Mathematics

The courses at the high school are designed to offer a broad range of experiences to the student body from Math Essentials to Mathematical Modeling:

Math Essentials

Introduction to Algebra

Practical Algebra I

Algebra I

Practical Geometry

Geometry

Geometry Honors

Practical Algebra 2

Algebra 2

Algebra 2 Honors

Mathematical Investigations*

Personal Finance*

Trigonometry*

Advanced Mathematics

PreCalculus

Probability and Statistics*

Introduction to Calculus*

Calculus

Mathematical Modeling*

Probability and Statistics Honors*

* 1 semester courses

Movement between the levels is possible according to student performance and desire. Prerequisites are defined for most courses indicating past performance levels which should lead to success in the next course in the sequence. Each full year course is divided into two semester courses (the A course is first semester and the B course is second semester). Each semester course earns 1/2 credit toward graduation. Students are advised by their current math teacher (or by the department coordinator for students not currently enrolled in math) regarding the next appropriate course in the sequence. The current math teacher, or the coordinator, must approve the student’s registration selection. Students electing to take an honors level class are expected to complete the semester in that class. A math placement exam will be administered to students entering grade 9 to assist in determining initial placement. An additional placement test may be administered to Geometry students to determine their readiness for Algebra 2.

Students who choose to take a course without department recommendation may find that the expectations regarding homework are not accurate.

Students who wish to consider the Advanced Placement option for Calculus AB, Calculus BC, or Statistics please refer to the Advanced Placement Opportunities section in this handbook.

Math Essentials A (1st Semester)

Math Essentials B (2nd Semester)

Grades: 9-12

CR: ½ Per Semester

Prerequisite: Teacher Recommendation

This course is designed to provide a broad spectrum of math applications for the student. Emphasis is on life skills experiences. Projects and simulations provide much of the activity for this class. Topics to be covered in this course include, but are not limited to, the following:

    • Money

    • Banking

    • Fractions

    • Measurement

    • Percents

    • Decimals

    • Graph & Statistics

    • Transportation

    • Proportions and Comparison Shopping

    • Time

Expectations: Much of the student’s work will be completed during class time. Personal calculators and the computer are used to assist with the calculations when appropriate. Work not completed during class time will become homework. Work ethic, quizzes, tests, projects, and exercises will form the basis of the student’s grade.

Introduction to Algebra A (1st Semester)

Introduction to Algebra B (2nd Semester)

Grades: 9-11

CR: 1/2 Per Semester

Prerequisite: Teacher recommendation.

This course is intended as a basic introduction to the concepts of algebra. This course gives the student an opportunity to learn and solidify basic algebraic concepts prior to beginning a full year study of Algebra I. Topics to be covered during this course include the following:

    • Patterns and Relationships

    • Decimals

    • Fractions

    • Rational numbers

    • Working with integers and inequalities.

    • Algebraic expressions and their manipulation

    • General solution techniques for linear equations

    • Graphing on a number line and on a coordinate system

    • Graphing linear functions

    • Exponents

Expectations: Students will have daily homework of fifteen to thirty minutes. Homework, work ethic, quizzes, tests, and projects will form the basis of the student’s grade.

Practical Algebra 1A (1st semester)

Practical Algebra 1B (2nd semester)

Grades 10-12

CR: 1/2 Per Semester

Prerequisite: C in Introduction to Algebra, and department recommendation. This course is restricted to 10-12 graders.

This course is intended as one option to the first course in the traditional sequence Algebra 1-Geometry- Algebra 2 . The approach used is more informal than that used in Algebra 1A/B and depends more on problem solving than on theorizing. The topics covered in this course include all of those listed in Algebra 1A and 1B. Successful completion of this course will satisfy the State of NH graduation requirement for Algebra 1.

Expectations: Students are expected to keep a binder with class notes and homework. Daily homework of fifteen to thirty minutes will be assigned. Occasional projects that utilize the material presented will be assigned. Homework, class work, quizzes, tests and projects will form the basis of the student’s grade.

Algebra IA (1st semester)

Algebra IB (2nd semester)

Grades: 9-12

CR: 1/2 Per Semester

Prerequisite: Department recommendation

This course is intended as the first course in the traditional Algebra 1 - Geometry - Algebra 2 high school sequence. Many colleges specify this three-year sequence as an entrance requirement for admission. Successful completion of this course will satisfy the State of NH graduation requirement for Algebra 1. The topics covered in this course include the following:

    • Algebraic expressions and order of operations

    • General solution and graphing techniques for linear equations and inequalities

    • Rates, ratios and proportions

    • Graphing linear equations in standard, point-slope and slope-intercept form

    • Systems of linear equations and inequalities

    • Laws of exponents

    • Add, subtract, and multiply polynomials

    • Roots and Radicals

    • Solving quadratic equations by factoring, completing the square, and quadratic formula

    • Graphing quadratic functions

Expectations: Students are expected to keep a binder with class notes and homework. Daily homework of twenty to thirty minutes will be assigned. Homework, class work, quizzes, tests, and projects will form the basis of the student’s grade.

Practical Geometry A (1st semester)

Practical Geometry B (2nd semester)

Grades 10-12

CR: 1/2 Per Semester

Prerequisite: C in Algebra I or Practical Algebra 1, and department recommendation

This course is intended as one option to the second course in the traditional sequence Algebra 1-Geometry- Algebra 2. This course investigates the properties of geometric figures. All the problem solving techniques normally found in a regular college preparatory geometry course are included here with the exception of the formal geometric proof. The approach used is more informal than that used in Geometry A/B and depends more on problem solving than on theorizing. The topics to be covered in this course include all of those listed in Geometry A and B. The solving of proportions, graphing, and linear equations are the only algebraic skills necessary to the course.

Expectations: Daily homework of twenty to thirty minutes will be assigned. Occasional projects that utilize the material presented will be assigned. Homework, class work, quizzes, tests and projects will form the basis of the student’s grade.

Geometry A (1st semester)

Geometry B (2nd semester)

Grades 9-12

CR: 1/2 Per Semester

Prerequisite: C in Algebra I and department recommendation

This course is intended as the second course in the traditional sequence Algebra 1-Geometry- Algebra 2. Many colleges specify this three-year sequence as an entrance requirement for admission. Group work in a cooperative learning environment will be used as an integral part of the learning experience. Students will be expected to use their Algebra skills in this course. The topics to be covered in this course include the following:

    • Basic structural idea of a system of mathematics

    • An introduction to inductive reasoning

    • Angles and lines in the plane and in space

    • Definitions and properties of polygons

    • Perpendiculars and parallels in the plane and in space

    • Geometric constructions

    • Triangle congruence

    • Geometric proportions and similarity

    • Plane coordinate geometry

    • Circles and spheres - arcs, secants, and tangents

    • Areas of polygons and circles

    • Surface areas and volumes of solids

    • Methods of proof in a deductive system of mathematics

    • Pythagorean Theorem

    • Triangle trigonometry

Expectations: Daily homework of thirty to fortyminutes will be assigned. Students are expected to keep a binder with class notes and homework. Binders, projects, quizzes, tests, and participation in the cooperative learning experience will form the basis of the student’s grade.

Geometry Honors A (1st semester)

Geometry Honors B (2nd semester)

Grade: 9-10

CR: 1/2 Per Semester

Prerequisite: Department recommendation

This course is intended as one option to the second course in the traditional sequence Algebra 1 - Geometry - Algebra 2 . The topics covered in this course include all of those listed in Geometry A,B. The difference between the regular course and the honors alternative is reflected in the pace, degree of rigor and number of topics studied. The treatment given to all topics is more theoretical and the exercises are more challenging. Students are expected to synthesize and apply the material beyond examples discussed in class. Quizzes and tests require an extension of the knowledge gained in homework.

Expectations: Daily homework of thirty to forty-five minutes will be assigned. Evaluation will be based on class work, homework, participation in class discussions, quiz grades, test grades and projects.

Practical Algebra 2A (1st semester)

Practical Algebra 2B (2nd semester)

Grades: 11-12

CR: 1/2 Per Semester

Prerequisite: C in both Algebra I and Geometry or Practical Geometry and department recommendation. This course is restricted to juniors and seniors.

Although following a traditional Algebra 2 curriculum, this course covers fewer topics than Algebra 2, spending more time on skills, applications, and projects. The next course in the sequence would be Mathematical Investigations .

Expectations: Daily homework of approximately twenty minutes will be assigned. Homework, class work, quizzes, tests, projects and participation will form the basis of the student’s grade.

Algebra 2A (1st semester)

Algebra 2B (2nd semester)

Grades: 10-12

CR: 1/2 Per Semester

Prerequisite: B in both Algebra I and Geometry and department recommendation

This course is intended as one option to the third course in the traditional sequence Algebra 1-Geometry- Algebra 2. Many colleges specify this three-year sequence as an entrance requirement for admission. This course makes use of various technologies. The topics to be covered in this course include the following:

    • Properties of the real number system

    • Functions

    • Polynomial expressions

    • Linear equations and inequalities

    • Quadratic equations and inequalities

    • Transformations

    • Matrices and determinants

    • Conic sections

    • Systems of quadratic functions in two variables

    • Logarithmic and exponential functions

    • Arithmetic and geometric series

    • Probability

Expectations: Daily homework of twenty to thirty minutes will be assigned. Homework, class work, quizzes, tests, and projects will form the basis of the student’s grade.

Algebra 2 Honors A (1st semester)

Algebra 2 Honors B (2nd semester)

Grade: 9-10

CR: 1/2 Per Semester

Prerequisite: B in Geometry Honors and department recommendation

This course is intended as one option to the third course in the traditional sequence Algebra 1 - Geometry - Algebra 2. The difference between the regular course and the honors alternative is reflected in the pace, degree of rigor and number of topics studied. The treatment given to all topics is more theoretical and the exercises are more challenging with less review of Algebra 1. Students are expected to synthesize and apply the material beyond examples discussed in class. Quizzes and tests require an extension of the knowledge gained in homework. This course makes use of various technologies. The topics covered in this course include the following:

    • Linear Functions

    • Solving Systems of Equations and Inequalities (linear and non-linear)

    • Translations of Functions

    • Modeling with Functions

    • Matrices

    • Quadratic Functions and complex numbers

    • Conic Sections

    • Parametric Equations

    • Exponential, Logarithmic, and Logistic Functions

    • Polynomial Functions

    • Rational Functions

    • Radical Functions

    • Trigonometry

    • Probability and Statistics

Expectations: Daily homework of thirty to forty-five minutes will be assigned. Evaluation will be based on class work, homework, participation in class discussions, quiz grades, test grades and projects. A grade of C+ or better in the A semester of the course is necessary to continue with the B semester.

Mathematical Investigations - Great Ideas in Mathematics (1st semester)

Grades: 12

CR: 1/2

Prerequisite:Department recommendation and a C in Advanced Math. (Algebra 2 for Seniors)

This course may be taken for dual credit, 4 credits per semester.

Mathematical Investigations is an introduction to various branches of mathematics, including number theory, functions and modeling, geometry, and probability and statistics. The course will focus on some of the most interesting ideas in the history of mathematics and various applications, including the infinitude of the primes, the non-denumerability of the real numbers, different sizes of infinity,golden rectangles, non-Euclidean geometry, and measuring risk. Students will complete research projects in areas such as cryptography, platonic solids, topology, chaos and fractals, and different voting methods. The course emphasizes mathematical thinking, habits of the mind, and problem solving. These strategies will allow students to apply mathematics to real-life situations. Along the way, students will confront issues that challenge their intuition and even experience mathematical questions that have remained unsolved for hundreds of years. The course is student centered and focuses on activity-based instruction that integrates technology.

The topics to be covered in this course include the following:

    • Introduction to Problem Solving and Critical Thinking

    • Functions and Modeling

    • Number Theory

    • Infinity

    • Geometry and Measurement

    • Probability and Statistics

Expectations: Daily homework of twenty to thirty minutes will be assigned. Evaluation will be based on class work, homework, participation in class discussions, quiz grades, test grades and projects.

Trigonometry (2nd semester)

Grades: 11-12

CR: 1/2

Prerequisite: C in Practical Algebra 2 or Algebra 2 and department recommendation. Students who have successfully completed Advanced Math should NOT sign up for Trigonometry.

This course supplements the content of Algebra 2 to include the topic of trigonometry. It includes a full study of trigonometric functions, formulas, graphs and identities..

The topics to be covered in this course include the following:

    • Trigonometric Functions

    • Graphing Trigonometric Functions

    • Right Triangle Trigonometry

    • Law of Sines

    • Law of Cosines

    • Trigonometric Identities

    • Inverse Trigonometric Functions

Expectations: Daily homework of thirty to forty-five minutes will be assigned. Homework, class work, quizzes, tests, and projects will form the basis of the student’s grade.

Personal Finance (2nd semester)

Grade: 12

CR: 1/2

Prerequisite: C in Algebra 1

This course is designed to provide students with knowledge of financial matters that they will need in the future. The course will include topics that students can use immediately such as opening and balancing a checking account, using debit and credit cards, and planning for college or household expenses. Other topics will include the impact of compound interest on investments and loans. Local business people will help with the instruction. Upon successful completion of this course, students will be better prepared to deal with financial matters.

The topics to be covered in this course include the following:

    • Banking: checking and savings accounts

    • Developing a budget

    • Loans: personal and business; mortgages

    • Credit Cards

    • College Funding

    • Insurance: health, life, property, car, and dental

    • Investing: stocks, bonds, real estate, mutual funds, Retirement Savings: Roth IRA, Traditional IRA, 401K, 403b

    • Taxes: federal, state, local, property, income and sales

    • Charitable Giving

    • Scams and how to avoid them

    • Starting a business

Expectations: Portfolios, special problems, projects, homework, class work, simulations and tests will form the basis of the student’s grade. Students make extensive use of spreadsheets.

Advanced Math A (1st semester)

Advanced Math B (2nd semester)

Grades: 11-12

CR: 1/2 Per Semester

Prerequisite: C in Algebra 2 and Geometry, and department recommendation

This course, following a preparation in Algebra 2, continues the exploration of algebra and trigonometry. This course makes use of various technologies. The topics to be covered include:

    • Parent Functions

    • Quadratic Functions

    • Linear and Nonlinear Programming

    • Polynomial functions

    • Rational Functions

    • Exponential and logarithmic functions

    • Modeling

    • Trigonometric functions

    • Trigonometric Identities

    • Polar Coordinates

    • Complex Numbers

    • Vectors

Expectations: Class preparation time (including homework) is 1-3 hours per week. Course activities include homework, in class work, quizzes, tests, and projects. Grade is based primarily on test scores, with a lesser contribution from quizzes, special homework problems and projects.

PreCalculus A (1st semester)

PreCalculus B (2nd semester)

Grade: 10-11

CR: 1/2 Per Semester

Prerequisite: B in Algebra II Honors and department recommendation

The difference between Advanced Math and PreCalculus is reflected in the pace, degree of rigor and number of topics studied. The treatment given to all topics is more theoretical and the exercises are more challenging. This course makes use of various technologies. The topics to be covered include:

    • Polynomial functions

    • Exponential and logarithmic functions

    • Conic sections

    • Trigonometric functions

    • Polar coordinates and complex numbers

    • Vectors

    • Sequences and series

    • Probability and statistics

Students are expected to synthesize and apply the material beyond examples discussed in class. Quizzes and tests require an extension of the knowledge gained in homework.

Expectations: Daily homework of thirty to forty-five minutes will be assigned. Evaluation will be based on class work, homework, quiz grades, test grades and projects.

Probability And Statistics (1st semester)

Grades: 11-12

CR: 1/2

Prerequisite: Department recommendation and a C in Advanced Math. (Algebra 2 for seniors)

This course may be taken for dual credit, 4 college credits per semester through the Running Start Program.

In this course students explore:

    • Probability

    • Random variables

    • Geometric and binomial models

    • The normal distribution

    • Confidence intervals and hypothesis testing

    • The t-distribution

    • The Chi-square distribution

    • Correlation and regression

    • Analysis of variance

Expectations: Daily homework of thirty minutes will be assigned. This course makes extensive use of graphing calculators and spreadsheets. A major project collecting, organizing and analyzing data will be undertaken during the second quarter. Evaluation will be based on group work, written assignments and assessments, class participation, and the semester project.

Introduction To Calculus (2nd semester)

Grades: 11-12

CR: 1/2

Prerequisite: B in Advanced Math and department recommendation

This course is designed to introduce students to some fundamental calculus concepts and to prepare them for a rigorous college level course in calculus. The topics to be covered in this course include the following:

    • Continuity and limits

    • Differentiation techniques

    • Exponential and logarithmic functions

    • The definite and indefinite integral

    • Area under a curve

Expectations: Daily homework of thirty to forty-five minutes will be assigned. Homework, participation in class discussions, quizzes, tests, and projects will form the basis of the student’s grade.

Calculus A (1st semester)

Calculus B (2nd semester)

Grades: 11-12

CR: 1/2 Per Semester

Prerequisite: B in Precalculus and department recommendation

This course may be taken for dual credit, 4 credits per semester.

This course is treated with the rigor that characterizes such a course at the college level. Students learn to solve problems algebraically, numerically, and graphically. By May, students are prepared to take the Calculus BC AP Exam. This course makes use of various technologies. Students are expected to synthesize and apply the material beyond examples discussed in class. After a quick review of polynomials, trigonometry, conic sections, and logarithms, students study the following topics:

    • Theory of limits and continuity

    • Derivatives of functions

    • Chain rule for differentiation

    • Logarithmic differentiation

    • Derivatives of implicit and inverse functions

    • Simple differential equations

    • Relationship of distance, velocity, and acceleration

    • Related rates of change and applications

    • Integration

    • Techniques of integration

    • Volumes of solids of revolution

    • Taylor and MacLaurin series

Expectations: Daily homework of approximately one hour will be assigned. Evaluation will be based on homework, class work, special problems, tests, and projects.

Mathematical Modeling

Grades: 11-12 (1st Semester)

CR: 1/2

Prerequisite: Calculus and department recommendation

This course is a seminar-style, project-based course. Students explore:

    • Introduction to modeling

    • Discrete dynamical systems

    • Stochasticity in modeling

    • Motion

    • Other topics as time and interest permit

There will be an emphasis on technology-based modeling tools, including graphing calculators, Excel, Geogebra and NetLogo. Students are expected to synthesize and apply the material beyond examples discussed in class.

Expectations: Weekly homework of 2-3 hours integrating classroom topics will be assigned. Evaluation will be based on homework, class work, quizzes, and projects.

Probability And Statistics Honors

Grades: 11-12 (2nd Semester)

CR: 1/2

Prerequisite: Calculus and department recommendation

This course may be taken for dual credit, 4 credits per semester.

In this course students explore:

    • Probability

    • Random variables Including derivations of Expected Value and Variance formulas

    • Geometric and binomial models and associated proofs

    • The normal distribution

    • Confidence intervals and hypothesis testing

    • The t-distribution

    • The Chi-square distribution

    • Correlation, regression, re-expressing data

    • Analysis of variance

Students will learn how to calculate confidence intervals and employ hypothesis testing. Connections between statistics and calculus will be developed. This course will make extensive use of graphing calculators and spreadsheets. Students are expected to synthesize and apply the material beyond examples discussed in class.

Expectations: Daily homework of thirty to forty-five minutes will be assigned. Evaluation will be based on written work, class and group work, special problems, tests and the semester project.

Students will study all of the topics necessary to prepare them for the AP Statistics test (not required).

Math Courses At Dartmouth

Students must take Mathematical Modeling and Probability and Statistics Honors before enrolling in a Dartmouth Class.

Mathematics Independent Study

The Mathematics Department offers independent study opportunities to students who show genuine interest in mathematics and who have demonstrated excellence in previous math courses. An independent-study structure is intended for students who wish to study mathematics above and beyond what they can study in the standard curriculum. Students may create a course based on a number of different topics in mathematics. In the past, students have successfully completed independent studies in Probability and Statistics, Number Theory, Computer Programming, Student Teaching, Projective Geometry and Fractals. The Math Department will accept independent-study proposals from students who are approaching their last semester at Hanover High School. Students who feel they could effectively complete a course independently and wish to explore mathematics in more depth are welcome to apply.