This course will solidify all the arithmetic from elementary school and expand upon those concepts to build a strong foundation for Pre-Algebra in B, and Pre-AP Algebra 1. Topics of study include: Numerical Expressions and Factors, Fractions and Decimals, Algebraic Expressions and Properties, Areas of Polygons, Ratios and Rates, Integers and the Coordinate Plane, Equations and Inequalities, Surface Area and Volume, Statistical Measures, and Data Displays. Application problems will be discussed throughout each unit of study. Many of the concepts will use computer enhanced instruction and manipulatives to reinforce concepts and skills. Throughout the year students will take notes and practice checking homework, including evaluating mistakes for clarity of understanding and showing the steps to working problems.
Pre-Algebra B links the arithmetic and foundations of Pre-Algebra A to Pre-AP Algebra 1. Topics of study include: operations and properties of rational numbers (including positive and negative numbers), number theory, ratio and proportion, percent, personal finance, statistics, plane and solid geometry, formulas involving area, perimeter, surface area, and volume, the Pythagorean Theorem, similar shapes, solving multistep equations and inequalities, combining like terms, and the use of a scientific or graphing calculator to solve application problems. Application problems will be discussed throughout each unit of study. Many of the concepts will use computer-enhanced instruction and manipulatives to reinforce concepts and skills. Throughout the year emphasis will be on taking notes as well as a more extended approach to checking homework, which includes evaluating mistakes for clarity of understanding and showing the steps to working problems.
Algebra 1 is organized around families of functions, with special emphasis on foundational algebraic skills and linear functions. As students learn about each family of functions, they will learn to represent them in multiple ways--verbally, numerically, graphically, and analytically. This is a problem-based course designed to introduce new methods of mathematical modeling as well as build upon prior knowledge. The course is structured to allow students the opportunity to pursue higher-level mathematics in a supportive Seabury Hall environment. The mathematical content consists of the following:
Number Sense, Algebraic Fluency, and Order of Operations
Pre-AP Algebra 1 Introduces students to foundational algebraic concepts and skills that are essential for higher-level mathematics and real-world problem-solving. The course focuses on developing a strong understanding of variables, expressions, equations, and functions. Students will learn to analyze and solve linear, quadratic, and exponential equations, represent data graphically, and apply algebraic methods to model and solve real-world scenarios.
Key Topics Include:
Understanding and manipulating expressions, equations, and inequalities.
Solving linear equations and inequalities in one and two variables.
Graphing linear functions and understanding slope and intercepts.
Working with systems of linear equations and inequalities.
Exploring exponential functions and their properties.
Introduction to polynomials and factoring.
Solving quadratic equations by factoring, completing the square, and using the quadratic formula.
Data interpretation and modeling using algebraic concepts.
Learning Objectives:
Develop critical thinking and problem-solving skills through algebraic methods.
Use mathematical reasoning to represent real-world scenarios algebraically and graphically.
Gain proficiency with graphing technology to enhance understanding of functions and data visualization.
This course provides the foundational skills necessary for success in higher-level mathematics courses like Geometry, Algebra 2, and Precalculus.
Pre-AP Geometry and Statistics is designed to provide students with a meaningful conceptual bridge between Algebra 1 and Geometry to deepen their understanding of mathematics. In this course, students are expected to use the mathematical knowledge and skills they have developed previously to problem-solve across the domains of algebra, geometry, and statistics. The components of this course have been crafted to prepare not only the next generation of mathematicians, scientists, programmers, statisticians, architects, and engineers but also a broader base of mathematically informed citizens who are well-equipped to respond to an array of mathematics-related issues that impact our lives at the personal, local, and global levels. Students will learn to problem solve, reason and proof, communicate, represent and connect algebra, geometry, and statistics in four in-depth units of study: Measurement in Data, Tools and Techniques of Geometric Measurement, Measurement in Congruent and Similar Figures, and Measurement in Two and Three Dimensions.
Pre-AP Algebra 2 is designed to optimize students' readiness for college-level mathematics classes. This course extends conceptual understanding of applications, connections, and procedural fluency with functions and data analysis that students developed in their previous math courses. The Pre-AP Algebra 2 framework is organized into four units of study: Modeling with Functions, The Algebra of Functions, Function Families, and Trigonometric Functions. Pre-AP Algebra 2 takes the student deeper into the language of mathematics and introduces new ways to think analytically, numerically, and graphically. Students will then apply their understanding to real-world problems modeling rates, interest, exponential growth and decay, and periodic behavior just to name a few. By the end of this course, students will be able to create and use mathematical models to understand and explain authentic scenarios, use evidence to craft mathematical conjectures and prove or disprove them, and represent mathematical concepts in a variety of forms and move fluently among them.
This course lays the groundwork for the further study of mathematics by building a strong foundation of standard precalculus topics. During this course, students acquire and apply mathematical tools in real-world modeling situations in preparation for using these tools in college-level calculus. These topics include functions and their properties, graphs, polynomials, exponents and logarithms, trigonometry, complex numbers/polar coordinates, vectors, and sequences and series. Students will study each of these topics in depth through multiple representations and analysis (e.g. graphical, numerical, verbal, and analytical).
AP Precalculus centers on functions modeling dynamic phenomena. This research-based exploration of functions is designed to better prepare students for college-level calculus and provide grounding for other mathematics and science courses. In this course, students study a broad spectrum of function types that are foundational for careers in mathematics, physics, biology, health science, social science, and data science. During this course, students acquire and apply mathematical tools in real-world modeling situations in preparation for using these tools in college-level calculus. Modeling, a central instructional theme for the course, helps students come to a deeper understanding of each function type. By examining scenarios, conditions, and data sets, as well as determining and validating an appropriate function model, students develop a greater comprehension of the nature and behavior of the function itself. The formal study of a function type through multiple representations (e.g. graphical, numerical, verbal, and analytical), coupled with the application of the function type to a variety of contexts, provide students with a rich study of precalculus.
Advanced Algebra is a course that will explore and develop applications of functions, emphasizing algebra skills of solving, graphing, and combining functions, while developing proficiency with trigonometry, probability, and descriptive statistics. The first semester of this course will focus on polynomial functions, inverse functions, and modeling data with linear functions, while the second semester will explore right triangle trigonometry, trigonometric functions, probability, and descriptive statistics. Students will develop mathematical tools and techniques that will allow them to apply quantitative and algebraic reasoning to successfully engage in collegiate coursework and life beyond.
This curriculum will introduce students to the main ideas in data science through tools such as Google Sheets, Python, Data Commons, and Tableau. Students will learn to be data explorers in project-based units, through which they will develop their understanding of data analysis, sampling, correlation/causation, bias and uncertainty, probability, modeling with data, making and evaluating data-based arguments, the power of data in society, and more! At the end of the course, students will have a portfolio of their data science work to showcase their newly developed skills.
The purpose of this course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to data collection and comparisons of data through the use of classroom experience, student generated projects and accessing information from reliable sources. The course jumps into data collection, graphical and numerical statistical summaries from the very beginning exploring sampling techniques and patterns within data. Students explore probability and computer simulation, as well as designing and implementing controlled experiments. The course culminates in inference procedures to estimate population parameters from representative and unbiased samples of data. Students will be able to make informed decisions using data, and develop a critical eye for the misrepresentation of statistics.
The AP Statistics course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes evident in the content, skills, and assessment in AP Statistics course: exploring data, sampling and experimentation, probability and simulation, and statistical inference. Students use technology, investigations, problem-solving, and writing as they build conceptual understanding.
An Advanced Placement (AP) course in calculus consists of a full high school academic year of work that is comparable to a calculus course in colleges and universities. AP Calculus AB focuses on students’ understanding of calculus concepts and provides experience with methods and applications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and analysis of functions), AP Calculus becomes a cohesive whole, rather than a collection of unrelated topics. This course requires students to use definitions and theorems to build arguments and justify conclusions.
The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Exploring connections among these representations builds an understanding of how calculus applies limits to develop important ideas, definitions, formulas, and theorems. A sustained emphasis on clear communication of methods, reasoning, justifications, and conclusions is essential. A major objective of the class is to prepare students for the AP Calculus AB exam to be given in the spring. Most universities award credit to students based upon their scores on this exam. All students are required to take the AP exam.
An Advanced Placement (AP) course in calculus consists of a full high school academic year of work that is comparable to Calculus 1 and 2 in most colleges and universities. AP Calculus BC focuses on students’ understanding of calculus concepts and provides experience with methods and applications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and analysis of functions), AP Calculus becomes a cohesive whole, rather than a collection of unrelated topics. This course requires students to use definitions and theorems to build arguments and justify conclusions.
Calculus is the mathematical study of change. Students will apply derivatives and integrals to real world situations in which rates of change and accumulation of change are measured. Students will learn integration techniques to include integration by parts and partial fractions. Students will then apply differentiation to create infinite series approximating transcendental functions. They will master multiple techniques to test series convergence. We will end the course with a full study of parametric and polar curves, as well as vector-valued functions. Emphasis will be placed equally on procedures, conceptual understanding, application, and communication of mathematics. Students will make connections between graphical, symbolic, numerical, and verbal representations of mathematics. Students will work collaboratively and are expected to bring their graphing calculators to class daily, as we will use both the graphing and tabular capabilities often. Students will leave the course well-prepared to take on the challenges of a mathematically rigorous course of study in college.
This course explores the fundamental concepts of trigonometry and analytic geometry, providing a strong mathematical foundation for advanced studies in Calculus and other STEM-related fields. Students will study the properties and applications of trigonometric functions, identities, and equations, as well as polar coordinates, parametric equations, and vectors. The course also delves into conic sections, transformations, and coordinate-based problem-solving techniques.
Through analytical reasoning, real-world applications, and technology integration, students will develop a deeper understanding of mathematical relationships and their geometric representations. Emphasis will be placed on algebraic techniques, graphing technology, and mathematical modeling to analyze and solve problem.
Math Lab is a required course for any Seabury Hall students who require supplemental instruction to master foundational math skills and concepts. Students who are beneath grade level in foundational math skills as measured by the STAR assessment will be assigned to Math Lab to receive targeted instruction for the semester/year. Individualized programs will be developed for each math lab student and progress will be individually monitored. The goal of Math Lab is to support students with the foundational skills they need to succeed in Seabury's accelerated, Pre-AP math program.
This course explores the fundamental concepts of trigonometry and analytic geometry, providing a strong mathematical foundation for advanced studies in Calculus and other STEM-related fields. Students will study the properties and applications of trigonometric functions, identities, and equations, as well as polar coordinates, parametric equations, and vectors. The course also delves into conic sections, transformations, and coordinate-based problem-solving techniques.
Through analytical reasoning, real-world applications, and technology integration, students will develop a deeper understanding of mathematical relationships and their geometric representations. Emphasis will be placed on algebraic techniques, graphing technology, and mathematical modeling to analyze and solve problem.
Trigonometry:
Right triangle trigonometry and applications
Unit circle and radian measure
Trigonometric functions, identities, and equations
Graphing sine, cosine, tangent, and reciprocal functions
Inverse trigonometric functions
Law of Sines and Law of Cosines
Trigonometric applications in real-world and geometric contexts
