INTEGRATED MATH I18 weeks 1 credit
The objective of this course is to strengthen the students' number sense and basic arithmetic skills. The basic operations with whole numbers, fractions, and decimals are practiced throughout the course. Differentiated instruction, team teaching, and a strong student support system will be available. The topics found in the Number and Operations; Functions and Algebra; Data, Statistics, and Probability; and Geometry and Measurement strands of the 9-10 Grade Span Expectations will gradually be introduced throughout the course. Students completing Integrated Math I are encouraged to take Integrated Math II as well where they will continue to prepare for their first algebra experience.
INTEGRATED MATH II18 weeks 1 credit
The basic operations with whole numbers, fractions, and decimals are reviewed throughout this course. More emphasis is placed on the 9-10 GSE's than in Integrated Math I. Experiential learning including manipulatives, discovery experiments, and group problem solving will overshadow the traditional teacher lecture approach. An introduction to variables and algebraic thought in general will be included.
PRE-ALGEBRA18 weeks 1 credit
This course is an introduction to Algebra intended for the student needing a gradual initiation into Algebra I. The course introduces basic algebraic concepts such as operations with positive and negative numbers, work with fractions, decimals, and percents, evaluating algebraic expressions, solving simple equations, factoring, and introductory word problems. Topics from the Data, Statistics, and Probability; and Geometry and Measurement strands are included to align with the GSE's.
FOUNDATIONS OF ALGEBRA I18 weeks 1 credit
This course meets the state requirement for Algebra I. It is intended for the two-year technical college, military,
or career-bound student. Specific algebraic topics include the properties of real numbers, sets, equations, inequalities,
systems of equations, polynomials, factoring, rectangular coordinate graphing, rational algebra expressions, radicals,
and quadratics. Topics from the Data, Statistics, and Probability; and Geometry and Measurement strands of the
9-10 Grade Span Expectations will also be addressed.
FOUNDATIONS OF GEOMETRY18 weeks 1 Credit
Foundations of Geometry maintains the methodology and philosophy found in foundations of Algebra I. That is, less
emphasis placed on theory and more emphsis placed on applications. Exploration activities and computer similations
will be used to formulate the traditional geometric theorems as opposed to formal deductive proofs. Constructions
and other hands on activities help provide the student with skills needed in technical fields such as surveying
or CAD programs. Students will study properties and applications of angles, polygons, and circles. Units on area
and volume will be included. Trigonometry and coordinate geometry will be introduced.
FOUNDATIONS OF ALGEBRA II18 weeks 1 credit
This course requires that students apply topics studied in Foundations of Algebra and Geometry. Students will be exposed to problems analogous to those they will encounter in vocational-technical schools and industry. The course materials used are chosen to help develop problem solving skills. Aside from applying the fundamental properties of equations and inequalities, the student will be presented with topics from geometry, trigonometry, logarithms, systems of equations, and quadratic equations. Both British and metric measurements are used throughout the course.
COLLEGE PREPARATORY ALGEBRA I18 weeks 1 credit
College Preparatory Algebra I is a study of the properties of the real number system. Specific topics include the properties of real numbers, sets, equations, inequalities, systems of equations, polynomials, factoring, rectangular coordinate graphing, rational algebra expressions, radicals, and quadratics. Deductive thinking is emphasized here as methods of proof are included. Topics from the Data, Statistics, and Probability; and Geometry and Measurement strands of the 9-10 Grade Span Expectations will also be addressed.
COLLEGE PREPARATORY GEOMETRY18 weeks 1 credit
College Preparatory Geometry is a study of logic with applications of both inductive reasoning, as in scientific thought, and deductive reasoning, as needed in mathematical proofs. This logical basis is applied to one, two, and three-dimensional figures such as point, line, plane, angle, polygons, circles, spheres, and solids. Specific topics include congruence and similarity, two-dimensional coordinate geometry, two-column, statement and reason proofs, and applications of algebra to geometrical figures such as in computing areas and volume.
COLLEGE PREPARATORY ALGEBRA II
(Offered as a Running Start course through the NHCTC system)18 weeks 1 credit
Algebraic topics presented in college preparatory Algebra I and College Preparatory Geometry are solidified in College Preparatory Algebra II. The theme of functions is applied throughout college preparatory algebra II as the students study the theory and applications of linear, quadratic, polynomial, exponential, logarithmic, rational, irrational algebraic, trigonometric and circular functions. The complex number system is also presented in this course.
ADVANCED ALGEBRA and TRIGONOMETRY(Offered
as a Running Start course through the NHCTC system)18 weeks 1 credit
This course reviews and, most importantly, applies topics from College Preparatory Algebra II. Topics include: functions and graphs, trigonometric functions, systems of linear equations, quadratics, vectors, exponents and radicals, complex numbers, progressions, the binomial theorem, plane analytic geometry, an introduction to statistics, curve fitting, and an informal introduction to differential calculus.
HONORS ALGEBRA I18 weeks 1 Credit
Honors Algebra I covers topics comparable to the college preparatory algebra I topics but exposes the student to more of the theory behind these topics. The homework problems require more critical thinking skills. Methods of proof are included.
HONORS GEOMETRY18 weeks 1 credit
This course presents traditional Euclidean geometry as related to plane surfaces and solids. The building of a logical deductive system via undefined words, definitions, postulates, and theorems based upon the before mentioned ideas is stressed. The course starts with the development of conditional statements, their converses, inverses and contrapositives, and proceeds to show how they are used in direct and indirect proofs. Both the paragraph and two-column forms of proof are emphasized. Specific topics include proving triangles congruent, transformations, triangle inequalities, parallel lines, quadrilaterals, area similarity, the right triangle, circles, concurrence theorems, regular polygons, solids, and non-Euclidean geometry. Historical topics as to the development of mathematics and anecdotes about famous mathematicians are interspersed throughout the course. Because geometry is such a visual subject, numerous models, transparencies, and slides are used to enhance the student's understanding and appreciation of geometry.
HONORS ALGEBRA II(Offered as
a Running Start course through the NHCTC system)18 weeks 1 Credit
Honors Algebra II covers topics comparable to the College Preparatory Algebra II topics but exposes the student to more of the theory behind these topics. The homework problems require more critical thinking skills in that they are less drill and practice by nature. The problems are designed to help build a strong foundation for the study of calculus and other advanced math courses. Supplementary topics in statistics, limit theory, and introductory calculus concepts are included as time permits.
PRE CALCULUS(Offered as a Running
Start course through the NHCTC system)18 weeks 1 credit
This course provides a strong background for the student's further studies in mathematics and related areas. A review and extension of many topics in Honors Algebra II are included. Function is the underlying and unifying concept of almost every topic in the course, including the polynomial, logarithm, exponential, rational, and circular (trigonometric) functions. Other upper level topics included are polar coordinates, parametric equations, complex numbers, vectors, sequences and series, and the limit concept all geared toward preparing the student for a formal calculus course.
ADVANCED PLACEMENT CALCULUS WITH
ANALYTIC GEOMETRY (AB)(Offered as a Running Start course through the NHCTC system)18 weeks 1 credit
This course follows the College Board Advanced Placement syllabus. Some key prerequisite topics may be reviewed but the majority of the course will assume a reasonably sound working knowledge of algebra, geometry, trigonometry, and elementary functions. Topics to be covered include: limits and continuity, the derivative, the differential and anti-differentiation, slope fields, the definite integral and its application, logarithm and exponential functions, trigonometric functions, and techniques of integration. It is a general objective of the course to adequately prepare the student for the Calculus AP exam given in May.
ADVANCED PLACEMENT CALCULUS WITH
ANALYTIC GEOMETRY (BC)(Offered as a Running Start course through the NHCTC system)18 weeks 1 credit
This course is intended for students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry and trigonometry. Most often Calculus BC is taken by students who have completed Calculus AB. Calculus BC is an intensive course in the calculus of functions of a single variable. During the first few weeks of the course Calculus AB topics are reviewed. Emphasis is placed on methods of proof here and problems of a challenging nature are encountered. The remainder of the course presents a variety of new topics to the students. Topics such as Newton's Method, techniques of integration, graphs in polar coordinates, derivatives of vector functions and parametrically defined functions, approximate integration, improper integrals, sequences and series, convergence tests, and elementary differential equations are discussed.
Along with these calculus topics, topics from number theory, linear algebra, abstract algebra, and analysis will be presented from time to time to give the student a better appreciation of what mathematics is. The use of computer algebra systems will also be incorporated throughout the course.
PROBABILITY AND STATISTICS(Offered
as a Running Start course through the NHCTC system)18 weeks 1 Credit
Probability and Statistics is the study of how to collect, organize, analyze, and interpret information. The subject is becoming increasingly important in all fields of endeavor. Topics will include probability theory, descriptive statistics and inferential statistics. Measures of central tendency, measures of variability, estimation, hypothesis testing, and linear regression are amoung the specific topics covered. For those students interested, college credit may be obtained through this course via the "Running Start" program that exists in partnership with the Community-Technical Colleges in New Hampshire.