Math
Year-Long Courses
Year-Long Courses
Algebra 1
- Prerequisite: None
[One Credit]
Open to: All grades
This course introduces the use of variables to represent numbers and solve arithmetic equations. Students will enhance their arithmetic and problem-solving abilities while exploring key topics such as:
- Properties of real numbers
- Basic operations
- Writing and solving algebraic equations and inequalities with one and two variables
- Polynomials and factoring
- First- and second-degree functions and their graphs
- Quadratic equations
- Rational and radical expressions
Additionally, students will engage in hands-on learning through a mathematics laboratory, which incorporates technology and real-world mathematical modeling.
Geometry
- Prerequisite: Algebra 1
[One Credit]
Open to: All grades
This standard geometry course focuses on the principles of Euclidean geometry, including definitions, postulates, and theorems. Key areas of study include:
- Angles and parallel lines
- Congruent and similar triangles
- Polygons
- The Pythagorean Theorem
- Trigonometry and circles
- Area and volume
The course also integrates concepts from analytical geometry and emphasizes strengthening algebraic skills. A significant component involves constructing and analyzing proofs. Students will engage in hands-on learning through a mathematics laboratory, incorporating technology and real-world mathematical modeling.
Advanced Geometry
- Prerequisite: Algebra 1 and departmental approval
[One Credit]
Open to: All grades
This advanced geometry course delves into the principles of Euclidean geometry with a focus on definitions, postulates, and theorems. Topics covered include:
- Angles and parallel lines
- Congruent and similar triangles
- Polygons
- Points of concurrence
- The Pythagorean Theorem
- Trigonometry and circles
- Area and volume
The content is examined in greater depth than a standard geometry course, with an increased emphasis on proofs and algebraic problem-solving. Students will also participate in hands-on learning through a mathematics laboratory, incorporating technology and real-world mathematical modeling.
Conceptual Algebra 2
- Prerequisite: Algebra 1
[One Credit]
Open to: All grades
This course focuses on core topics in Algebra 2, with a student-centered pacing that allows ample time for mastering the material.
Major topics include:
- Linear functions and equations
- Quadratic functions and equations
- Polynomial functions and equations
Minor topics include:
- Rational functions
- Powers and roots
- Exponential and logarithmic functions
Additionally, students engage in hands-on learning through a mathematics laboratory, utilizing technology and real-world mathematical modeling to deepen their understanding.
Algebra 2
- Prerequisite: Algebra 1 and departmental approval
[One Credit]
Open to: All grades
This course explores mathematical concepts both symbolically and graphically. Major topics include:
- Polynomials (linear, quadratic, and higher degree)
- Rational functions
- Powers and roots
- Exponential and logarithmic functions
Within these areas, the course emphasizes transformations, systems of equations, inequalities, applications, and modeling. Students also engage in hands-on learning through a mathematics laboratory, incorporating technology and real-world mathematical modeling to enhance their understanding.
Advanced Algebra 2
- Prerequisite: Algebra 1; Concurrent: Advanced Geometry, with departmental approval
[One Credit]
Open to: All grades
This advanced course examines mathematical concepts through symbolic, graphical, verbal, and numerical approaches. Major topics include:
- Numbers and notation
- Modeling relationships
- Functions and transformations
- Quadratics
- Polynomial functions
- Radical functions
- Rational functions
- Powers and roots
- Exponentials and logarithms
- Systems of equations and inequalities
- Mathematical proof
The topics are explored in depth, emphasizing both skill development and the ability to explain and articulate concepts. Students also engage in hands-on learning through a mathematics laboratory, integrating technology and real-world mathematical modeling to enrich their understanding.
Conceptual Precalculus
- Prerequisite: Conceptual Algebra 2 or Algebra 2
[One Credit]
Open to: All grades
This course covers the topics outlined in the Precalculus curriculum but at a pace and level tailored for a less rigorous experience. Topics include:
- Linear, quadratic, and polynomial functions
- Rational functions
- Logarithmic and exponential functions
- Basic and Advanced Trigonometry
- Systems of equations and inequalities
- Conic sections and vectors
- Probability
Students also engage in hands-on learning through a mathematics laboratory, utilizing technology and real-world mathematical modeling to deepen their understanding. Upon successful completion, students are well-prepared to advance to Discrete Math, AP Statistics, or Calculus.
Precalculus
- Prerequisite: Algebra 2 and departmental approval
[One Credit]
Open to: All grades
Precalculus focuses on modeling dynamic phenomena by studying various function types foundational to fields such as mathematics, physics, biology, health science, social science, and data science. Students will deepen their understanding of the nature and behavior of functions through multiple representations, including graphical, numerical, verbal, and analytical approaches. Key topics include:
- Polynomial and rational functions
- Exponential and logarithmic functions
- Trigonometric and polar functions
- Functions involving parameters, vectors, and matrices
The curriculum is designed to support algebraic skills as students are prepared for placement in AP Calculus AB. Additionally, students participate in a mathematics laboratory, offering hands-on experience with technology and real-world mathematical modeling to enhance their understanding. This course will prepare students to take the AP Precalculus exam.
AP Precalculus
- Prerequisite: Geometry and Advanced Algebra 2, and demonstrated mastery of Adv Algebra 2 and Adv Geometry concepts on an in person placement test
[One Credit]
Open to: All grades
AP Precalculus focuses on modeling dynamic phenomena by studying various function types foundational to fields such as mathematics, physics, biology, health science, social science, and data science. Students will deepen their understanding of the nature and behavior of functions through multiple representations, including graphical, numerical, verbal, and analytical approaches. The course provides a comprehensive exploration of precalculus concepts, emphasizing both formal study and real-world applications. Key topics include:
- Polynomial and rational functions
- Exponential and logarithmic functions
- Trigonometric and polar functions
- Functions involving parameters, vectors, and matrices
Students also engage in a mathematics laboratory, gaining hands-on experience with technology and real-world mathematical modeling. This course is designed to prepare students for placement in AP Calculus BC.
Calculus
- Prerequisite: Conceptual Precalculus, Precalculus, or AP Precalculus
[One Credit]
Open to: All grades
This conceptual calculus course explores foundational topics, including:
- Limits
- Differentiation
- Applied maximum/minimum problems
- Related rates
- Techniques of integration
- Applications of the integral
While covering the same material as AP Calculus, the course provides a foundational understanding for students to build upon in future studies. Emphasis is placed on practical applications of calculus in fields such as business, economics, science, and engineering. The course incorporates group collaboration and a mathematics laboratory, enabling students to solve challenging problems and gain hands-on experience with technology to perform real-world mathematical modeling.
AP Calculus AB
- Prerequisite: Precalculus or AP Precalculus and department approval
[One Credit]
Open to: All grades
This course covers topics such as limits, differentiation, applied maximum/minimum problems, related rates, transcendental functions, and techniques of integration. Following the AP syllabus, it is designed to be roughly equivalent to a semester and a half of a college calculus course. This course is recommended for students who have demonstrated strong analytical and mathematical skills in prior courses, and who can quickly grasp and apply new concepts. Students should be prepared to devote significant time to daily homework and preparation and are committed to taking the AP examination. A mathematics laboratory is included, providing students with handson experience using technology and engaging in real-world mathematical modeling. This course is recommended for students who have earned a B- or higher AP Precaclulus or a B or higher in Precalculus.
AP Calculus BC
- Prerequisite: Precalculus or AP Precalculus and department approval
[One Credit]
Open to: All grades
This course covers all topics included in AP Calculus AB, with additional topics such as Euler’s method, advanced techniques of integration, infinite series, vectors, and polar and parametric functions. Following the AP syllabus, this course is designed to be equivalent to two semesters of a college-level calculus course. It is recommended for students who have demonstrated excellent analytical and mathematical skills in prior courses and have the ability to quickly understand and apply new concepts. Students should be prepared to dedicate significant time to daily homework and preparation. A mathematics laboratory is incorporated to provide students with hands-on experience using technology and real-world mathematical modeling. This course is recommended for students who have earned an A- or higher in AP Precalculus or an A+ in Precalculus.
AP Statistics
- Prerequisite: Algebra 2
[One Credit]
Open to: All grades
This course introduces key concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will explore nine topics:
- One-variable data
- Two-variable data
- Data collection
- Probability and random variables
- Sampling distributions
- Inference for categorical data (Proportions)
- Inference for quantitative data (Means)
- Inference for categorical data (Chi-Square)
- Inference for quantitative data (Slopes)
Following the AP syllabus, students in this course commit to taking the AP examination. The curriculum incorporates computer simulations, real-world studies, and hands-on experiences with technology and real-world mathematical modeling to enhance students’ understanding and application of statistical concepts.
Fall Semester Courses
Electives - Fall Semester Courses
Discrete Math: Fundamentals
- Prerequisite: Conceptual Algebra 2 or Algebra 2
[One-half Credit]
Open to: All grades
This semester-long course covers the fundamental concepts of finance. It begins with simple interest and progresses to more complex topics such as compound interest, annuities, present value (loans), future value (retirement savings), and investment strategies for building wealth over time. The course focuses on key financial elements that can significantly impact students’ financial futures, including stocks, options, bonds, commodities, futures contracts, and mutual funds. Students will complete four projects to reinforce the material:
- Presentation on bonds, mutual funds, and commodities
- Spreadsheet analyzing a paycheck
- Presentation of a budget plan
- Stock market challenge
Data Science: Fundamentals
- Prerequisite: None or departmental approval
[One-half Credit]
Open to: All grades
This course explores the role of data in society and how it can be used to identify patterns and solve problems. Students will work on project-based units covering topics such as:
- Data visualization
- Modeling
- Analysis
- Sampling
- Correlation vs. Causation
- Bias
- Uncertainty
- Probability
- Evaluating Data-based Arguments
Projects will introduce students to key concepts in data science using free tools like Google Sheets, CODAP, Tableau, and Python. This handson course will help students develop skills in using spreadsheets, building visualizations, and basic programming, which can be applied to future STEM courses such as Discrete Math, AP Statistics, AP Computer Science, AP Environmental Science, and Experimental Psychology.
Game Theory
- Prerequisite: Calculus
[One-half Credit]
Open to: Sophomores, Juniors, & Seniors
This course serves as a foundational introduction to the field of game theory, exploring the principles of strategic decision-making. The curriculum is divided into three major units:
- Two-person zero-sum games
- Non-zero-sum games
- N-person games
Key topics include the Prisoner’s Dilemma, Nash Equilibrium, games against nature, utility theory, and a variety of applications in fields such as economics, computer programming, logic, and political science. The course incorporates a Mathematics laboratory component, providing students with hands-on experience using technology and real-world mathematical modeling.
Formal Logic
- Prerequisite: Calculus
[One-half Credit]
Open to: Sophomores, Juniors, & Seniors
This introductory course in Abstract Mathematics focuses on teaching students how to read and write formal proofs. Key topics include:
- Basics of sets and logic
- Truth tables and Venn diagrams
- Cartesian products
- Types of proofs:
- Direct proof
- Proof by contrapositive
- Proof by contradiction
- Existence proofs
- Mathematical induction
The course incorporates a Mathematics laboratory component, providing students with hands-on experience using technology and real-world mathematical modeling.
Linear Algebra
- Prerequisite: Precalculus or departmental approval
[One-half Credit]
Open to: All grades
Linear algebra is a key branch of pure mathematics and a crucial tool in various applications, including finance, cryptography, stochastic processes, web search, and image processing. This course introduces the foundational concepts of linear algebra, covering topics such as:
- Matrix algebra
- Determinants
- Vector spaces
- Eigenvalues
- Characteristic equations
Time and resources permitting, students will also use computing technologies to explore and apply linear algebra in real-world scenarios.
Spring Semester Courses
Electives - Spring Semester Courses
Discrete Math: Applications
- Prerequisite: None
[One-half Credit]
Open to: All grades
This semester-long course explores practical finance applications. It begins with completing a U.S. tax return, covering tax schedules, 1040 forms, and itemization. Next, students study automobile ownership, using statistics and depreciation to determine pricing for cars and parts, which is especially helpful for those who did not take AP Statistics. The course also covers automobile insurance policies, analyzing coverage and accident data. The course then focuses on independent living, including finding a home, understanding floor plans and mortgages, and comparing property types like single-family homes, condos, and cooperatives. Finally, students learn about owning a business, using graphing calculators to model financial viability, culminating in a final project.
Data Science: Applications
- Prerequisite: Data Science: Fundamentals or
Exposure to Statistics or Computer Science and
department approval
[One-half Credit]
Open to: All grades
The Applications in Data Science course builds on concepts introduced in the Introduction to Data Science course, covering topics such as:
- Data analysis
- Sampling
- Correlation versus causation
- Bias and uncertainty
- Probability
- Machine learning
- Data visualization
- Natural language processing
- Constructing and evaluating data-driven arguments
- Societal impact of data
Students will work on project-based assignments that involve using coding tools like Python and R-Studio to clean and prepare raw data for problem-solving. These projects will include techniques such as sorting, machine learning, web scraping, advanced data visualization, and applications of artificial intelligence.
Multivariable Calculus
- Prerequisite: Calculus and department approval
[One-half Credit]
Open to: All grades
This course reviews concepts from single-variable calculus and extends them to functions of two or more variables. Key topics include:
- Limits, derivatives, and integrals for functions of multiple variables
- Partial derivatives
- Directional derivatives and gradients
- Tangent planes and normal lines
- Extrema of functions of two variables
- Iterated integrals
- Double and triple integrals
- Applications of multivariable calculus
The course emphasizes understanding these topics from analytical, numerical, and graphical perspectives. A mathematics laboratory is included for hands-on experience with technology and real-world mathematical modeling.