Mathematics 9-12

The high school Mathematics curriculum is designed around important, integrated strands of Mathematics.  The courses encompass vital content in algebra, geometry, trigonometry, statistics, and discrete mathematics and are presented consecutively with increasing levels of difficulty.  In the context of realistic problems and applications, students develop a deep understanding of mathematical concepts, principles, and techniques.  At the completion of their coursework, students will have knowledge equivalent to that of a traditional pre-calculus course.

 SCOPE AND SEQUENCE FOR MATH

Required courses are in bold

In order to transition from one course to the next, students must receive a grade of C or better.  Students receiving a grade below C will be required to re-take the course.

COURSE 1	COURSE 2	COURSE 3	COURSE 4	COURSE 5
H Integrated Math 2	H Integrated Math 3	H Integrated Math 4	H Calculus BC (1 semester)	AP Calculus BC (2 semesters)
H Integrated Math 2	H Integrated Math 3	H Integrated Math 4	AP Calculus AB (2 semesters)
H Integrated Math 2	H Integrated Math 3	H Integrated Math 4	H Calculus
Integrated Math 1	Integrated Math 2	Integrated Math 3	Integrated Math 4	Integrated Math 5/ H Calculus
Algebra 1A	Algebra 1B	Geometry	Applications of Trigonometry	Algebra 2/ Pre-Calculus

 

Calculator Policy: The mathematics curriculum at PWHS relies on the theme of mathematics as "sense making".  Each year the curriculum features the four strands of mathematics: algebra, geometry, statistics, and discrete.  To enhance these strands, the department supports the use of graphing calculators and other forms of technology to facilitate student learning.  Therefore, a    TI-84 or TI-84+ graphing calculator is required.  Once a student reaches the AP Calculus level, a TI-89 graphing calculator will be required.  It is expected that students will independently purchase the appropriate calculator for their use in most mathematics courses.  If you qualify for free and reduced lunch pricing and are unable to afford a graphing calculator, please contact the department head and one will be made available for use throughout the semester.  Courses where calculators are used are clearly delineated in the individual course descriptions.

Integrated Math 1

This is the first course in the college preparatory program.  It focuses on the building of skills connected with the core concepts of algebra, geometry, statistics, and discrete mathematics.  It begins the integrated math sequence of the high school curriculum as it continues to build upon the middle school experience.  Emphasis is placed on the development of real number skills, data analysis, linear and exponential rates of change, properties of plane and space shapes, edge length, surface area and volume, the Pythagorean Theorem, algebraic representations, simulation models, and recursive thinking.  The TI graphing calculator is used to enrich problem solving skills and to develop graphing techniques.  A graphing calculator is required.  Prerequisite:Math 8 (CMS)

Integrated Math 2

This course is the second course in the college preparatory program.  This course will continue to explore the mathematical strands of algebra, geometry, statistics, and discrete mathematics using the collaborative, investigative approach.  The following topics are studied in this second course:  matrix models, systems, coordinate geometry, patterns of association, power, inverse, quadratic, and radical models, quadratic functions, and patterns in chance.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  A graphing calculator is required.  Prerequisite: Math 8H (CMS) or Integrated Math 1. 

H Integrated Math 2

This course is an honors level course intended for those students who completed Math 8H in 8^th grade.  It continues the math sequence of the high school curriculum from the middle school experience in Math 8H.  Students will cover course content in greater depth and scope than is covered in Integrated 2.  The following topics are studied in this second course:  matrix models, linear systems, transformations, patterns of association, power models, quadratic functions, and patterns in chance.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  A graphing calculator is required.  Prerequisite: Math 8H (CMS) or Integrated Math 1 with recommendation from teacher.

Integrated Math 3

This course is the third course in the college preparatory program.  This course will continue to explore the mathematical strands of algebra, geometry, statistics, and discrete mathematics using the collaborative, investigative approach.  The following topics are studied in this third course:  properties of circles, right triangle trigonometry, the unit circle, periodic models of change, multiple variable models, linear programming, and algebraic and geometric proof.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  A graphing calculator is required.  Prerequisite: Integrated Math 2.0p

H Integrated Math 3

This course is the second course in the honors level program.  This course will continue to explore the mathematical strands of algebra, geometry, statistics, and discrete mathematics using the collaborative, investigative approach.  Students will cover course content in greater depth and scope than is covered in Integrated 3.  The following topics are studied in this course: properties of circles, right triangle trigonometry, the unit circle, periodic models of change, multiple variable models, linear programming, algebraic and geometric proof, standard deviation, normal curve, and families of functions.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  H Integrated 3 teachers will meet with students on an individual basis to determine which AP course(s) will best meet their needs.  A graphing calculator is required.  Prerequisite: H Integrated Math 2. 

Integrated Math 4

This course is the fourth course in the college preparatory program. This course will continue to explore the mathematical strands of algebra, geometry, statistics, and discrete mathematics using the collaborative, investigative approach.  The following topics are studied in this fourth course:  standard deviation, normal curve, families of functions, arithmetic and geometric sequences and series, combinatorics, polynomial and rational functions.  This course will place emphasis on mathematical problem solving in preparation for the PSSA.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  A graphing calculator is required.  Prerequisite: Integrated Math 3

Integrated Math 4H

This course is the third course in the honors level program.  This course will continue to explore the mathematical strands of algebra, geometry, statistics, and discrete mathematics using the collaborative, investigative approach.  Students will cover course content in greater depth and scope than is covered in Integrated 4 and 5.  The following topics are studied in this course:  the derivative and integral, polynomial, rational, logarithmic, and trigonometric functions and equations, the complex number set, arithmetic and geometric sequences and series, combinatorics, trigonometric identities, and conic sections.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  Upon completion, students will be prepared for H Calculus, H Calculus BC, or AP Calculus AB.   A graphing calculator is required.  Prerequisite: H Integrated Math 3. 

Integrated Math 5

This course is the fifth course in the college preparatory program.  This elective course will continue to explore the mathematical strands of algebra, geometry, statistics, and discrete mathematics using the collaborative, investigative approach.  The following topics are studied in this fifth course:  logarithmic and exponential functions, the complex number set, trigonometric identities, and conic sections.  The TI graphing calculator is used to facilitate the students’ investigations and learning.  Upon completion with an A or B, students will be prepared for H Calculus.  A graphing calculator is required.  Prerequisite: Integrated Math 4 with a minimum of a "B" and recommendation of the teacher. 

Algebra 1A

This course is the first of five courses in a technology-enhanced sequence of high school mathematics that utilizes the Carnegie Learning Cognitive Tutor.  This program is a balance of collaborative classroom exercises with interactive software for students in personalized computer sessions.  The Cognitive Tutor software responds to a student's individual problem solving strategies.  It also assesses student progress and diagnostically assigns problems based on each student's strengths, weaknesses, and individual problem solving approach.  Topics include organizing single variable data, simplifying linear expressions, mathematical modeling of linear expressions and equations, and analyzing data to make predictions.  To facilitate understanding a graphing calculator will be used.  Students are provided with a graphing calculator for use throughout the semester.

Algebra 1B

This is the second course in the technology-enhanced program utilizing the Carnegie Learning Cognitive Tutor.  Topics include filtering linear equations from graphs, solving linear equations and inequalities, mathematical modeling of linear expressions and equations, solving and graphing equations involving absolute values, and problem solving using proportional reasoning.  Along with the interactive software, the curriculum emphasizes collaborative student activities and projects.  To facilitate understanding a graphing calculator will be used.  Students are provided with a graphing calculator for use throughout the semester.  Prerequisite: Algebra 1A.

Geometry

This is the third course in the technology-enhanced program utilizing the Carnegie Learning Cognitive Tutor.  Geometry develops organizational and logical thinking skills.  Topics include plane, solid, and coordinate geometry with heavy emphasis on perimeter, area, surface area, volume, similarity and proportion, transformations, and circle relationships.  To facilitate understanding a graphing calculator will be used.  Students are provided with a graphing calculator for use throughout the semester.  Prerequisite: Algebra 1B.

Applications of Trigonometry

This is the fourth course in the technology-enhanced progra utilizing the Carnegie Learning Cognitive Tutor.  Cognitive Tutor engages students by presenting geometric and trigonometric principles through authentic application in real world contexts.  Topics include the Pythagorean Theorem, the sine, cosine and tangent functions, special right triangles and a right triangle view of trigonometry, parellel and perpendicular lines and special angle properties, and quadrilaterals on teh coordinate plane.  This course also reinforces skills, concepts and mathematical problem-solving in preparation for the PSSA.  To facilitate understanding a graphing calculator will be used.  Students are provided with a graphing calculator for use throughout the semester.  Prerequisite: Geometry.

Algebra 2

This course is the fifth required course in the technology-enhanced program.  Topics include linear functions, systems and inequalities using modeling and multiple representations, matrices, quadratic functions, higher order polynomials and rational functions, exponentials, sequences and series, complex numbers, functional notation, and probability and statistics.  Cognitive Tutor promotes the understanding of both linear and non-linear functional forms, as well as the relationship between text, equations, graphs, and tables through the mathematical modeling of real world situations.  This course will place emphasis on mathematical problem solving in preparation for the PSSA.  To facilitate understanding a graphing calculator will be used.  Student are provided with a graphing calculator for use throughout the semester.  Prerequisite: Applications of Trigonometry.

Pre-Calculus

This course is the sixth course in the technology-enhanced program.  This course has been designed for college bound students taking Algebra 2 in their junior year.  This is a 12th grade course providing advanced algebra and trigonometric concepts needed for college.  Integrated 5 students who need reinforcement in algebra but are not ready to advance to H Calculus are also candidates for this course.  Topics include linear, quadratic, and polynomial functions, inequalities, composite and inverse functions, exponential, logarithmic, and trigonometric functions, conic sections, trigonometric identities, angle/radian measure and solutions of triangles.  Prerequisite: Algebra 2 with a minimum of a "B" and recommendation of the teacher, or Integrated Math 5.

H Calculus

This course is an honors level calculus course.  Topics include functions and their graphs, limits and continuity, techniques of differentiation, derivatives of various functions, applications of the derivative, graphs of the derivative, and techniques and applications of integration.  To facilitate understanding of the topics, learning will be enhanced with the use of a graphing calculator and MathXL.  MathXL is an online study plan directly linked to the H Calculus curriculum that provides practice, testing, and diagnosis of individual student progress.  A graphing calculator is required.  Prerequisite: H Integrated Math 4 or Integrated Math 5 with recommendation of the teacher.

H Calculus BC

This is the first semester of the AP Calculus (BC) curriculum.  Topics include review of linear, polynomial, trigonometric, exponential, logarithmic, and rational functions, limits, continuity, techniques of differentiation, and applications of the derivative.  To facilitate understind of the topics, much of the learning will be aided by the use of the graphing calculator.  A TI-89 graphing calculator is required.  Prerequisite: H Integrated Math 4 with recommendation of the teacher.