Course Descriptions – Math

Introductory Algebra

Introductory Algebra provides a curriculum focused on foundational concepts that prepare students for success in Algebra I. Through a “Discovery-Confirmation-Practice”-based exploration of basic concepts, students are challenged to work toward a mastery of computational skills, to deepen their understanding of key ideas and solution strategies, and to extend their knowledge through a variety of problem-solving applications.

Course topics include integers; the language of algebra; solving equations with addition, subtraction, multiplication, and division; fractions and decimals; measurement; exponents; solving equations with roots and powers; multi-step equations; and linear equations.

Within each Introductory Algebra lesson, students are supplied with a scaffolded note-taking guide, called a Study Sheet, as well as a post-study Checkup activity that provides them the opportunity to hone their computational skills by working through a low-stakes, 10-question problem set before starting formal assessment. Unit-level Introductory Algebra assessments include a computer-scored test and a scaffolded, teacher-scored test.

To assist students for whom language presents a barrier to learning or who are not reading at grade level, Introductory Algebra includes audio resources in both Spanish and English.

Algebra I-A

Algebra I-A and I-B provide an expanded, two-year course sequence designed for students who are not prepared for the academic challenges of the traditional one-year Algebra I curriculum.

Focusing on review of pre-algebra skills and introductory algebra content, Algebra I-A allows students to deepen their understanding of real numbers in their various forms and then extend their knowledge to linear equations in one and two variables.

Algebra I-A features ample opportunity for students to hone their computational skills by working through practice problem sets before moving on to formal assessment.

To assist students for whom language presents a barrier to learning or who are not reading at grade level, Algebra I-A includes audio resources in both Spanish and English.

Two versions of the Algebra I-A course are offered: one aligned with Florida’s Next Generation Sunshine State Standards and Benchmarks, and the other with California’s Algebra I Mathematics Content Standards. Detailed correlations to standards for other states are available upon request.

Algebra I-B

Algebra I-A and I-B provide an expanded, two-year course sequence designed for students who are not prepared for the academic challenges of the traditional one-year Algebra I curriculum.

Algebra I-B course topics include a review of introductory algebra; measurement; graphing data; linear equations; systems of linear equations; polynomials; factoring of polynomials; factoring of quadratic functions; rational expressions; and radical expressions.

Algebra I-B features ample opportunity for students to hone their computational skills by working through practice problem sets before moving on to formal assessment.

To assist students for whom language presents a barrier to learning or who are not reading at grade level, Algebra I-B includes audio resources in both Spanish and English.

Two versions of the Algebra I-B course are offered: one aligned with Florida’s Next Generation Sunshine State Standards and Benchmarks, and the other with California’s Algebra I Mathematics Content Standards. Detailed correlations to standards for other states are available upon request.

Algebra I

Algebra I builds students’ command of linear, quadratic, and exponential relationships. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations.

Course topics include problem-solving with basic equations and formulas; measurement; an introduction to functions and problem solving; linear equations and systems of linear equations; exponents and exponential functions; sequences and functions; descriptive statistics; polynomials and factoring; quadratic equations and functions; and function transformations and inverses.

This course supports all students as they develop computational fluency and deepen conceptual understanding. Students begin each lesson by discovering new concepts through guided instruction, and then confirm their understanding in an interactive, feedback-rich environment. Modeling activities equip students with tools for analyzing a variety of real-world scenarios and mathematical ideas. Journaling activities allow students to reason abstractly and quantitatively, construct arguments, critique reasoning, and communicate precisely. Performance tasks prepare students to synthesize their knowledge in novel, real-world scenarios and require that they make sense of multifaceted problems and persevere in solving them.

Geometry

Geometry builds upon students’ command of geometric relationships and formulating mathematical arguments. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations.

Course topics include reasoning, proof, and the creation of sound mathematical arguments; points, lines, and angles; triangles and trigonometry; quadrilaterals and other polygons; circles; congruence, similarity, transformations, and constructions; coordinate geometry; three-dimensional solids; and applications of probability.

This course supports all students as they develop computational fluency and deepen conceptual understanding. Students begin each lesson by discovering new concepts through guided instruction, and then confirm their understanding in an interactive, feedback-rich environment. Modeling activities equip students with tools for analyzing a variety of real-world scenarios and mathematical ideas. Journaling activities allow students to reason abstractly and quantitatively, construct arguments, critique reasoning, and communicate precisely. Performance tasks prepare students to synthesize their knowledge in novel, real-world scenarios and require that they make sense of multifaceted problems and persevere in solving them.

Algebra II

Algebra II introduces students to advanced functions, with a focus on developing a strong conceptual grasp of the expressions that define them. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations.

Course topics include quadratic equations; polynomial functions; rational expressions and equations; radical expressions and equations; exponential and logarithmic functions; trigonometric identities and functions; modeling with functions; probability and inferential statistics; probability distributions; and sample distributions and confidence intervals.

This course supports all students as they develop computational fluency and deepen conceptual understanding. Students begin each lesson by discovering new concepts through guided instruction, and then confirm their understanding in an interactive, feedback-rich environment. Modeling activities equip students with tools for analyzing a variety of real-world scenarios and mathematical ideas. Journaling activities allow students to reason abstractly and quantitatively, construct arguments, critique reasoning, and communicate precisely. Performance tasks prepare students to synthesize their knowledge in novel, real-world scenarios and require that they make sense of multifaceted problems and persevere in solving them.

Algebra, Functions, and Data Analysis

In this course, students will study the broad characteristics of functions and their behaviors and solve problems that require the formulation of linear, quadratic, polynomial, exponential, logarithmic equations or a system of equations or inequalities. Probability, experimental design and implementation, and analysis of data will be incorporated into the study of functions, and data will be generated by practical applications derived from real life scenarios.

This course is aligned with Virginia’s standards for Algebra, Functions and Data Analysis.

Mathematics I

Mathematics I builds students’ command of geometric knowledge and linear and exponential relationships. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations.

Course topics include relationships between quantities; linear and exponential relationships; reasoning with equations; descriptive statistics; congruence, proof, and constructions; and connecting algebra and geometry through coordinates.

This course supports all students as they develop computational fluency and deepen conceptual understanding. Students begin each lesson by discovering new concepts through guided instruction, and then confirm their understanding in an interactive, feedback-rich environment. Modeling activities equip students with tools for analyzing a variety of real-world scenarios and mathematical ideas. Journaling activities allow students to reason abstractly and quantitatively, construct arguments, critique reasoning, and communicate precisely. Performance tasks prepare students to synthesize their knowledge in novel, real-world scenarios and require that they make sense of multifaceted problems and persevere in solving them.

Mathematics II

Mathematics II extends students’ geometric knowledge and introduces them to quadratic expressions, equations, and functions, exploring the relationship between these and their linear and exponential counterparts. Students learn through discovery and application, developing the skills they need to break down complex challenges and demonstrate their knowledge in new situations.

Course topics include extending the number system; quadratic functions and modeling; expressions and equations; applications of probability; similarity, right-triangle trigonometry, and proof; and circles with and without coordinates.

This course supports all students as they develop computational fluency and deepen conceptual understanding. Students begin each lesson by discovering new concepts through guided instruction, and then confirm their understanding in an interactive, feedback-rich environment. Modeling activities equip students with tools for analyzing a variety of real-world scenarios and mathematical ideas. Journaling activities allow students to reason abstractly and quantitatively, construct arguments, critique reasoning, and communicate precisely. Performance tasks prepare students to synthesize their knowledge in novel, real-world scenarios and require that they make sense of multifaceted problems and persevere in solving them.

Precalculus

Precalculus is a course that combines reviews of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. The first semester includes linear, quadratic, exponential, logarithmic, radical, polynomial, and rational functions; systems of equations; and conic sections. The second semester covers trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers.

Within each Precalculus lesson, students are supplied with a post-study Checkup activity that provides them the opportunity to hone their computational skills by working through a low-stakes problem set before moving on to formal assessment. Unit-level Precalculus assessments include a computer-scored test and a scaffolded, teacher-scored test.

Financial Literacy .5

Financial Literacy helps students recognize and develop vital skills that connect life and career goals with personalized strategies and milestone-based action plans. Students explore concepts and work toward a mastery of personal finance skills, deepening their understanding of key ideas and extending their knowledge through a variety of problem-solving applications.

Course topics include career planning; income, taxation, and budgeting; savings accounts, checking accounts, and electronic banking; interest, investments, and stocks; cash, debit, credit, and credit scores; insurance; and consumer advice on how to buy, rent, or lease a car or house.

These topics are solidly supported by writing and discussion activities. Journal activities provide opportunities for students to both apply concepts on a personal scale and analyze scenarios from a third-party perspective. Discussions help students network with one another by sharing personal strategies and goals and recognizing the diversity of life and career plans within a group.

To assist students for whom language presents a barrier to learning or who are not reading at grade level, Financial Literacy includes audio resources in English.

This course is aligned with state standards as they apply to Financial Literacy and adheres to the National Council of Teachers of Mathematics’ (NCTM) Problem Solving, Communication, Reasoning, and Mathematical Connections Process standards.

Liberal Arts Math

Liberal Arts Math addresses the need for an elective course that focuses on reinforcing, deepening, and extending a student’s mathematical understanding. Liberal Arts Math starts with a review of problem-solving skills before moving on to a variety of key algebraic, geometric, and statistical concepts. Throughout the course, students hone their computational skills and extend their knowledge through problem solving and real-world applications.

Course topics include problem solving; real numbers and operations; functions and graphing; systems of linear equations; polynomials and factoring; geometric concepts such as coordinate geometry and properties of geometric shapes; and descriptive statistics.

Within each Liberal Arts Math lesson, students are supplied with a scaffolded note-taking guide, called a Study Sheet, and are given ample opportunity to practice computations in low-stakes Checkup activities before moving on to formal assessment. Additionally, students will have the opportunity to formulate and justify conclusions as they extend and apply concepts through printable exercises and “in-your-own-words” interactive activities.

To assist students for whom language presents a barrier to learning or who are not reading at grade level, Liberal Arts Math includes audio resources in English.

Mathematics of Personal Finance

Mathematics of Personal Finance focuses on real-world financial literacy, personal finance, and business subjects. Students apply what they learned in Algebra I and Geometry to topics including personal income, taxes, checking and savings accounts, credit, loans and payments, car leasing and purchasing, home mortgages, stocks, insurance, and retirement planning.

Students then extend their investigations using more advanced mathematics, such as systems of equations (when studying cost and profit issues) and exponential functions (when calculating interest problems). To assist students for whom language presents a barrier to learning or who are not reading at grade level, Mathematics of Personal Finance includes audio resources in both Spanish and English.

This course is aligned with state standards as they apply to Mathematics of Personal Finance and adheres to the National Council of Teachers of Mathematics’ (NCTM) Problem Solving, Communication, Reasoning, and Mathematical Connections Process standards.

Probability and Statistics .5

Probability and Statistics provides a curriculum focused on understanding key data analysis and probabilistic concepts, calculations, and relevance to real-world applications. Through a “Discovery-Confirmation-Practice”-based exploration of each concept, students are challenged to work toward a mastery of computational skills, deepen their understanding of key ideas and solution strategies, and extend their knowledge through a variety of problem-solving applications.

Course topics include types of data; common methods used to collect data; and the various representations of data, including histograms, bar graphs, box plots, and scatterplots. Students learn to work with data by analyzing and employing methods of prediction, specifically involving samples and populations, distributions, summary statistics, regression analysis, transformations, simulations, and inference.

Ideas involving probability — including sample space, empirical and theoretical probability, expected value, and independent and compound events — are covered as students explore the relationship between probability and data analysis. The basic connection between geometry and probability is also explored.

To assist students for whom language presents a barrier to learning or who are not reading at grade level, Probability and Statistics includes audio resources in English.

Math Foundations I

Math Foundations I offers a structured remediation solution based on the NCTM Curricular Focal Points and is designed to expedite student progress in acquiring 3rd- to 5th-grade skills. The course is appropriate for use as remediation for students in grades 6 to 12. When used in combination, Math Foundations I and Math Foundations II (covering grades 6 to 8) effectively remediate computational skills and conceptual understanding needed to undertake high school–level math courses with confidence.

Math Foundations I empowers students to progress at their optimum pace through over 80 semester hours of interactive instruction and assessment spanning 3rd- to 5th-grade math skills. Carefully paced, guided instruction is accompanied by interactive practice that is engaging and accessible. Formative assessments help students to understand areas of weakness and improve performance, while summative assessments chart progress and skill development. Early in the course, students develop general strategies for honing their problem-solving skills. Subsequent units provide a problem-solving strand that asks students to practice applying specific math skills to a variety of real-world contexts.

Math Foundations II

Based on the NCTM Curricular Focal Points, Math Foundations II is designed to expedite student progress in acquiring 6th- to 8th-grade skills. The course is appropriate for use as remediation at the high school level or as middle school curriculum. The program simultaneously builds the computational skills and conceptual understanding needed to undertake high school-level math courses with confidence.

The course’s carefully paced, guided instruction is accompanied by interactive practice that is engaging and accessible. Formative assessments help students to understand areas of weakness and improve performance, while summative assessments chart progress and skill development. Early in the course, students develop general strategies for honing their problem-solving skills. Subsequent units provide a problem-solving strand that asks students to practice applying specific math skills to a variety of real-world contexts.

The content is based on the National Council of Teachers of Math (NCTM) April 2006 publication, Curricular Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, and is aligned with state standards.