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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.
  
Algebra 1 - Part 1, Part 2

Algebra 1, Part 1 is the first part in a multipart sequence of Algebra 1. This course generally covers the same topics as the first semester of Algebra 1, including the study of properties of rational numbers (i.e., number theory), ratio, proportion, and estimation, exponents and radicals, the rectangular coordinate system, sets and logic, formulas, and solving first-degree equations and inequalities.

Algebra 1, Part 2 is the second part in a multipart sequence of Algebra 1. This course generally covers the same topics as the second semester of Algebra 1, including the study of properties of the real number system and operations, evaluating rational algebraic expressions, solving and graphing first-degree equations and inequalities, translating word problems into equations, operations with and factoring of polynomials, and solving simple quadratics.​

Pre/Corequisite(s):
Algebra 1, 2

​Algebra 1 includes the study of properties and operations of the real number system; evaluating rational algebraic expressions; solving and graphing first-degree equations and inequalities; translating word problems into equations; operations with and factoring of polynomials; and solving simple quadratic equations.

Algebra 2 topics typically include field properties and theorems; set theory; operations with rational and irrational expressions; factoring of rational expressions; in-depth study of linear equations and inequalities; quadratic equations; solving systems of linear and quadratic equations; graphing of constant, linear, and quadratic equations; properties of higher-degree equations; and operations with rational and irrational exponents.

Pre/Corequisite(s):
Algebra Functions Data Analysis

​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.

Pre/Corequisite(s):
AP Calculus AB

​Following the College Board’s suggested curriculum designed to parallel college-level calculus courses, AP Calculus AB provides students with an understanding of the concepts of calculus and experience with its methods and applications. These courses introduce calculus and include the following topics: functions, graphs, limits, and continuity; differential calculus (including definition, application, and computation of the derivative; derivative at a point; derivative as a function; and second derivatives); and integral calculus (including definite integrals and antidifferentiation).

Pre/Corequisite(s):
AP Calculus BC

​Following the College Board’s suggested curriculum designed to parallel college-level calculus courses, AP Calculus BC courses provide students with an understanding of the concepts of calculus and experience with its methods and applications. These courses cover all of the calculus topics in AP Calculus AB as well as the following topics: parametric, polar, and vector functions; applications of integrals; and polynomial approximations and series, including series of constants and Taylor series.

Pre/Corequisite(s):
College Algebra/Trigonometry

​Trigonometry/Algebra courses combine trigonometry and advanced algebra topics, and are usually intended for students who have attained Algebra 1 and Geometry objectives. Topics typically include right trigonometric and circular functions, inverses, and graphs; trigonometric identities and equations; solutions of right and oblique triangles; complex numbers; numerical tables; field properties and theorems; set theory; operations with rational and irrational expressions; factoring of rational expressions; in-depth study of linear equations and inequalities; quadratic equations; solving systems of linear and quadratic equations; graphing of constant, linear, and quadratic equations; and properties of higher-degree equations.

Pre/Corequisite(s):
Consumer Math

​Consumer Mathematics courses reinforce general mathematics topics (such as arithmetic using rational numbers, measurement, ratio and proportion, and basic statistics) and apply these skills to consumer problems and situations. Applications typically include budgeting, taxation, credit, banking services, insurance, buying and selling products and services, home and/or car ownership and rental, managing personal income, and investment.

Pre/Corequisite(s):
Geometry

​Geometry courses, emphasizing an abstract, formal approach to the study of geometry, typically include topics such as properties of plane and solid figures; deductive methods of reasoning and use of logic; geometry as an axiomatic system including the study of postulates, theorems, and formal proofs; concepts of congruence, similarity, parallelism, perpendicularity, and proportion; and rules of angle measurement in triangles.

Pre/Corequisite(s):
Geometry and the Visual Arts

​​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.

Pre/Corequisite(s):
IB Math: Analysis and Approaches

This course focuses on developing important mathematical concepts in a coherent and rigorous way, with an emphasis on communication and independent inquiry. The course reviews the fundamentals of algebra, geometry and trigonometry, before delving into an in-depth investigation of statistics and single-variable calculus.

Pre/Corequisite(s):
IB Math: Applications and Interpretations I, II

​The course focuses on introducing important mathematical concepts with an emphasis on statistics and introductory calculus. Instruction will focus on the application of mathematics to real-world phenomena and the interpretation of advanced mathematical notions in terms of concrete scenarios.

Pre/Corequisite(s): Trigonometry/Math Analysis
Mathematical Analysis/Pre-Calculus

​Mathematic Analysis courses include the study of polynomial, logarithmic, exponential, and rational functions and their graphs; vectors; set theory; Boolean algebra and symbolic logic; mathematical induction; matrix algebra; sequences and series; and limits and continuity. They may also include some study of trigonometry and/or pre-calculus topics.

Pre/Corequisite(s):
Probability & Statistics

​Probability and Statistics courses introduce the study of likely events and the analysis, interpretation, and presentation of quantitative data. Course topics generally include basic probability and statistics: discrete probability theory, odds and probabilities, probability trees, populations and samples, frequency tables, measures of central tendency, and presentation of data (including graphs). Course topics may also include normal distribution and measures of variability.

Pre/Corequisite(s):
PVCC MTH 154/155 Quantitative Reasoning/Statistics

PVCC MTH 154 Quantitative Reasoning​ 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. This is a Passport Transfer course.

PVCC MTH 155 Statistics presents elementary statistical methods and concepts including visual data presentation, descriptive statistics, probability, estimation, hypothesis testing, correlation, and linear regression. Emphasis is placed on the development of statistical thinking, simulation, and the use of statistical software. This is a Passport Transfer course.

Pre/Corequisite(s): Algebra II
PVCC MTH 161/261 PreCalculus I/Applied Calculus I

​MTH 161 PreCalculus I presents topics in power, polynomial, rational, exponential, and logarithmic functions, and systems of equations and inequalities. Credit will not be awarded for both MTH 161: Precalculus I and MTH 167: Precalculus with Trigonometry or equivalent. This is a Passport Transfer course.

MTH 261 Applied Calculus I introduces limits, continuity, differentiation and integration of algebraic, exponential and logarithmic functions, and techniques of integration with an emphasis on applications in business, social sciences and life sciences. This is a Passport Transfer course.

Pre/Corequisite(s):
Skills Development Math 1, 2, 3

​This is an individualized and comprehensive course that covers the concepts and skills necessary to be successful in Algebra 1.

Pre/Corequisite(s):
Trigonometry/Math Analysis

​Covering topics of both Trigonometry and Mathematic Analysis, these courses prepare students for eventual work in calculus. Topics typically include the study of right trigonometric and circular functions, inverses, and graphs; trigonometric identities and equations; solutions of right and oblique triangles; complex numbers; numerical tables; polynomial, logarithmic, exponential, and rational functions and their graphs; vectors; set theory; Boolean algebra and symbolic logic; mathematical induction; matrix algebra; sequences and series; and limits and continuity.

Pre/Corequisite(s):
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