The Foundation for a Meaningful Life
Kindergarten - Grade 9 in Southborough, MA

# Upper School - Math Courses

## About the Upper School Math Program

Based on a student’s ability to work independently and persevere with problems, along with his or her past mathematical performance, he or she is placed into one of our Upper School math courses. A major goal at this level is to help students learn to write and to interpret 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, students take Algebra I, Algebra I Part 1, or Extended Topics in Algebra (ETA). Following coursework in algebra, students take Geometry or Geometry Advanced, which is then followed by Algebra II, depending on prior mathematics coursework, standardized testing, and/or teacher recommendation.

Student placement is evaluated in the 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 private school math program.

## Courses

### List of 8 items.

• #### Pre-Algebra

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.
• #### Algebra 1

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 their ability to manipulate symbols.
• #### Algebra, Part 1 and Part 2

This course covers the topics of the complete Algebra 1 course over two school years. It is offered to those grade eight and nine students 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 (ETA)

Extended Topics in Algebra is a course designed for students who have had some initial exposure to Algebra 1 and Geometry coursework. Students in this course have demonstrated strong interest, independence, and achievement in mathematics. Students move beyond the straightforward application of algorithms, focusing on solving problems in context. Students spend time investigating, conjecturing, predicting, analyzing, and verifying. This course delves more deeply into algebra topics, using algebraic processes to tackle geometry topics, and it moves at a more challenging pace in order to increase connectedness of the students’ understanding of algebra. Topics covered include data analysis; linear equations and inequalities in one variable; systems of equations in two variables; polynomials; functions and their transformations; non-linear functions; quadratic and rational functions; and quadratic equations and their solutions. Geometry topics covered include parallel lines, circles, congruent triangles, right triangles and trigonometry, and quadrilaterals. Students solve problems by learning how to design and apply mathematical models. A TI 84 Plus graphing calculator, in addition to apps such as Geometer’s Sketchpad, Geogebra, and Desmos, are used to support investigations and projects.