Mathematics

Geometry

Geometry focuses on concepts of Euclidean Geometry with opportunities for students to apply and practice Algebra I skills. Geometric topics examined include parallel and perpendicular lines, transformations, triangle congruence and similarity, quadrilaterals, right triangle trigonometry, and area and volume. The dynamic geometry software GeoGebra is used to develop students’ inductive and deductive reasoning, explore fundamental geometric and algebraic relationships, and aid in geometric problem-solving. In addition, students are expected to develop patience and resilience as they solve more lengthy application tasks (projects) and communicate their results through write-ups and oral presentations. Prerequisite: Algebra I, Algebra IB,  the equivalent, or placement. 

Algebra IB

Algebra IB provides the opportunity for students to finish mastering fundamental algebraic topics and techniques including evaluation and simplification of algebraic expressions, solving and graphing linear equations, solving linear systems, operations with polynomials, simplifying radical and rational expressions, graphing and solving quadratic equations, and introduction to exponential equations and functions. Throughout the course, students develop their problem-solving strategies and number sense by using multiple methods to understand abstract concepts, engaging in mathematical modeling, and communicating using graphical, numeric, and algebraic representations. Prerequisite Algebra IA, the equivalent, or placement. 

Algebra II

In Algebra II, students apply new elementary functions (e.g., polynomial and logarithmic) and algebraic techniques to model and solve problems that extend their work in Algebra and Geometry. Topics examined include transforming and modeling with linear functions, complex numbers, applications using quadratic, polynomial, radical, exponential, and logarithmic functions, and an introduction to rational functions. In addition, students continue to refine their problem-solving abilities by engaging with application tasks (projects) that require independently making mathematical conjectures about patterns and relationships, sometimes using technology. They are expected to communicate their results through oral presentations and written reports that integrate prose, presentation of collected data using tables and graphical representations, and mathematical justification. Prerequisite: Geometry, the equivalent, or placement. 

Honors Algebra II

Honors Algebra II covers all of the topics of Algebra II at a faster pace with greater depth. Additional topics may be presented as times allows. Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses, but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers typically serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Prerequisite: Geometry and recommendation of the math department (components include: Excellent or Outstanding performance in Geometry, recommendation of your Geometry teacher, and strong performance on the Honors Algebra II placement test).

Precalculus

Precalculus begins with a short review of the concepts of functions and their properties and is followed by a thorough study of circular and triangular trigonometry (topics include: right triangle trigonometry, inverse trigonometric functions, the law of sines and cosines, trigonometric identities and proofs, and solving and graphing the six trigonometric functions and their inverses). Students also study logarithmic and exponential functions, the graphs of rational functions, the Binomial Theorem, arithmetic and geometric sequences and series, polar coordinates, 2-D vectors, and polynomial graphs and functions. Students will also have the opportunity to put together and use all of the graphical representations, technology, and resources they have learned in their core math classes.

Honors Precalculus

Honors Precalculus covers all of the topics of Precalculus at a faster pace with greater depth. Additional topics may be presented as time allows. Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses, but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers typically serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems.

Calculus

Calculus introduces students to the basics of differential and integral calculus. Concepts of the derivative as a slope and the integral as area will be explored using real-world examples as well as from a graphical, numerical, algebraic, and verbal perspective. Activities using technology will be utilized to help students understand concepts. Introductory rules for finding derivatives and integrals will be mastered and applied.

Honors Calculus I

Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses (Honors Calculus I is taught at the pace and rigor of a college-level course), but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers typically serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Honors Calculus I integrates key topics such as slope and area from earlier courses with new concepts such as infinity and limits, to develop a strong understanding of the key parts of a beginning calculus course. Students will also study continuity, derivatives, and integrals, as well as their applications, slope fields, and differential equations. Concepts are approached through a four-step process: graphically, numerically, analytically, and verbally. The use of technology to visualize concepts is prevalent.

Honors Calculus II

Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses (Honors Calculus II is taught at the pace and rigor of a college-level course), but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers typically serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. Honors Calculus II is recommended for students with strong backgrounds in the problem-solving aspects of one-variable calculus. Students will prove the key theorems and results from first year calculus and make connections between calculus and other disciplines through projects. Topics examined include limits and continuous mappings, the interval theorems (Intermediate Value, Extreme Value, and Mean Value Theorems), significance of the derivative, integrability, modeling with differential equations, improper integrals, techniques of integration (integration by parts, trigonometric substitution, and partial fractions), sequences and series, Taylor polynomials, and parametric curves and polar coordinates.

Statistics

Statistics covers both descriptive and inferential statistics connecting current events and students’ backgrounds and interests. In descriptive statistics, students obtain the tools to assess the validity of data that they are confronted with in the media and their everyday lives. Students will learn how to describe and analyze professional data sets or those that they gather (e.g., through conducting censuses, surveys, and other experiments) and communicate the results of their analyses. Statistical topics examined include central tendency and variation, data displays (e.g., bar charts, histograms, box plots, line plots, scatter plots, and dot plots), the normal model, and bivariate linear regression. In Inferential Statistics, students learn to analyze variation in data by using confidence intervals and apply inferential statistical tests. Statistical methods examined include hypothesis tests for regression, proportions, and means. Both the computer and the calculator are integral to the course.

Honors Statistics

Honors classes are designed for enthusiastic, curious, and resilient mathematicians that are developmentally ready to dive deeply into math. Not only is the pace faster in these courses (Honors Statistics is taught at the pace and rigor of a college-level course), but students are challenged every day to apply their knowledge to unfamiliar and novel situations. Students are expected to think flexibly across different areas of math and solutions are not always immediately clear from the prompts given. Teachers typically serve as coaches, guiding students and offering advice as needed (as opposed to telling students exactly how to solve a problem), while students work collaboratively during class to solve challenging problems. In Honors Statistics we begin by examining the topics of central tendency and variation, data displays, and probability. This leads to the study of inferential statistical topics that include the concepts of statistical models and use of samples, variation, statistical measures, sampling distributions, probability theory, and tests of significance. Students are expected to critically analyze quantitative research, evaluate the evidence on which generalizations are made, and communicate the results of their analyses orally and in writing. The format and stylistic tendencies of professional research papers are also explored and understood to retain and question extant work and as a model for our own work.

Math Teaching Assistants

Teaching assistants are vital contributors to our classes. TAs attend class each day, help students with practice problems and resolve homework difficulties, answer questions, and grade homework. They run review and extra-help sessions and volunteer at math cafe once per week. As the year progresses, TAs plan and teach full lessons. This course is graded Pass / No Pass.

See Global Online Academy Math offerings in the GOA 2023-24 Course Catalog.