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Math

Mathematics

Students today require more rigorous mathematical knowledge and skills to pursue higher education, to compete in a technologically sophisticated connected work-force, and to be informed citizens. By taking a concept-centered approach to instruction and utilizing ACPS K-12 Essential Standards, teachers help build capacity in students to make connections across content areas. This approach will help students gain an understanding of fundamental ideas in arithmetic, measurement, geometry, probability, data analysis and statistics, and algebra and functions while developing proficiency in mathematical skills.

Students will also learn to use a variety of methods and tools to compute, including paper and pencil, mental arithmetic, estimation, and calculators. Graphing utilities, spreadsheets, calculators, computers, and other forms of electronic information technology are now standard tools for mathematical problem solving in science, engineering, business and industry, government, and practical everyday affairs. Hence, the use of technology must be an integral part of teaching, learning, and assessment.

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At the heart of developing the mathematical capacity of our students, Mathematics Habits of Mind and Lifelong Learner Standards, both developed by ACPS, are embedded within mathematical process goals congruent with goals set forth by the Virginia Department of Education and the National Council of Teachers of Mathematics. Therefore, courses in mathematics are designed to build students’ ability to:

  • analyze situations in mathematical terms; pose and solve problems based on observed situations
  • select and use various types of reasoning to develop and evaluate mathematical arguments and proof
  • organize and consolidate mathematical thinking through precise verbal, written, and graphical communication
  • understand how mathematical ideas interconnect and build on one another to produce a coherent whole
  • use representations to model and interpret physical, social, and mathematical phenomena
  • evaluate and use technology appropriately as a tool to support and apply the problem solving process

Mathematics

  
Algebra I
Standards of Learning

​Algebra I develops the properties and structure of the real-number system. Content includes linear equations, functions, inequalities, polynomials, special products, graphs, and quadratic equations. Graphing calculators are used and problem-solving techniques are stressed. A student can earn one math credit and one verified mathematics credit upon successful completion of the course and the SOL test.

Prerequisite(s): Standard: 8th Grade Math
Corequisite(s):
Credit: 1
Standard . . . . . . . . . . . . . . . . . . . . 3130
Advanced. . . . . . . . . . . . . . . . . . . . 3136
Offered at: AHS, MoHS, WAHS
Algebra I, Part I

​Part I is the first year course for Algebra I. This is an individualized and comprehensive course that covers the concepts and skills necessary to be successfully complete both parts of Algebra I.

Prerequisite(s):
Corequisite(s):
Credit: 1 Elective Credit
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3131
Offered at: AHS, MoHS, WAHS
Algebra I, Part II

​Part II is the second year course for Algebra I. This is an individualized and comprehensive course that covers the concepts and skills necessary to be successfully complete both parts of Algebra I. Successful completion of this course will result in the student being awarded one (1) math credit, the second Math credit in this sequence.

Prerequisite(s): Algebra I, Part I
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3132
Offered at: AHS, MoHS, WAHS
Algebra II
Standards of Learning

​The development of the topics of Algebra I is continued in greater depth in Algebra II. There is a more in-depth examination of relations and functions including linear, quadratic, polynomial, radical, exponential and logarithmic functions, conic sections, and matrices. The course also includes irrational numbers, properties of radicals, systems of linear equations, and linear inequalities. There is extensive use of technology, including the graphing calculator, and emphasis is placed on problem solving. A student can earn one math credit and one verified mathematics credit upon successful completion of the course and the SOL test.

Prerequisite(s): Algebra I
Corequisite(s):
Credit: 1
Standard . . . . . . . . . . . . . . . . . . . . 3135
Advanced. . . . . . . . . . . . . . . . . . . . 3102
Honors. . . . . . . . . . . . . . . . . . . . . . 3104
Offered at: AHS, MoHS, WAHS
Algebra, Functions, and Data Analysis (AFDA)

​This course may be used to fulfill the requirements of Advanced Studies, Standard, and Modified Standard Diplomas. Within the context of mathematical modeling and data analysis, students will study functions and their behaviors, systems of inequalities, probability, experimental design and implementation, and analysis of data. Data will be generated by authentic applications arising from science, business, and finance. Students will solve problems that require the formulation of linear, quadratic, exponential, or logarithmic equations or a system of equations. The infusion of technology (graphing calculator and/or computer software) in this course will assist in modeling and investigating a transformational approach to functions and data analysis.

Prerequisite(s): Algebra I
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3134
Offered at: AHS, MoHS, WAHS
College Algebra and Trigonometry

​The emphasis is on functions and their graphs, including the six trigonometric functions and their applications. After a review of functions and fundamental concepts of the real-number system, quadratic, polynomial, rational, exponential, and logarithmic functions are studied and graphed. The conics are studied in detail. Other topics studied include finding real and complex roots to polynomial equations, theory and application of logarithms, and partial fractions. The course emphasizes problem solving and the use of technology, including the graphing calculator, the CBL, and appropriate software.

Prerequisite(s): Algebra II and Geometry
Corequisite(s):
Credit: 1
Standard . . . . . . . . . . . . . . . . . . . . 3171
Advanced. . . . . . . . . . . . . . . . . . . . 3164
Offered at: AHS, MoHS, WAHS
Computer Science A, Advanced Placement

​This course covers object-oriented programming methodology with an emphasis on problem solving and algorithm development and is meant to be the equivalent of a first-semester course in computer science. It also includes the study of data structures and abstraction.

Prerequisite(s): Algebra II or Programming
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3219
Offered at: AHS, WAHS
Computer Science Principles, Advanced Placement

​This course is for students who are interested in computing. The course is designed to be a first semester introductory college computing course. The major areas of study in the course are organized around seven big ideas, which encompass ideas foundational to studying computer science. 

Full curriculum and framework are available at AP College Board. This course is a newly developed course by the College Board. This school year is the last of five pilot years; the 2016-17 school year will be the first year the AP exam will be fully accessible for all students. The AP Exam format will be similar to AP Studio Art, in that there is a portfolio component as well as a written component.

Prerequisite(s): Geometry and/or Algebra II (may be taken concurrently)
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3293
Offered at: AHS
ESOL Math: The Language of Mathematics

​The ESOL Math course prepares students to be successful in Algebra I by teaching the academic vocabulary of mathematics and applying this vocabulary to mathematical problem solving. Students review math concepts that serve as the foundation for algebraic thinking and apply these to real-world examples and word problems that require writing, speaking, listening and reading in English. The course is designed for students who are learning basic English and need a review of pre-Algebraic math concepts; students who have already mastered these may be placed in a sheltered Algebra I course.

Prerequisite(s):
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3312
Offered at: AHS
Geometry
Standards of Learning

​The properties of plane and threedimensional figures are studied in this course. Students will learn constructions, logical and deductive reasoning, angle relationships; parallel and perpendicular line relationships, congruence and similarity of polygons, triangle relationships and inequalities, and attributes and properties of quadrilaterals. Also included are properties and attributes of polygons; right triangle theorems and relationships; applications and practical problems involving circles and chords; tangents; secants; area, volume, and surface area of three dimensional objects; drawing two dimensional figures from three dimensional objects; perspective and scale drawings; coordinate geometry; and symmetry, rotation, and reflection of an object. Technology is used to reinforce geometric concepts throughout the course.

The Geometry SOL test is given upon completion of this course. A student can earn one math credit and one verified mathematics credit upon successful completion of the course and the SOL test.

Prerequisite(s): Algebra I
Corequisite(s):
Credit: 1
Standard . . . . . . . . . . . . . . . . . . . . 3143
Advanced . . . . . . . . . . . . . . . . . . . 3145
Honors . . . . . . . . . . . . . . . . . . . . . 3147
Offered at: AHS, MoHS, WAHS
Mathematical Inference and Applications (Discrete Math)

​Discrete mathematics is the mathematics of decision making. Connections between contemporary mathematics and modern society will be presented. There will be an emphasis on statistics as well as applications to business and management, social choices and decision making, information codes, patterns in growth, and patterns in art.

Prerequisite(s): Geometry and Algebra II
Corequisite(s):
Credit: 1
Standard . . . . . . . . . . . . . . . . . . . . 3119
Advanced . . . . . . . . . . . . . . . . . . . 3120
Offered at: WAHS
Probability and Statistics

​Grades 11-12 (MoHS, Advanced only); Grade 12 (AHS, Standard or Advanced)

The course presents topics in displaying and analyzing data using different statistical measurements and testing techniques. The topics in probability include methods of counting, distribution curves, and elementary probability. Quantitative literacy is incorporated and emphasized within the course. The topics in probability and statistics are at the concrete level using manipulatives and simulations.

Prerequisite(s): Algebra II
Corequisite(s):
Credit: 1
Standard (AHS). . . . . . . . . . . . . . . . . . . . 3190
Advanced (AHS, MoHS). . . . . . . . . . . . . . . 3193
Offered at: AHS, MoHS
Quantitative Reasoning / MTH 154
PVCC

Presents topics in proportional reasoning, modeling, financial literacy, and validity studies (logic and set theory). Focuses on the process of taking a real-world situation, identifying the mathematical foundation needed to address the problem, solving the problem, and applying what is learned to the original situation.

Prerequisite(s): Meet dual enrollment admission requirements; Geometry and Algebra II
Corequisite(s):
Credit: 1; 3 dual enrollment college credits with PVCC
Honors . . . . . . . . . . . . . . . . . . . . . . 3207
Offered at: WAHS
Skills Development Math / Algebra Lab

​This is an individualized and comprehensive course that covers the concepts and skills necessary to be successful in Algebra I.

Prerequisite(s):
Corequisite(s):
Credit: 1 Math elective credit each
I . . . . . . . . . . . . . . . . . . . . . . . . . . . 3301
II . . . . . . . . . . . . . . . . . . . . . . . . . . 3302
Algebra Lab . . . . . . . . . . . . . . . . . . 3306
Offered at: AHS, MoHS, WAHS
Statistics, Advanced Placement

​Taking Statistics in high school can help students become more informed citizens who are better prepared to recognize patterns, interpret graphs, analyze data, and make inferences to draw valuable conclusions on a daily basis. Topics for the course are grouped around four themes: exploratory analysis, planning a study, probability, and statistical inference. Within each theme, the topics stress statistical thinking and use of technology, primarily the graphing calculator and computers with appropriate software. 

This course prepares students to take the Advanced Placement Statistics exam.

Prerequisite(s): Algebra II
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3192
Offered at: AHS, MoHS, WAHS
Trigonometry / Math Analysis, Honors

This course presents students with a comprehensive study of trigonometry concepts and skills. Students will grow in mathematical communication and logic through an emphasis on application of trigonometric and algebraic functions. Technology will be utilized to explore real life applications, mathematical modeling and verification of solutions to equations and inequalities. An in-depth study of mathematical relationships includes creating and analyzing piecewise functions, composing functions, and examining relations for 1:1 and inverse characteristics. Polar coordinates and vectors and introduced in connection to future study in calculus. Real world applications and problem-based learning are utilized to enrich learning experiences beyond stated standards.

This course may be taken concurrently or consecutively with Honors Math Analysis / Pre-Calculus.

Prerequisite(s): Geometry and Algebra II
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3155
Offered at: AHS, MoHS, WAHS

Calculus

​​​The study of calculus provides a culminating study of secondary mathematics inclusive of many concepts and understandings put into motion! Many students who are pursuing careers in STEM fields find calculus a valuable stepping-stone toward further study and application of mathematics in college and beyond.

  
Applied Calculus / MTH 271
PVCC

​Covers topics in applied calculus for business, life sciences, and social sciences. It includes description and application of functions, limits, derivatives, graphing, and integrals.

Prerequisite(s): Meet dual enrollment admission requirements; Pre-Calculus I / Math 163
Corequisite(s):
Credit: 0.5; 3 dual enrollment college credits with PVCC
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3180
Offered at: AHS
Calculus AB, Advanced Placement

​This course is concerned with developing the student’s understanding of the concepts of calculus and providing experience with its methods and application. It emphasizes a multi-representational approach to calculus with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Technology, especially graphing calculators, is used regularly by students to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. The topics studied in this course include functions, graphs, limits, asymptotic and unbounded behavior, continuity, concept and definition of derivative, derivative as a function, computation and applications of derivatives, slope fields, Riemann sums, interpretations and properties of definite integrals, applications of integrals, Fundamental Theorem of Calculus, and techniques of anti-differentiation. 

The course prepares students to take the Advanced Placement AB Calculus exam given by ETS.

Prerequisite(s): Honors Trigonometry / Math Analysis; Honors Math Analysis / Pre-Calculus
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3177
Offered at: AHS, MoHS, WAHS
Calculus BC, Advanced Placement

​Calculus BC will include a quick review of all topics covered in AB Calculus and sequentially will cover the additional topics not covered in the year long AB Course including parametric equations, polar curves, infinite series, L’Hopital’s Rule, and vectors. The course will also explore the rudiments of multivariable calculus and differential equations (sequential courses to BC Calculus). Similar to AB Calculus, BC is also concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and application. This course emphasizes a multirepresentational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.

Prerequisite(s): Calculus AB, Advanced Placement
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3178
Offered at: AHS, MoHS, WAHS
Calculus, Honors

​This course is concerned with developing the student’s understanding of the concepts of calculus and providing experience with its methods and application. It emphasizes a multi-representational approach to calculus with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Technology, especially graphing calculators, is used regularly by students to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. The topics studied in this course include functions, graphs, limits, asymptotic and unbounded behavior, continuity, concept and definition of derivative, derivative as a function, computation and applications of derivatives, slope fields, Riemann sums, interpretations and properties of definite integrals, applications of integrals, Fundamental Theorem of Calculus, and techniques of anti-differentiation.

This course prepares students to take the AP Exam or to enroll in AP Calculus AB the following year.

Prerequisite(s): Honors Trigonometry / Math Analysis; Honors Math Analysis / Pre-Calculus
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3175
Offered at: MoHS
Geometry and the Visual Arts
Standards of Learning

​Students will discover how mathematics is related to art by studying examples of works of art from cultures around the world, examining the mathematical concepts and techniques underlying these works, and using graphic design software and other software tools to create original works of art employing these ideas and techniques. A tentative list of topics to be covered includes: recursion, symmetry transformations, perspective and projections, color mixing, the golden ratio, and sequences. Examples will be drawn from Asian, African and Arabic art, as well as European art.

Prerequisite(s): Algebra I
Corequisite(s):
Credit: 2 (1 Geometry and 1 Art credit)
. . . . . . . . . . . . . . . . . . . . . . . . . . . 9830
Offered at: WAHS
Math Analysis / Pre-Calculus, Honors

This course presents many of the topics previously introduced in algebra course in a much greater depth and with more emphasis on derivation and analysis of functions. The course includes a study of the complex number system. Students will study functions inclusive of polynomial, logarithmic, exponential and rational functions. Systems of equations and matrices are explored. The concept of the limit is introduced through analysis of sequence and series. Limits of functions are introduced and applied to the development of the concept of the derivative. Basic differential calculus and applications are introduced. The course emphasizes problembased learning problem solving and analysis by integrating the use of technology when appropriate. Real world applications and problem-based learning are utilized to enrich learning experiences beyond stated standards.

This course may be taken concurrently or consecutively with Honors Trigonometry / Math Analysis.

Prerequisite(s): Geometry and Algebra II
Corequisite(s):
Credit: 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3162
Offered at: AHS, MoHS, WAHS
Ordinary Differential Equations / MTH 279
PVCC

​Introduces ordinary differential equations. Includes first order differential equations, second and higher order ordinary differential equations with application. Also includes Laplace transforms and introduces eigenvalues and eigenvectors in solutions of systems. Designed for mathematical, physical and engineering science programs.

Prerequisite(s): Meet dual enrollment admission requirements; Vector Calculus / MTH 277
Corequisite(s):
Credit: 0.5; 4 dual enrollment college credits with PVCC
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3188
Offered at: AHS
Pre-Calculus I / MTH 163
PVCC

​Covers topics in algebra such as equations and inequalities, graphing and functions, exponents and logarithms, systems of equations, inequalities, linear programming, and matrices.

Prerequisite(s): Meet dual enrollment admission requirements
Corequisite(s):
Credit: 0.5; 3 dual enrollment college credits with PVCC
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3169
Offered at: AHS
Vector Calculus / MTH 277
PVCC

​Presents vector valued functions, partial derivatives, multiple integrals and topics from the calculus of vectors. Includes Greens theorem, Stokes theorem and the Divergence theorem. Designed for mathematical, physical and engineering science programs.

Prerequisite(s): Meet dual enrollment admission requirements; Calculus AB and/or BC
Corequisite(s):
Credit: 0.5; 4 dual enrollment college credits with PVCC
. . . . . . . . . . . . . . . . . . . . . . . . . . . 3174
Offered at: AHS
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Program Areas

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