10 minute read
Mathematics
The mission of the Rivers mathematics department is to inspire curiosity and foster enthusiasm for learning and applying mathematics. Through meaningful work and student-centered classrooms, we create an environment that encourages students to collaborate with their peers and teachers while also taking ownership of their own learning process. We aim for students to feel both challenged and successful by pushing them outside their comfort zones, but always instilling in them a confidence that they have the tools to tackle complex and unfamiliar problems. They learn to think creatively and develop critical thinking skills that allow them to approach any problem like a mathematician. We believe this way of teaching and learning leads to self-assured students who will graduate with an appreciation for and excitement of the study of mathematics.
MIDDLE SCHOOL COURSES
Pre-Algebra, Grade 6
The Pre-Algebra 6 course begins students ’ formal preparation for algebra. The program helps students gain mastery of computation and estimation through various small-group problem-solving activities and independent skills practice. The course develops students ’ thinking in the key mathematical processes of counting, visualizing, comparing, estimating, measuring, modeling, reasoning, connecting, representing, and using tools. Among the topics covered are factors, multiples, fractions, decimals, percents, ratios, proportions, Cartesian coordinates, area, perimeter, volume, and data analysis. Emphasis is placed on real-life applications, oen involving multiple-step word problems that require students to apply what they have learned to new situations. During the year, the Pre-Algebra 6 course is integrated with the sixth-grade science (Earth Science) and Humanities (The World and Water) courses through projects.
Pre-Algebra, Grade 7
This course continues students ’ preparation for algebra and is designed to address four main topics: number theory, statistics, geometry, and basic algebra skills. In number theory, students explore the number system through the use of patterns, fractions, decimals, and percents. The statistics unit examines probability, data collection, data presentation, and decision-making, and the geometry unit investigates properties and patterns of geometric shapes and theories. Students are also exposed to methods and skills of manipulating symbolic representations. This course uses activities, labs, games, and projects to help students comprehend and master the concepts covered.
Algebra I
Prerequisite: Pre-Algebra This course includes the study of signed numbers, operations with literal expressions, factoring, fractions, linear equations and systems, fractional equations, radicals, and quadratic and exponential equations, and their applications to problems. Students are expected to achieve proficiency with the basic techniques of factoring and simplifying Catalog of Courses • THE RIVERS SCHOOL 52
expressions. The ideas and rules of algebra learned in this course form the foundation for much of high school math and science.
Honors Algebra I
Prerequisites: Pre-Algebra and recommendation of the department Honors students study all topics from Algebra I in addition to more difficult ideas and techniques. Students derive formulas, clearly explain the advantages of different problem-solving strategies, and study more topics than are covered in Algebra I.
UPPER SCHOOL COURSES
Geometry
1 credit Prerequisite: Algebra I or equivalent This course covers properties and relationships of two- and three-dimensional objects. Deductive and inductive reasoning techniques are stressed as methods of investigating properties and relationships between figures and means of drawing conclusions. Students learn in a collaborative environment and concepts are reinforced through a variety of hands-on activities. Students are introduced to constructing formal proofs, and algebra skills are reinforced consistently throughout the curriculum. Students will be taught effective strategies for taking notes, studying for assessments, and completing group work. Emphasis on recall, mindset, and learning will be used so that they will be able to navigate their transition to high school math with the most opportunity for success.
Honors Geometry
1 credit Prerequisite: Recommendation of the department This challenging course is for students of demonstrated ability who have a strong desire and capability to learn and work independently and to think creatively. The entire content of the Geometry course is completed in more depth and with greater rigor. Constructing logical arguments, especially through formal proof, and using the coordinate plane to reinforce geometric concepts are central features of the course. Additionally, algebra skills are reviewed and developed, with particular emphasis on setting up and solving linear equations, quadratic equations, and systems of equations.
Algebra II
1 credit Prerequisite: Algebra I or equivalent This course reinforces and extends the concepts and methods covered in Algebra I, including mathematical properties, solving linear equations and inequalities, absolute value equations and inequalities, quadratic equations and factoring techniques, and systems of equations. The primary focus is learning the concept of a function and using parent functions to model real world situations. Families of functions studied include linear, quadratic, absolute value, exponential, logarithmic, polynomial, radical, and rational functions. Students are instructed in the use of graphing technology to explore and investigate concepts and learn about the behavior of the different families of functions. Catalog of Courses • THE RIVERS SCHOOL 53
Advanced Algebra II
1 credit Prerequisite: Recommendation of the department This course covers concepts of algebra and prepares students to be successful in precalculus and higher-level math courses. Students will study linear, absolute value, piecewise, quadratic, polynomial, radical, exponential and logarithmic functions and rational expressions. Students will create and draw connections between graphical, algebraic, and analytical models, in order to identify critical information and transfer understanding between modes of representation. By completing projects that apply functions to real-life situations, students gain an understanding of how mathematics can be employed to solve complex real-world problems.
Honors Algebra II
1 credit Prerequisite: Recommendation of the department This rigorous course is intended for students of demonstrated ability who have the desire and capability to learn independently and think creatively. Combining the Algebra II curriculum with advanced graphing techniques and topics from Precalculus, this course introduces the concept of a function and examines properties and applications of linear, absolute value, piecewise, radical, exponential, logarithmic, quadratic, polynomial, and rational functions. Additionally, the course may include topics such as sequences and series, conic sections, and systems of nonlinear equations. The frequent use of real-world applications illustrates and reinforces mathematical ideas, and students are instructed in the use of graphing technology.
Precalculus
1 credit Prerequisite: Algebra II This course will review and build upon concepts from Algebra II that are a vital foundation for higher level math courses. Students will analyze linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions by sketching graphs, exploring their transformations, and making interpretations in a real world context. This course challenges students to effectively employ problem solving skills, while also sharpening their critical thinking skills.
Advanced Precalculus
1 credit Prerequisites: Advanced Algebra II and recommendation of the department This course introduces students to new concepts needed for the study of calculus and strengthens understanding of topics in algebra and geometry. Students study functions with particular attention to graphing and manipulating polynomial, rational, exponential, logarithmic, and trigonometric functions. Students learn to work with functions numerically, visually, algebraically, and verbally. In addition, students may study sequences, series, and conic sections. Graphing technology is utilized throughout the course to enhance student understanding of mathematical concepts. The frequent use of real-world applications illustrates and reinforces mathematical ideas.
Honors Precalculus
1 credit Prerequisites: Honors Algebra II, taking Advanced or AP Physics during junior year, and recommendation of the department This course is for students of demonstrated ability and includes all of the topics covered in Advanced Precalculus in addition to polar coordinates, vectors, parametric equations and plane curves, and other advanced topics. The material in this course provides a strong preparation for Advanced Placement Calculus, with the study of formal calculus topics beginning in the second half of the year. The course covers all of differential calculus by the end of the year. Students are exposed to the power of mathematical modeling through examination of real-world applications and interdisciplinary connections. Through this course students develop the intellectual disposition to continue studying mathematics and related fields at a high level.
Statistics
1 credit Prerequisites: Precalculus and recommendation of the department The goal of this course is for students to conduct and assess statistical analyses by utilizing statistical tools and technology in order to tell a clear story with data that informs decision making. It serves as an introduction to the fundamental concepts of statistics involved in displaying, summarizing, and drawing inferences from data. Topics include generating statistical questions, sampling methods, exploratory data analysis, design of surveys and experiments, probability, sampling distributions, estimation, significance testing, and regression. Students frequently engage in hands-on activities and explorations to learn the concepts and how they are applied across a variety of industries. The statistical programming language R is used to wrangle and analyze real datasets. Through the work done in this class, students also practice the iterative nature of statistical analysis that includes asking questions, collecting data, conducting statistical analyses, and generating conclusions. Overall, this course prepares students to positively impact a world that is increasingly generating and utilizing vast amounts of data.
AP Statistics
1 credit Prerequisites: Advanced Precalculus and recommendation of the department This course follows the College Board AP Statistics syllabus. The four main units of study are: data analysis, data collection and experimental design, probability, and statistical inference. This course differs from the non-AP statistics course in the rigor and type of content to be examined and in the quantity of work asked of the student. Topics are taught through extensive investigations of real-world examples. Students are required to take the AP Statistics exam in May.
AP Microeconomics
1 credit Prerequisites: Honors Algebra II or Advanced Precalculus and recommendation of the department The purpose of this course is to give students a thorough understanding of the principles of economics that apply to the functions of individual decision makers, both consumers and producers, within the economic system. This course focuses on introducing students to the principles of microeconomics, placing primary emphasis Catalog of Courses • THE RIVERS SCHOOL 55
on the nature and functions of product markets. Additionally, the course includes the study of factor markets and of the role of government in promoting greater efficiency and equity in the economy. Concepts are taught and brought to life through a variety of means including readings, class simulations, projects, and debates. At the conclusion of the course, students are required to take the AP Microeconomics exam.
Calculus
1 credit Prerequisites: Precalculus and recommendation of the department This course is designed for those who plan to continue the study of calculus in college and/or who may need this background for courses in applied sciences. The curriculum introduces the fundamental concepts of calculus, including the ideas of functions, limits, continuity, and standard differentiation formulas and their applications. Through applications of derivatives to problems in maxima and minima, students gain experience in the power of calculus. In addition, basic methods of integration are discussed. This course does not prepare students for either of the Calculus AP exams.
AP Calculus AB
1 credit Prerequisites: Advanced Precalculus or Honors Precalculus and recommendation of the department This course in differential and integral calculus follows the AP Calculus AB syllabus. Topics covered include limits, continuity, differentiation and integration of algebraic and transcendental functions, optimization and related rates, areas bounded by curves, volumes of revolution, techniques of integration and differential equations. An emphasis on the role of calculus in real-world applications exposes students to the power of mathematics and encourages strong critical thinking skills. This course prepares students to pursue advanced topics in mathematics, science and business. Students are required to take the AP Calculus AB exam in May.
AP Calculus BC
1 credit Prerequisites: Honors Precalculus and recommendation of the department In addition to completing the syllabus of Calculus AB, this course completes the preparation for the BC level of the AP exam in calculus. Students are exposed to the power of calculus through examination of real-world applications and interdisciplinary connections. Through this course students develop the intellectual disposition to continue studying mathematics and related fields. Additional topics include integration by parts and by partial fractions, improper integrals, L’Hospital’ s rule, first-order separable differential equations, logistic differential equations, infinite series and power series, and the calculus of parametric, polar, and vector functions. Students are required to take the AP Calculus BC exam in May.
Post-AP Multivariable Calculus and Topics in Mathematics
1 credit. Cross-listed with Interdisciplinary Studies Prerequisites: AP Calculus BC and recommendation of the department This course is designed for students who have completed AP Calculus BC and are interested in studying mathematics or a related field at the college level. Topics include vectors and matrices in 2-space and 3-space, matrices and systems of Catalog of Courses • THE RIVERS SCHOOL 56
equations, parametric equations, partial derivatives and applications, double integrals, and integrals in the plane. Throughout the course, students will examine applications to physics, probability and statistics, and graph theory. Students will explore the history of some of the most important theorems and processes in calculus like Green ’ s Theorem and Lagrange multipliers. This course will also serve as a way for students to explore the nature of mathematics through reading excerpts from books on some of the most important mathematical developments and discussing how mathematics plays an integral role in so much of our world today.
