The Foundation for a Meaningful Life Kindergarten - Grade 9 in Southborough, MA
Upper School - Math Courses
About the Upper School Math Program
Students are placed into one of our Upper School math courses based on their ability to work independently and persevere with problems, along with their past mathematical coursework and performance, and standardized test scores. Students in each course engage in productive struggle while tackling problem sets as part of our problem-based learning model. A major goal of all Upper School math classes is to help students learn to write, interpret, and discuss mathematical arguments.
Many students in grade seven study pre-algebra topics in courses designed to develop an understanding of mathematics as a system of thought. After Pre-Algebra or Pre-Algebra Advanced, students take Algebra 1, Algebra 1 Advanced, Algebra 1 Part 1 and Part 2, or Extended Topics in Algebra and Geometry (ETAG). Following coursework in algebra, students take Geometry or Geometry Advanced, which is then followed by Algebra 2.
Student placement is evaluated in the fall and spring of each year, recognizing that students at this age develop at different rates and appreciating that there is more than one path through Fay’s math program.
This math course is designed to consolidate computational skills, enhance understanding of underlying mathematical concepts, and extend the skills of working with proportion, percent, linear equations, and geometric relationships. Students gain proportional reasoning skills and become proficient with integer operations.
This course covers a sequence of topics similar to Pre-Algebra, but it covers more complex problems, and it requires a demonstration of some independence in mathematical thinking. It is designed for students who have already mastered computational skills, who have demonstrated the ability to think more abstractly about mathematics, and who are self-motivated to work independently to solve problems.
This is a complete Algebra 1 course. Topics in this class include proportional reasoning; direct and inverse variation; writing, solving and graphing linear equations and inequalities; systems of equations; functions and their transformations; non-linear functions; and quadratic equations and solutions. A TI-84 Plus graphing calculator is required and used for investigations, data analysis, graphing functions, and verifying results. Application of skills, procedures, and concepts to solve real world problems is an integral part of this course. An important goal of this course is for students to begin to see algebra as a language to model situations, in addition to solidifying the ability to manipulate symbols.
This course covers the same sequence of topics as Algebra 1, but it covers more in-depth and complex problems and requires a demonstration of independence and flexible thinking in mathematics. Students will learn through theory and abstract thinking, problem-solving, application, and investigation.
This course covers the topics of the complete Algebra 1 course over two school years. It is offered to eighth and ninth graders who benefit from a more supportive pace to learn new topics and who need more guidance in learning how to tackle each new problem and recognize which skills to use when confronted with an unfamiliar format. In Part I, concepts include data exploration; proportional reasoning; direct and inverse variation; writing, solving and graphing linear equations and inequalities; and systems of linear equations. During year two, in Part 2, concepts include exponential growth and decay, rational numbers and radicals, and a full study of quadratic equations and their solutions. The textbook for this class is the same as the one used in the one-year Algebra I course.
Extended Topics in Algebra and Geometry is a course designed for students who have had some initial exposure to Algebra 1 and Geometry and who have demonstrated strong interest, independence, and achievement in mathematics. Students move beyond straightforward application of algorithms, focusing on problem-solving in context. This course delves deeply into algebra topics, uses algebraic processes to tackle geometry topics, and moves at a more challenging pace. Topics covered include linear equations and inequalities; systems of equations and inequalities; linear and nonlinear (quadratic, exponential and rational) functions and their transformations; and quadratic equations and their solutions. Geometry topics covered include proof, logic and reasoning; extended work with coordinate geometry; circles; triangles (including right triangle trigonometry); quadrilaterals; and measuring irregular shapes for area, volume, and surface area. Graphing calculators, including Desmos and TI-84s, are used to support learning, along with other applications such as Geogebra.
Geometry is a secondary school course that deepens students’ understanding of plane and solid geometric figures while fostering their abilities to analyze, justify, and communicate information about geometric relationships and write geometric proofs. Topics include congruent and similar triangles; parallel and perpendicular lines; right triangle trigonometry; polygons; circles and solids; transformations; and constructions. Algebra topics are integrated throughout the course to provide a solid and broad foundation for advanced mathematics courses. Geometry has a balanced focus on inductive and deductive reasoning, providing students with some practice with proofs. The Geometry Advanced course is for more independent learners and is a proof-based curriculum focusing on the development of inductive reasoning. Students in both courses use technology such as Geogebra or Desmos to further demonstrate understanding of the geometry topics.
This course is a full-year study of advanced algebra for students who have completed Algebra I and a formal geometry course. Evidence of readiness and approval by the chair of the Mathematics Department is required to enroll. Topics include data analysis; sequences and recursion; functions; trigonometry; matrices; exponential and logarithmic functions; and conic sections. Students will also study irrational and complex numbers, polynomial equations, analytic geometry, and statistics. A TI 84 Plus graphing calculator is required in order to fully explore functions.
Pre-Calculus is a full-year course that prepares students for Calculus. Drawing on algebra, geometry, and arithmetic, the course synthesizes students’ prior mathematical work while introducing ideas of calculus. Topics include analysis of polynomial, rational, exponential, logarithmic, and trigonometric functions; complex numbers; mathematical induction; vectors in the plane; polar geometry; analytic geometry and conic sections; statistics, the normal distribution, and basic combinatorics; and area under curves. Moving at a challenging pace, the course emphasizes conceptual understanding, problem solving, and proof.