Academics

Mathematics

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he math program strives to equip each student to think logically and analytically and to effectively communicate strategies for solving problems, particularly those related to math and science. We seek to develop a student’s understanding of algebra and other mathematical concepts throughout the curriculum. Topics in each subject are explored visually, symbolically, and verbally. Scientific and graphing calculators and various software applications are used as instruments for exploration and deeper understanding. Our aim is to encourage students to become confident in their math abilities and to recognize math as a powerful subject and tool.

Starting in 8th grade, accelerated courses are offered at each grade level. Placement in accelerated courses is based on student performance, teacher recommendation, and the approval of the department head. These courses move at a faster pace and explore topics in greater depth and breadth. Many 12th grade students complete a college level calculus course.

6th Grade

The sixth grade math curriculum has three main components. In the first trimester, students focus on exploring math concepts with data covering the collection, organization, interpretation and analysis of data through the design and reading of graphs. Students investigate the meaning and application of mean, median and mode and the use of range creating graphs. Through this study, students also explore magnitude of large and small numbers, patterns and concepts in number relationships through a variety of problem solving situations. During the second trimester, students move on to an exploration of concepts, algorithms, interpretations and applications of operations with fractions, decimals and percents. During the third trimester Geometry unit, studies center on the vocabulary, logic and formulas of spatial mathematics and the exploration of properties of two-dimensional polygons using manipulative materials and models. Arriving at formulas for finding perimeter and area, students then apply these formulas to solving problems based on drawings and word problems. In working with circles, students discuss the concept of mathematical constants and apply pi to finding circumference and area.

7th Grade

The primary goal of 7th grade mathematics instruction is to equip all students to reason and communicate proficiently in mathematics. By the end of the year students should have the ability to use the vocabulary, forms of representation, materials, tools & techniques, and intellectual methods of the discipline. The curriculum is designed to impart the basic skills and knowledge to succeed in the study of Algebra in 8th grade.

The approach blends problem-centered instruction with basic skills work to make sure that students are not only successful problem solvers but also have the ability to perform mathematical computations accurately and efficiently. Students are asked to explore engaging problems in number operations, probability and algebra. Modules from the Connected Mathematics Program are used in conjunction with carefully selected outside resources to provide an enriching mathematics curriculum.

8th Grade

A firm grounding in algebra is essential for success in all higher level mathematics and sciences. The eighth grade curriculum is designed to meet the needs of students at different levels based upon a continuum of concrete to abstract thinking abilities. Our students will take a full Algebra I course which incorporates graphical investigations using the TI-84 Plus graphing calculator. One section of eighth grade math will work with algebraic topics at a more accelerated level.

Students who continue taking math each year will complete their senior year with AB calculus and/or statistics. They should be prepared to take the Advanced Placement exam at the end of their calculus or statistics course, if they choose.

Students taking the accelerated algebra-based course are eligible to take the accelerated course the following year. If they continue at that level, they will stay in the enhanced courses through the twelfth grade when they would prepare for the BC level Advanced Placement calculus exam.

132 Geometry
required major
prerequisite: Algebra I
Grade: 9

This course in Euclidean geometry includes the study of geometric figures, shapes, angles, parallel lines, similarity and congruence, area and volume, coordinate geometry, some analytic geometry, and some trigonometry. The deductive thought process is emphasized throughout this course and algebraic skills are reviewed and reinforced.

OR

131 Geometry Acc. (Accelerated)
required major
prerequisite: Algebra I
Grade: 9

This course takes a strongly analytical approach to the study of Euclidean geometry. Proofs are emphasized throughout the year to develop strong deductive reasoning. Algebra will be used extensively in the development and solving of problems. Students will begin the study of trigonometry. Students new to GFS may be asked to take a placement test.

142 Algebra II
required major
prerequisite: Geometry
Grade: 10

Clear, logical thinking is developed in this course as students investigate applications of mathematical concepts and develop their problem solving abilities. Topics studied include linear and quadratic equations and inequalities, higher degree equations and functions, irrational and complex numbers, exponential and logarithmic functions. The graphing calculator is used for graph exploration.

OR

141 Algebra II/ Trigonometry (Accelerated)
required major
prerequisite: Geometry-Accelerated
Grade: 10

This course moves at a brisk pace while covering topics in depth. The graphing calculator is used for modeling and analyzing functions. Conventional Algebra II and precalculus topics are integrated to prepare students for calculus. Topics studied include: solving algebraic equations and inequalities, function operations, polynomial and rational function analysis, exponential and logarithmic functions and trigonometric functions and trigonometric applications. Upon completion of this course and in consultation with the teacher, students in strong standing may take the appropriate SAT subject area test.

152 Precalculus
required major
prerequisite: Algebra II or Functions and Trigonometry
Grade: 11

This course consolidates algebra and geometry skills and emphasizes application and synthesis of those topics as a preparation for calculus. Topics include solving algebraic equations and inequalities, function operations, polynomial, rational, exponential and logarithmic functions, trigonometric functions and applications, function analysis, and polar graphing. Upon completion of this course and in consultation with the teacher, students in strong standing may take Calculus.

153 Functions and Trigonometry
required major
prerequisite: Algebra II
Grade: 11

Functions and Trigonometry is an alternative to Precalculus. This course expands on topics from Algebra II and focuses on enhancing students’ skills in problem solving. Topics include exponential and logarithmic functions, polynomial and rational functions, trigonometric functions; and probability, sequences and series. This course is for students who have completed Algebra II and wish to strengthen and broaden their mathematical background before taking Statistics. Students planning to take Calculus must take Precalculus.

151 Differential Calculus-Advanced
required major
prerequisite: Algebra II-Accelerated
Grade: 11

This is the first year course of a two-year sequence. Students taking this course are required to take Integral Calculus and Series in their senior year. This course will cover topics including mathematical induction, polar coordinates, the complex plane, and data analysis using the graphing calculator. Students will cover much of the differential calculus using Howard Anton’s Calculus Eighth Edition/Brief Edition. The students will be taking a rigorous approach to the mathematics and proofs will be emphasized.

162 Calculus- Advanced
major elective
prerequisite: Precalculus or Algebra II/Trigonometry.-Acc.
Grades: 11, 12

This course covers the fundamental concepts of differential and integral calculus. First semester topics studied include limits, average and instantaneous rate of change, the definition of derivative and techniques of differentiation. The product, power, quotient and chain rules are applied to polynomial, rational, trigonometric, exponential and logarithmic functions. Second semester topics are Riemann sums, integration techniques, area between two curves and volumes of revolution. The topics covered are topics included in the AB level of the Advanced Placement curriculum.

OR

161 Integral Calculus and Series Advanced
major elective
prerequisite: Differential Calculus- Advanced
Grade: 12

This is the required second year of a two-year sequence. Upon entering the course, students will have a working knowledge of differential calculus, thus we will start with integral calculus. The topics covered include the BC level Advanced Placement curriculum.

163 Statistics- Advanced
major elective
prerequisite: Functions and Trigonometry or Pre Calc
Grade: 12

Exploratory analysis of data will make use of graphical and numerical techniques to study patterns and departure from patterns. Students will learn to collect data according to a well-developed plan in order to obtain a valid conjecture on the information. Probability will be used for anticipating what the distribution of data should look like under a given model. Statistical inference will guide the selection of appropriate models. We will generally follow the AP Statistics curriculum.

  • AMC Math Test

    The AMC 8 is a twenty-five-question, forty minute multiple-choice examination in middle school mathematics, designed to promote the development and enhancement of problem solving skills.

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