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## Summer Homework Packets

## Sequencing

## Level designations

## Advancing levels

## GENERAL COURSES

### ELEMENTS OF MATH

### PRE-ALGEBRA 100

## ALGEBRA I COURSES

### ALGEBRA I WITH LAB100

### ALGEBRA I 200

### ALGEBRA I 200 Part II

## GEOMETRY COURSES

### GEOMETRY 100

### GEOMETRY 200

## ALGEBRA II COURSES

### ALGEBRA II 100

### ALGEBRA II 200

### ALGEBRA II HONORS 300

## ADDITIONAL MATHEMATICS COURSES

### MATH OF FINANCIAL LITERACY

### ALGEBRA & TRIGONOMETRY 100

### PROBABILITY & STATISTICS

### PRE-CALCULUS 200

### HONORS PRE-CALCULUS 300

### AP STATISTICS 300

### CALCULUS 200

### AP CALCULUS (AB) 300

### AP CALCULUS (BC) HONORS 300

### AP COMPUTER SCIENCE A 300

The Mathematics team at Essex High School strives to offer a variety of courses to provide a solid foundation for all students.

Bring me to the Mathematics Department page.

Throughout each Mathematics course at Essex High School, teachers will reinforce the following eight mathematical practices in order to develop logical and critical thinking skills, which will enhance students’ problem solving, modeling and investigative abilities.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Most students follow the sequence of Algebra I, Geometry, and Algebra II to prepare for College Entrance examinations (SAT and ACT) during Grade 11. In addition to this sequence of courses, it is recommended that all students take a course in probability and statistics due to the increased focus on this field of study on standardized tests including the latest versions of the SAT and ACT. st.

Some course titles include level designations related to the rigor of the course:

300 level (also referred to as AP, Honors, or Advanced) courses are designed for students who have demonstrated exceptional ability in the subject matter.

200 level courses are designed for students who have demonstrated a high performance record in the subject matter.

100 level courses are designed to help students meet course proficiencies and graduation requirements.

Courses with no level assigned are open to students who have taken any indicated prerequisites.

Historically, students not receiving teacher recommendations have not been successful when moving on to the next course.

It is also recommended that students earn a grade of C or better to move from one 100 level course to the subsequent 100 level course, that they earn a grade of B- or better to move from one 200 level course to the subsequent 200 level course, and that they earn a grade of A- or better to move from a 100 level course to the subsequent 200 level course.

**Course Number: M315 1 Mathematics Credit Grades: 9-12 **

This course allows for individualized instruction for those students who would benefit from more preparation and support with fundamental mathematical concepts. Appropriate math interventions will be designed for each student dependent upon the student’s developmental level and current math skills

*Prerequisite**: Teacher recommendation*

**Course Number: M316 1 Mathematics Credit Grades: 9-12 **

This course is meant to prepare students for the study of Algebra. Course content will explore mathematical concepts that provide a foundation for success in Algebra. Students will become familiar with properties of mathematics and the language of algebra. Topics to be covered include algebraic expressions, integers, equations, decimals, fractions, exponents, ratios, proportions, percents, area, and graphing.

*Prerequisite**: Teacher recommendation*

Algebra I gives students a foundation in algebra to prepare for further mathematics courses. It is designed to provide students with the necessary algebraic techniques to solve practical problems. It is intended for more independent students who are confident in their skills with fractions, decimals and proportional reasoning.

Topics covered include the development of the language and structure of algebra, the real number system, a study of linear functions and inequalities, operations with algebraic expressions, factoring, polynomials, radicals, graphing, and an introduction to quadratic and exponential functions. Lessons integrate the use of technology, including graphing calculators.

**Course Number M317 1 Mathematics and .5 Elective credits Grades 9-12**

This course includes a .5-credit lab to allow students time to reinforce, develop, and practice concepts taught in class.

*Prerequisites**: Teacher recommendation and Pre-Algebra*

**Course Number M207 1 Mathematics credit Grades 9-12**

*Prerequisites**: Teacher recommendation and Pre-Algebra*

**Course Number M207II .5 Mathematics credit Grades 9-12**

This course is for students who have demonstrated proficiency with linear equations, functions and systems of equations in 8th grade math or Algebra I. The emphasis of this course is on topics covered primarily in the second half of Algebra 1 including factoring, radicals, polynomials, and an introduction to exponential and quadratic functions. Students in this .5-credit course are advised to enroll in Geometry concurrently. 9th grade students in this course who are not concurrently enrolled in Geometry are advised to enroll in Probability and Statistics immediately following completion of this course.

*Prerequisite**: Teacher recommendation*

The emphasis of these courses is on plane geometry but it also includes basic solid and coordinate geometry. Major topics include triangles, quadrilaterals, polygons, parallel lines, perpendicular lines, circles, area of polygons, transformations, right triangle trigonometry, and volume of polyhedra. A variety of problems and proofs provide the student with the opportunity to do some independent, creative and original thinking. This course also enables students to use the techniques of logical inference so they can discover and establish geometrical relationships. A strong understanding of algebra is an important prerequisite skill for geometry.

**Course Number M322 1 Mathematics credit Grades 10-12**

*Prerequisites**: Teacher recommendation and credit in Algebra I or concurrent enrollment in Algebra I 200 Part 2*

**Course Number M209 1 Mathematics credit Grades 9-12**

*Prerequisites**: Teacher recommendation and credit in Algebra I or concurrent enrollment in Algebra I 200 Part 2*

Algebra II gives college-bound students a more in-depth exposure to algebraic concepts and structures. Some of the topics covered are real numbers, equations and inequalities, fractions, exponents, radicals, sequences and series, complex numbers, and graphing and analysis of functional relationships, including quadratic, polynomial, exponential, and logarithmic functions.

There will be an emphasis on transformations of these functions. Lessons integrate the use of technology, including graphing calculators. Geometric concepts are brought in as review and to emphasize the connection between the mathematical fields.

**Course Number M310 1 Mathematics credit Grades 10-12**

*Prerequisites**: Teacher recommendation, Algebra I, and Geometry*

**Course Number M211 1 Mathematics credit Grades 10-12**

*Prerequisites**: Teacher recommendation, Algebra I, and Geometry*

**Course Number M111 1 Mathematics credit Grades 10-12**

This course is the first in a three-credit series of mathematics courses intended for students who have demonstrated a superior aptitude for, and interest in, the discipline of mathematics. The topics of instruction include both traditional Algebra II and Precalculus subjects. Among these are rational expressions, equations and inequalities, complex numbers, functions, conic sections, logarithms, systems, sequences, series, and probability. A CAS TI-Nspire graphing calculator is highly recommended for all students in this course.

*Prerequisite**: Recommendation of the Geometry teacher. Considerations for recommendation include exceptionally strong performance in Algebra I 200, and Geometry 200.*

**Course Number M309 1 Mathematics credit Grades11-12**

This course is designed for students who are interested in gaining an understanding of financial topics and the mathematics behind them. This course will investigate in depth such topics as: income and budgeting, financial goal setting, the time value of money, banking and personal income taxes, renting vs. owning, and debt repayment. This course is designed to help students understand the impact of individual choices on occupational goals and future earnings potential. Lessons integrate the use of technology, including graphing calculators, spreadsheet programs, and many Internet sources to perform mathematical calculations. By the end of the course, students will have a detailed understanding of the mathematics behind some key personal finance issues that affect their lives, as well as the skills and knowledge needed to improve their financial future.

*Prerequisites**: Teacher recommendation and Algebra I*

**Course Number M312 .5 Mathematics credit Grades 11-12**

This course is intended for college bound students as an alternative to taking Pre-Calculus (cannot be taken concurrently with Pre-Calculus). The course will include a review of algebra skills as well as the further development of advanced algebra concepts covered in Algebra 2. Time will be given for preparation for standardized tests such as the ACT and SAT. The fundamentals of trigonometry will also be explored. Students looking for 1 full credit of math are encouraged to also sign up for Probability and Statistics.

*Prerequisites**: Teacher recommendation and Algebra *

**Course Number M313 .5 Mathematics credit Grades 9-12**

How can we become more informed consumers of information? This course is designed to explore and understand the role statistics play in our everyday lives. Data collection, description, and analysis are studied as ways to report findings and build mathematical models for prediction and decision making. Probability is used to assess the usefulness of models.

Lessons integrate the use of technology, including graphing calculators and/or computer software to produce charts and graphs. Examples from fields such as economics, business, education, psychology, sociology, biology, and medicine will be examined.

*Prerequisites**: Credit or concurrent enrollment in Algebra 1*

**Course Number M216 1 Mathematics credit Grades 10-12**

This course will focus on topics from Trigonometry and Analytic Geometry. Trigonometric functions of the general angle in the coordinate plane are discussed along with such topics as standard position, co-terminal angles, positive and negative angles, reference angles and radian measure. Various relationships between functions are developed and formulas derived which are used in solving trigonometric equations and proving identities.

Graphing of the various functions and the inverse relations are included. The laws of sines and cosines are derived and used with applied problem-solving. The rectangular coordinate system is reviewed. Various formulas are used such as distance, midpoint, the angle between two lines, and distance from a point to a line. Graphs of relations and functions emphasizing domain, range, symmetry, and asymptotes are included. Exponential and logarithmic functions are discussed and graphed, as are parametric equations and conic sections. This course is designed for students planning a career with an emphasis on mathematics.

*Prerequisites**: Teacher recommendation and Algebra II*

**Course Number M115 1 Mathematics credit Grades 10-12 **

This course is designed for students who plan to study AP Calculus (level BC) following the end of the course. This course covers topics including trigonometry, vectors, polar and parametric equations, limits, and some work with derivatives with an emphasis on problem solving and applications throughout. A CAS TI-Nspire graphing calculator is highly recommended for all students in this course.

*Prerequisites**: Teacher recommendation and Algebra II Honors 300*

**Course Number M112 1 Mathematics credit Grades 11-12**

This course is designed for students interested in pursuing a career in natural science, social science, engineering, mathematics or any other career that involves performing research and/or interpreting research results. This course will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. This course emphasizes the use of graphical and numerical techniques to study patterns and departures from patterns, experimental design, probability, sampling distributions, and statistical inference. A graphing calculator is highly recommended for all students in this course.

Students who use a dual enrollment voucher or pay 50% tuition for college credit and pass the course could earn 3 UVM credits through the College of Engineering and Mathematical Sciences in addition to 1 EHS credit.

*Students can take this course to fulfill a STEM Academy endorsement requirement.*

*Prerequisites**: Teacher recommendation and Algebra II or higher*

**Course Number M217 1 Mathematics credit Grades 11-12**

This course is designed for students who want to continue their studies of mathematics but are not interested in taking the Advanced Placement test at the end of the year. Students planning on a career in science, mathematics, or engineering will be well prepared to take a college Calculus course and in some cases can use this credit to start at a higher level of Calculus in college. The curriculum will be very similar to the AP Calculus AB course listed below with a less rigorous coverage of the material in some areas.

*Prerequisites**: Teacher recommendation and Pre-Calculus*

**Course Number M117 1 Mathematics credit Grades 11-12**

This course is designed to prepare students to take the AP Calculus AB exam. Any student planning on a career in science, mathematics, or engineering is urged to take this course. Topics include limits and continuity, concepts of a derivative, derivatives of functions and applications, integrals, areas, advanced topics in algebra, and volumes of revolution. Students planning to take the Advanced Placement test should confer with the teacher in early November. A graphing calculator is highly recommended for all students in this course.

*Prerequisites**: Teacher recommendation and Pre-Calculus*

**Course Number M122 1 Mathematics credit Grades 11-12**

This course is the culmination of the honors program in mathematics. Students are expected to enter the course with knowledge of limits and basic derivatives. The curriculum for the course will include techniques and applications of derivatives, integration techniques and applications, the calculus of transcendental functions, the calculus of parametric and polar equations, and infinite series. A CAS TI-Nspire graphing calculator is highly recommended for all students in this course. Students are required to take the Advanced Placement test.

**Course Number M127 1 Mathematics credit Grades 10-12**

This course emphasizes object-oriented programming methodology with a concentration on problem solving and algorithm development and is meant to be the equivalent of a first-semester college level course in Computer Science. It also includes the study of data structures, design, and abstraction. Students will learn to: design and implement solutions to problems by writing, running, and debugging computer programs; use and implement commonly-used algorithms and data structures; develop and select appropriate algorithms and data structures to solve problems; code fluently in an object-oriented paradigm using the programming language Java; read and understand a large program consisting of several classes and interacting Objects; and recognize the ethical and social implications of computer use. In evaluating student programming solutions, consideration will be given to program correctness, error handling, and the organization, format, and documentation of the code. This course is recommended for students who intend to pursue study in scientific or technical fields. Students in this course may be candidates for the AP Computer Science A exam in May. Additional time outside of class is required. No prior programming knowledge is required.

*Students can take this course to fulfill a STEM Academy requirement.*

*Prerequisites**: Teacher recommendation and Geometry 200 or Algebra II*