational functions. More content will be covered as opposed to a regular Algebra II course as this course is designed to provide the necessary foundation for the successful study of higher mathematics such as Calculus and AP Calculus.

Calculus

Credit: 1

Grades Offered: 11th and 12th

Weight: 1.08


Calculus is the study of real valued functions in relationship to derivatives and integration. Major topics are: continuity, limits at a point and at infinity; derivative and integral rules for polynomial, rational, trigonometric, logarithmic, and exponential functions; applications to the first derivative including maximum and minimum word problems. Tangent and normal lines, linear acceleration, etc; applications to integration including falling body, area under curves, differential equations, etc. The prerequisite to this course is Trigonometry and PreCalculus.

College Algebra

Credit: 1

Grades Offered: 9th – 12th

Weight: 1.04


This course involves problem solving of negative exponents and fractional exponents. Students will study functions among which are: polynomials, rational, exponential, and logarithmic. Students will be able to use the appropriate formulas to solve a variety of sequence and skills problems including synthetic division, arithmetic and geometric progression. Relationships between and among systems of equations and inequalities will be discussed.

Geometry

Credit: 1

Grades Offered: 9th – 12th

Weight: 1.0


Our course in geometry begins with an introduction to basic symbols and terms associated with the subject matter. Postulates and theorems are developed as a means of developing the concept of congruent and similar triangles. Quadrilaterals and circles are also examined. Right triangles are studied extensively, including an introduction to Trigonometry. Other topics include transformations, symmetry, and construction.

Advanced Geometry

Credit: 1

Grades Offered: 9th – 12th

Weight: 1.0


Advanced Geometry includes the exploration of two dimensional and three-dimensional geometric concepts found in most Geometry courses such as perimeter, area, distance, surface area, and volume. Students will use formulas, theorems, and proof writing to solve problems. Advanced topics include Geometry in the coordinate plane, points of concurrence, and the golden ratio. Non-Euclidean geometries such as the study of shapes drawn on spheres will also be studied. Students will us geometric probability and basic trigonometric functions to solve algebra-based problems that are not limited to rational number solutions. The course exposes students to a variety of concepts, ideas, and problem solving strategies developed and extended through class discussion, compass and straight edge constructions, and interactive exploration using technology.

Topics in Math

Credit: 1

Grades Offered: 10th – 12th

Weight: 1.0


This course provides a general survey of mathematical topics that are useful in our contemporary world in interesting, enjoyable, and meaningful ways. The primary goals of this course are to (1) help students acquire and apply principles of fundamental mathematics, (2) use mathematics to solve authentic problems in everyday life that may be encountered in college, career, and life, and (3) to enable students to develop problem solving skills while fostering critical thinking.

Trigonometry/Analytical Geometry

Credit: 1

Grades Offered: 10th – 12th

Weight: 1.06


This course involves the study of size and measurement of sides, angles and areas of triangles. Some of the methods to be explored are Pythagorean Theorem, Study of Sine, Cosine, and Tangent Functions and Heron’s Formula.

Probability and Statistics

Credit: 1

Grades Offered: 10th – 12th

Weight: 1.04


Students will be introduced to the basic concepts and goals of statistics. They will learn various ways to collect and describe data for the purpose of writing summaries, forming conclusions, and making decisions. Students will learn to determine the probability that an event will occur, including conditional probabilities using the fundamental counting rule, multiplication rule and addition rule. Students will learn to create and use probability distributions using shape, center, and variability to make informed decisions. Students will learn how to recognize the normal curve and how to convert to a standard normal curve. This will include using sampling distributions and the central limit theorem as well as the normal approximations to binomial distributions. Additional topics may include hypothesis testing with one or two samples, correlation, linear regressions and multiple regressions.

Math - Grade 7

Credit: 2

Grades Offered: 7th

Weight: 1.0


Instructional time will be spent on four critical areas: (1) Developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) Solving problems involving scale drawings and informal geometric constructions, and working with two- and three- dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

 

 

 

Advanced Math - Grade 7

Credits: 2

Grades Offered: 7th

Weight: 1.0


The main focus of Math 8 for seventh graders is to prepare students for subsequent high school mathematics courses, mainly algebra. During this course, seventh grade students will complete the general seventh grade and general eighth grade curriculum all in one year. The course is laden with mathematical vocabulary so students can more appropriately express their mathematical solutions. Proper problem solving techniques are modeled so students can hone their procedural, as well as their computational skills.

Students will begin to expand their knowledge of the real number system by focusing on properties and computations of rational numbers. They will extend their arithmetic skills to algebraic problems as they will apply these properties to expressions and equations containing variables. Students will be able to set up and solve proportions as well as other multi-step one variable equations. They will also find and graph the solution set of algebraic inequalities. In addition to the focus on Algebra, Math 8 for seventh graders includes lessons on probability and statistics, where students will analyze various sets of data and graph and make predictions. The course also encompasses numerous topics in geometry, such as various 2-D and 3-D measurements, surface area and volume formulas.

 

 

Math - Grade 8

Credits: 2

Grades Offered: 8th

Weight: 1.0


The main focus of Math 8 is to prepare students for subsequent high school mathematics courses, mainly algebra. The course is laden with mathematical vocabulary so students can more appropriately express their mathematical solutions. Proper problem solving techniques are modeled so students can hone their procedural, as well as their computational skills.

Students will begin to expand their knowledge of the real number system by focusing on properties and computations of both rational and irrational number sets. They will extend their arithmetic skills to algebraic problems as they will apply these properties to expressions and equations containing variables. Students will be able to set up and solve multi-step one variable equations. They will also find and graph the solution set of algebraic inequalities. In addition to the focus on Algebra, Math 8 includes lessons on probability and statistics, where students will analyze various sets of data and graph and make predictions. The course also encompasses numerous topics in geometry, with a focus on students discovering the Pythagorean Theorem.