Noble and Greenough School Course Catalog

This course prepares students for subsequent algebra courses by reinforcing arithmetic skills while introducing students to more abstract arithmetic and mathematical reasoning skills, including the use of variables in problem solving. Students explore fractions, positive and negative numbers, exponent rules, like terms, equation solving, word problems, inequalities, personal finance, and basic concepts in planar and three-dimensional geometry.

This course covers the most fundamental and, therefore, most important skills in secondary school mathematics. Included in the course are a study of the rational and irrational numbers, extensive work with equations and inequalities, graphing of linear and quadratic functions, solving systems of equations, polynomial algebra, rational expressions and equations, and a variety of word problems. Use of the TI-84 graphing calculator will begin with the study of linear functions, and therefore is a required tool for the course.

Honors Algebra I is offered to those students who, in Pre-Algebra, have demonstrated very strong interest and ability in mathematics. All of the Algebra I topics described above will be included in the Honors course, but the formal operations and manipulations of algebra will receive greater emphasis in the Honors sections and the pace of coverage will be accelerated as well.

This year-long course has three main objectives: first, to impart an understanding and mastery of basic Euclidean geometric facts; second, to improve the student's ability to perceive problems visually and to improve the student’s use of perception, intuition, and pattern-recognition in problem-solving; and third, to introduce the student to a basic formal deductive mathematical system in which definitions and postulates lead to the discovery and proof of theorems. The year will be devoted to topics traditionally included in a high school geometry course: points, lines, planes, triangles, quadrilaterals, circles, parallelism, congruence, similarity, area, general polygons, and surface area and volume of solids.

While covering essentially the same syllabus as the regular geometry course, students in Honors Geometry will move at a faster pace, cover topics in greater depth, and be required to do significantly more formal proof-writing. A student must demonstrate strong interest and background in mathematics and high achievement in a comprehensive Algebra I course to earn consideration from the Department for honors placement.

Honors Algebra II covers the underlying theory and unifying connections between topics more deeply than the regular and accelerated sections of Algebra II, where more emphasis is given to exposure than to depth. It includes coverage of: polynomial functions, equations, and inequalities; the complex number system; advanced factoring techniques and binomial expansion; rational functions; trigonometry; properties of exponents and logarithms.