Mathematics
PDE STANDARDS FOR MATHEMATICS
The goal of the West Chester Area School District
mathematics program is to empower all students with mathematical
thinking
that will benefit them in the 21st Century. The curriculum
used at all grade levels is research based and aligned to
the Pennsylvania System of School Assessment (PSSA) Content
Anchors. The Pennsylvania Anchors and Eligible Content can
be found at www.pde.state.pa.us.
The mastery of these content
Anchors drives the instruction at each grade level. They
represent the foundation of our
mathematics curriculum. Assessments are used to guide instruction
and monitor student progress. Student data are collected,
analyzed, and then used to adjust or affirm instructional
practices and professional development. High expectations
are maintained for all students. Group work, writing for
mathematics, problem solving, and the use of performance
assessments all engage students in active participation
in their own learning. The appropriate use of technology
is
integral to learning 21st Century mathematics and is required.
The use of manipulatives in the classroom helps to motivate
all students by involving them in the learning process.
Teaching strategies that include differentiated instruction
allow
for students of all abilities and learning styles to succeed
in learning quality mathematics. These tools and strategies
enhance the quality of mathematics for all students.
The six principles developed by the National Council for
Teachers of Mathematics provide a framework for making decisions
about the teaching and learning of mathematics. The six principles
are:
- The Equity Principle: Excellence in
mathematics education requires equity – high expectations
and strong support for all students.
- The Curriculum Principle: A curriculum is more than a collection of activities:
it must be coherent, focused on important
mathematics, and well articulated across the grades.
- The
Teaching Principle: Effective mathematics teaching requires
understanding what students know and need to learn
and then challenging and supporting them to learn it well.
- The Learning Principle: Students must learn mathematics with understanding, actively
building new knowledge from
experience and prior knowledge.
- The Assessment Principle: Assessment should
support the learning of important mathematics and furnish
useful information
to both teachers and students.
- The Technology Principle: Technology
is essential in teaching and learning mathematics; it
influences
the mathematics
that is taught and enhances students’ learning.
These Principles help determine what mathematical content
and processes students should know and be able to do as they
progress through the West Chester Area School District. More
information on the NCTM Principles and Standards can be found
at www.nctm.org.
The following is a brief description of the texts that
are used in our schools. The texts are a guide to delivering
the curriculum, but they do not represent the only means
by which our teachers present mathematics content.
Elementary Math
Kindergarten through 5th Grade
Scott Foresman-Addison Wesley Math
Publisher: Pearson Scott Foresman
This math program has been developed to help students make
sense of mathematics in meaningful ways. Number sense is
a driving force of the program, which includes
estimation and mental math. Students who develop strong number sense will become
more proficient with computation and more efficient and powerful problem solvers.
Manipulatives and models are important to help students make sense of mathematics.
Working with numbers is connected to physical representations to enhance their
understanding of key concepts and skills. Reasoning and critical thinking are
integral to the program and are used to deepen students’ understanding.
Problem-solving strategies are practiced at all grade levels.
Investigations in Number, Data and Space
Publisher: Pearson Scott Foresman/TERC
The Investigations curriculum offers topics in number, data
analysis, and geometry. The number of units varies by grade
level. In each unit, students explore the central topics
in depth through a series of investigations, encountering
and using many important mathematical ideas. Students actively
engage in mathematical thinking to solve larger mathematical
problems. Students represent their thinking and use mathematical
tools and appropriate technology as a natural part of their
work. They work in a variety of groupings: as a whole class,
individually, in pairs, and in small groups. The curriculum
also includes classroom routines, ten-minute math activities,
family math, and games that support mathematical thinking.
Secondary Math
Grades 6 through 12
In general, as of 2006-2007, texts used in
the middle school accelerated and level 1 and the high
school seminar and honors levels use the McDougal Littell
texts.
The middle school level 2 and the high school academic
levels use the Pearson Prentice Hall texts. The high school
principles
level and the middle school strategic math use the Pearson
Prentice Hall texts. The middle school 8th grade strategic
math and the high school standards levels use the Carnegie
Learning texts and software.
Students taking middle school Math 6 or Math 7 will use
a scientific calculator (TI Explorer recommended). All students
taking courses from Pre-algebra through Pre-Calculus will
need to use a TI-84 (or TI-83) calculator. The TI-89 may
be used in the calculus classes in addition to the TI-84.
A letter to parents regarding the use of graphing calculators
in math courses may be obtained through any of the secondary
schools or from the district mathematics supervisor.
All students should be encouraged to take math at the highest
level possible based on ability using data from the PSSA
and other sources. We recommend and encourage upward movement
liberally and discourage placement in lower levels or place
conservatively. Students may remain in their current level
as long as they have passed the previous course or marking
period at that level or a lower level.
Please click above for full-size image.
Middle School Mathematics
Grades 6, 7, 8
Math (6) Level 1
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for sixth grade. Content
includes number sense, patterns, algebraic thinking, decimal
operations, data and statistics, fractions, integers, equations,
inequalities, functions, ratio and proportion, percents,
measurement, area, volume, and probability. The use of
calculators and other technologies are integral to the
course.
Text: Mathematics Course 2 (McDougal Littell, 2007).
Math (6) Level 2
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for sixth grade. Content
includes decimals, patterns, variables, number theory,
fractions, ratios, proportions, percents, data and graphs,
geometry, measurement, integers, probability, equations
and inequalities. The use of calculators and other technologies
are integral to the course.
Text: Mathematics Course 1 (Prentice Hall, 2004).
Strategic Math (6)
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for sixth grade. Content
includes expressing numbers in equivalent forms, comparing
numbers, modeling percents, factors, multiples, problem
solving using operations, rates, estimation strategies,
time, measurement conversions, length, perimeter, area,
volume, properties of angles, properties of polygons, lines
and segments, ordered pairs, patterns, number sentences,
graphing, data displays, mean, median, mode, range, and
probability. The uses of technology, including calculators
and computers, as well as collaborative activities are
integrated throughout the course.
Text: Mathematics Course 1 (Prentice Hall). Other resources
may be used.
Pre-algebra (6, 7)
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for sixth or seventh
grade. Content includes variables, expressions, integers,
equations, multi-step equations, inequalities, factors,
fractions, exponents, rational numbers and equations, ratio,
proportion, probability, percents, linear functions, real
numbers, right triangles, measurement, area, volume, data
analysis and probability, polynomials and non-linear functions,
angle relationships and transformations. The use of a graphing
calculator is integral to the course.
Text: Pre-Algebra (McDougal-Littell, 2005).
Algebra 1 Academic (7, 8) 1 credit
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for seventh or eighth
grade. Content includes connections to algebra, properties
of real numbers, solving linear equations, graphing linear
equations and functions, writing linear equations, solving
and graphing linear inequalities, systems of linear equations
and inequalities, exponents and exponential functions,
quadratic equations and functions, polynomials and factoring,
rational equations and functions, radicals and connections
to geometry. The use of a graphing calculator is integral
to the course.
Text: Algebra 1 (McDougal Littell, 2001).
Math (7) Level 2
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for seventh grade. Content
includes number sense, patterns, algebraic thinking, decimal
operations, data and statistics, fractions, integers, equations,
inequalities, functions, ratio and proportion, percents,
measurement, area, volume, and probability. The use of calculators
and other technologies are integral to the course.
Text: Prentice
Hall Mathematics (Prentice Hall, 2004).
Strategic Math (7)
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for seventh grade.
Content includes expressing numbers in equivalent forms,
comparing
numbers, order of operations, modeling percents, factors,
multiples, ratios, proportion, problem solving using
operations, rates, estimation strategies, measurement
conversions,
adding and subtracting measurements, length, perimeter,
area, volume, properties of angles, properties of two
and three dimensional shapes, congruence and similarity,
ordered
pairs on a coordinate plane, patterns, number sentences,
expressions, equations and inequalities, graphing and
tables, interpret data displays, describe data in box
and whisker
plots, compare mean, median, and mode, range, draw conclusions
based on data displays, and experimental and theoretical
probability. The uses of technology, including calculators
and computers, as well as collaborative activities are
integrated throughout the course.
Text: Mathematics Course 2 (Prentice Hall). Other resources
may be used.
Geometry Seminar (8) 1 credit
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for eighth grade. Content
includes basics of geometry, reasoning and proof, perpendicular
and parallel lines, congruent triangles, properties of
triangles, quadrilaterals, transformations, similarity,
right triangles and trigonometry, circles, area, surface
area and volume. The uses of technology, including calculators
and computers, as well as collaborative activities are
integrated throughout the course.
Text: Geometry (McDougal Littell, 2004).
Pre-algebra (8)
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for sixth, seventh or
eighth grade. Content includes algebraic expressions and
integers, equations and inequalities, decimals, factors,
fractions, exponents, ratio, proportion and percent, linear
functions and graphing, spatial thinking, area and volume,
right triangles, data analysis, nonlinear functions and
polynomials. The use of a graphing calculator is integral
to the course.
Text: Pre-Algebra (Prentice Hall, 2004).
Strategic Math (8)
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content for eighth grade. Content
includes number sense and algebraic thinking, fractions,
operations with fractions and mixed numbers, decimals,
ratio and proportion, percents, integers, geometric figures
and their properties, area and the Pythagorean Theorem,
probability and statistics, volume and surface area and
linear functions. The uses of technology, including calculators
and computers, as well as collaborative activities are
integrated throughout the course.
Text: Bridge to Algebra (Carnegie Learning, 2006).
High School Mathematics
Grades 9, 10, 11, 12
ALGEBRA I Standards (9) 1 credit
This course will develop algebraic concepts aligned to the
Pennsylvania Math Anchors and eligible content. Content includes
patterns, linear functions, proportional reasoning, modeling
situations, linear equations, statistical analysis, quadratics,
and laws of powers. The uses of technology, including graphing
calculators and computers, as well as collaborative activities
are integrated throughout the course.
Prerequisite: Placement based on PSSA math score or teacher
recommendation only. Text: Carnegie Learning Algebra 1 (2003).
GEOMETRY Standards (10) 1 credit
This course will develop geometric concepts aligned to the
Pennsylvania Math Anchors and eligible content. Content
includes area, perimeter, angles, triangles, parallel and
perpendicular lines, transformations, similarity, quadrilaterals,
three-dimensional geometry, and circles. The uses of technology,
including graphing calculators and computers, as well as
collaborative activities are integrated throughout the
course.
Prerequisite: Placement based on PSSA math score or teacher
recommendation only or successful completion of Algebra 1
Standards. Text: Prentice Hall Geometry (2004).
ALGEBRA II Standards (11) 1 credit
This course will continue the development of algebraic concepts
aligned to the Pennsylvania Math Anchors and eligible content.
Content includes linear, exponential, logarithmic and quadratic
functions, radicals and complex numbers, polynomial functions,
continuous and discontinuous functions, inverse functions,
periodic functions, and conic sections. The uses of technology,
including graphing calculators and computers, as well as
collaborative activities are integrated throughout the course.
Prerequisite: Placement based on PSSA math score or teacher
recommendation only or successful completion of Geometry
Standards. Text: Carnegie Learning Algebra 2 (2004).
ALGEBRA I Academic (9) 1 credit
This course will develop algebraic concepts aligned to the
Pennsylvania Math Anchors and eligible content. Content
includes the tools of algebra, solving equations and inequalities,
proportions, graphs and functions, systems of equations
and inequalities, polynomials, radicals, and rational functions.
The uses of technology, including graphing calculators,
as well as collaborative activities are integrated throughout
the course.
Prerequisite: Successful completion of pre-algebra. Text: Prentice Hall Algebra 1 (2004).
GEOMETRY Academic (10) 1 credit
This course will develop geometric concepts aligned to the
Pennsylvania Math Anchors and eligible content. Content
includes reasoning and proof, parallel and perpendicular
lines, congruent triangles, relationships within triangles,
quadrilaterals, area, similarity, right triangle trigonometry,
surface area and volume, circles and transformations. The
uses of technology, including graphing calculators, as
well as collaborative activities are integrated throughout
the course.
Prerequisite: Successful completion of Algebra 1. Text: Prentice
Hall Geometry (2004)
ALGEBRA 2 Academic (11) 1 credit
This course will develop algebraic concepts aligned to the
Pennsylvania Math Anchors and eligible content. Content
includes tools of algebra, functions, equations and graphs,
linear systems, matrices, quadratic equations and functions,
polynomials and polynomial functions, radical functions
and rational exponents, exponential and logarithmic functions,
rational functions, quadratic relations and conic sections,
sequences and series, probability and statistics, periodic
functions and trigonometry. The uses of technology, including
graphing calculators and computers, as well as collaborative
activities are integrated throughout the course.
Prerequisite: Successful completion of Algebra 1 and Geometry.
Text: Prentice Hall Algebra 2 (2004).
PRE-CALCULUS Academic (11, 12) 1 credit
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content and it will prepare students
for the study of calculus. Content includes functions and
graphs, polynomial and rational functions, exponential
and logarithmic functions, trigonometric functions, analytic
functions, topics in trigonometry, linear systems and matrices,
analytic geometry, discrete mathematics, and in introduction
to calculus. The uses of technology, including graphing
calculators and computers, as well as collaborative activities
are integrated throughout the course.
Prerequisite: Successful completion of Algebra 2. Text: Pearson
Pre-Calculus (2007).
CALCULUS Academic (12) 1 credit
This course is designed as an introduction to college level
calculus. Topics include a review of coordinate graphing,
trigonometry, functions, limits, continuity, derivatives,
integration and applications of differentiation and integration.
This course is not intended to prepare students for the
Advanced Placement (AP) exam. The uses of technology, including
graphing calculators and computers, as well as collaborative
activities are integrated throughout the course.
Prerequisite: Successful completion of Pre-calculus.
Text: McDougal Littell Calculus (Larson – 1999).
GEOMETRY Honors (9) 1 credit
This course will develop in-depth geometry concepts aligned
to the Pennsylvania Math Anchors and eligible content.
Content includes tools of geometry, reasoning and proof,
parallel and perpendicular lines, triangles, quadrilaterals,
area, similarity, right triangle trigonometry, surface
area and volume, circles, and transformations. The uses
of technology, including graphing calculators and computers,
as well as collaborative activities are integrated throughout
the course.
Prerequisite: Successful completion of Algebra 1. Text: Prentice
Hall Geometry (2004).
ALGEBRA 2 Honors (10) 1 credit
This course will develop in-depth algebraic concepts aligned
to the Pennsylvania Math Anchors and eligible content.
Content includes equations and inequalities, linear equations
and functions, systems of linear equations and inequalities,
matrices, quadratic functions, polynomials and polynomial
functions, powers, roots, and radicals, exponential and
logarithmic functions, rational equations and functions,
quadratic relations and conic sections, sequences and series,
probability and statistics, trigonometry. The uses of technology,
including graphing calculators and computers, as well as
collaborative activities are integrated throughout the
course.
Prerequisite: Successful completion of Algebra 1 and Geometry.
Text: McDougal Littell Algebra 2 (2006).
PRE-CALCULUS Honors (11) 1 credit
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content and it will prepare students
for the in-depth study of college level calculus. Content
includes functions and their graphs, polynomial and rational
functions, exponential and logarithmic functions, trigonometric
functions, analytic functions, topics in trigonometry,
linear systems and matrices, sequences, series, probability,
analytic geometry in two and three dimensions and limits
and an introduction to calculus. The uses of technology,
including graphing calculators and computers, as well as
collaborative activities are integrated throughout the
course.
Prerequisite: Successful completion of Honors Algebra 2.
Text: McDougall-Littell Pre-Calculus with Limits, 4th Edition
(2005).
GEOMETRY Seminar (9, 10) 1 credit
This course will develop geometric concepts aligned to the
Pennsylvania Math Anchors and eligible content. Content
includes rigorous reasoning and proof, perpendicular and
parallel lines, congruent triangles, properties of triangles,
quadrilaterals, transformations, similarity, right triangles
and trigonometry, circles, area and volume. The uses of
technology, including graphing calculators and computers,
as well as collaborative activities are integrated throughout
the course.
Prerequisite: Successful completion of Honors Algebra 1.
Text: Addison-Wesley Geometry (Forster-1989).
ALGEBRA 2 Seminar (9, 10) 1 credit
This course will develop rigorous algebraic concepts aligned
to the Pennsylvania Math Anchors and eligible content.
Content includes equations and inequalities, linear equations
and functions, systems of linear equations and inequalities,
matrices, quadratic functions, polynomials and polynomial
functions, powers, roots, and radicals, exponential and
logarithmic functions, rational equations and functions,
quadratic relations and conic sections, sequences and series,
probability and statistics, trigonometry. The uses of technology,
including graphing calculators and computers, as well as
collaborative activities are integrated throughout the
course.
Prerequisite: Successful completion of Algebra 1 and Geometry.
Text: McDougal Littell Algebra 2 (2006).
PRE-CALCULUS Seminar (10, 11) 1 credit
This course will develop concepts aligned to the Pennsylvania
Math Anchors and eligible content and it will prepare students
for rigorous study of college level calculus. Content includes
functions and their graphs, polynomial and rational functions,
exponential and logarithmic functions, trigonometric functions,
analytic functions, topics in trigonometry, linear systems
and matrices, sequences, series, probability, analytic
geometry in two and three dimensions and limits and an
introduction to calculus. The uses of technology, including
graphing calculators and computers, as well as collaborative
activities are integrated throughout the course. Prerequisite: Successful completion of Honors Algebra 2. Text: McDougall-Littell
Pre-Calculus with Limits, 4th Edition (2005).
ADVANCED PLACEMENT (AP) CALCULUS AB (11, 12) 1 credit
This course is designed to prepare students for the AB level
of the Advanced Placement Examination in Calculus. Topics
include algebraic, trigonometric, exponential and logarithmic
functions, limits, derivatives, continuity, applications
of the derivative, antiderivatives, definite integrals,
and applications of integration. The course is awarded
AP quality points. The uses of technology, including graphing
calculators and computers, as well as collaborative activities
are integrated throughout the course.
Prerequisite: Successful completion
of Honors or Seminar Pre-calculus. Text: McDougall-Littell
Calculus (Larson 1999)
ADVANCED PLACEMENT (AP) CALCULUS
BC (11, 12) 1 credit
This course is designed to prepare students for the BC level
of the Advanced Placement Examination in Calculus. Topics
include functions, limits, derivatives, continuity, polar
coordinates, vector functions and derivatives, indeterminate
forms, applications of the derivative, antiderivatives, definite
integrals, improper integrals, and applications of integration,
sequences, series, convergence, and elementary differential
equations. The course is awarded AP quality points. The uses
of technology, including graphing calculators and computers,
as well as collaborative activities are integrated throughout
the course.
Prerequisite: Successful completion of Honors or Seminar
Pre-calculus. Text: McDougall-Littell Calculus (Larson-1999).
STATISTICS ACADEMIC (11, 12) 1 credit
This course is designed to introduce students to the concepts
and tools for collecting, analyzing, and drawing conclusions
from data. Topics include exploring and understanding data,
exploring relationships between variables, gathering data,
and randomness and probability. This course will not prepare
students to take the AP Statistics Examination. The uses
of technology, including graphing calculators and computers,
as well as collaborative activities are integrated throughout
the course.
Prerequisite: Successful completion of Algebra 2. Text: Prentice
Hall Understanding Statistics (2003).
ADVANCED PLACEMENT (AP) STATISTICS (11, 12) 1 credit
This course is designed to introduce students to the concepts
and tools for collecting, analyzing, and drawing conclusions
from data in preparation for the AP Examination in Statistics.
Topics include exploring data (observing patterns and departures
from patterns), planning a study (deciding what and how
to measure), anticipating patterns (producing models using
probability theory and simulations), and statistical inference
(confirming models). The uses of technology, including
graphing calculators and computers, as well as collaborative
activities are integrated throughout the course.
Prerequisite: Successful completion of Honors or Seminar
Algebra 2. Text: Prentice Hall Understanding Statistics (2003).
FOUNDATIONS OF MATHEMATICS (12) 1 credit
This course is designed for seniors to introduce mathematical
concepts that are typically covered in a first year liberal
arts college-level math course. The course is also aligned
to the Pennsylvania Standards, Anchors and Eligible Content.
Topics will vary and may include a study of numbers and
number theory, logic, sets, probability, modeling, geometry,
chaos, and mathematical thinking as well as a review and
extension of algebra, geometry, data analysis, probability,
measurement and numbers and operations. Problem solving
and reasoning skills are processes that will be integral
to all topics covered. The uses of technology, including
graphing calculators and computers, as well as collaborative
activities are integrated throughout the course. Prerequisite: Successful completion of Algebra 2. Text: Pearson Thinking
Mathematically (2005).
SAT MATHEMATICS REVIEW (10, 11, 12) 0.5 credit
Semester course
This course reviews algebra and geometry using problems similar
to those included on the Scholastic Aptitude Test published
by the College Entrance Examination Board. The uses of technology,
including graphing calculators and computers, as well as
collaborative activities may be integrated throughout the
course.
Prerequisite: Successful completion of Algebra 1 and Geometry.
Text: Various resources used.
Mathematics is not a series of skills to be learned. It
is a way of thinking, a science of patterns, and the development
of proof. If students are able to experience the beauty of
mathematics in the classroom at all levels, then all students
will be well prepared for life in the twenty-first century.
